§ AnonCreds Specification

Specification Status: v1.0 Draft

Latest Draft:

https://github.com/hyperledger/anoncreds-spec

Editors:

• Stephen Curran
• Artur Philipp - Technische Universität Berlin, IDunion
• Hakan Yildiz - Technische Universität Berlin, IDunion
• Sam Curren
• Victor Martinez Jurado
• Aritra Bhaduri
• Artem Ivanov

Participate:

GitHub repo

Commit history

Discord

§ Abstract

The AnonCreds (Anonymous Credentials) specification is based on the open source verifiable credential implementation of AnonCreds that has been in use since 2017, initially as part of the Hyperledger Indy open source project and now in the Hyperledger AnonCreds project. The extensive use of AnonCreds around the world has made it a de facto standard for ZKP-based verifiable credentials, and this specification is the formalization of that implementation.

For more details on what AnonCreds are and how they work you can refer to the Anonymous credentials with type-3 revocation by Dmitry Khovratovisch, Michael Lodder and Cam Parra which is the compiled pdf from their official TeX document published under CC4.0 license.

§ Status of This Memo

This is a proposal for version v1.0 of AnonCreds which aims at AnonCreds being ledger agnostic.

This document is a product of the AnonCreds Working Group. It represents the consensus of the AnonCreds community. The proposal for v1.0 has partly been worked out at the RWOT2022 event in the Hague, Netherlands.

Information about the current status of this document, any errata, and how to provide feedback on it may be obtained at https://github.com/hyperledger/anoncreds-spec.

§ Copyright Notice

This specifications is subject to the Community Specification License 1.0 available at https://github.com/CommunitySpecification/1.0.

If source code is included in the specification, that code is subject to the Apache 2.0 license unless otherwise marked. In the case of any conflict or confusion within this specification between the Community Specification License and the designated source code license, the terms of the Community Specification License shall apply.

§ Introduction

AnonCreds ZKP verifiable credentials provide capabilities that many see as important for digital identity use cases in particular, and verifiable data in general. These features include:

• A full implementation of the Layer 3 verifiable credential “Trust Triangle” of the Trust over IP Model.
• Complete flows for issuing verifiable credentials (Issuer to Holder), and requesting, generating and verifying presentations of verifiable claims (Holder to Verifier).
• Fully defined data models for all of the objects in the flows, including verifiable credentials, presentation requests and presentations sourced from multiple credentials.
• Fully defined applications of cryptographic primitives.
• The use of a Blind Signature scheme in the issuance process to enhance the privacy protections available to the holder recieving the credential, including:
  • Only the holder learns the final credential signature, the issuer only learns a blinded version which only the holder can unblind.
  • The issuer can sign messages blindly, never learning their value, while still being able to guarantee that the holder knows the value of the message being signed. This is used for the link secret, which the holder commits to during the issuance, the issuer blindly signs this message along with the rest of the credential attributes and then the holder removes the blinding to get a signature over the credential attributes including the unblinded link secret value.
• The use of Zero Knowledge Proofs (ZKPs) in the verifiable presentation process to enhance the privacy protections available to the holder in presenting data to verifiers, including:
  • Proving that certain values are part of a signed credential without revealing them including: credential signature, link secret and any attributes a holder does not wish to reveal. This helps prevent correlation based on these values.
  • The use of unrevealed identifiers for holder binding to prevent correlation based on such identifiers.
  • The use of predicate proofs to reduce the sharing of PII and potentially correlating data, especially dates (birth, credential issuance/expiry, etc.).
  • A revocation scheme that proves a presentation is based on credentials that have not been revoked by the issuers without revealing correlatable revocation identifiers.

This version (v1.0) removes any dependence on Hyperledger Indy by removing any requirements related to the storage of the objects used in AnonCreds, whether they be stored remotely on a “verifiable data registry” (including Hyperledger Indy) or in local secure storage.

The following diagram and explanation below give a high-level overview of all AnonCreds Data objects, their relations and the owner respectively receiver of each of the data objects.

AnonCreds require a Verifiable Data Registry (VDR). A VDR (box in green) is a public registry (often a ledger) used for storing some of the AnonCreds data objects.

Schemas are public and reusable templates, which define the attributes of issued AnonCreds credentials and can be written (e.g. by an Issuer) to the VDR.

Based on a Schema, arbitrary Issuers (box in yellow) can create a Credential Definition (Credential Definition) which references the Schema. A Credential Definition enables Issuers to issue AnonCreds Credentials to Holders and enables Verifiers (box in red) to verify Credentials issued to and presented by a Holder. A Credential Definition consists of two pieces of information: First, the Private Credential Definition includes the private signing keys of the Issuer for signing and issuing AnonCreds Credentials to holders and is kept private by the Issuer. Second, the Public Credential Definition includes the public keys of the Issuer, has to be stored on a VDR and is used by holders and arbitrary Verifiers in order to verify AnonCreds Credentials issued to and presented by Holders.

Each Holder (box in blue) has a link secret, which enables Credential to Holder binding: Whenever a Credential is issued to a Holder by an Issuer, the Holder generates a blinding factor and uses this to commit to a blinded version of the link secret which is sent to the Issuer. The Issuer verifies the commitment, before producing a blind signature over the blinded link secret along with the other attributes within the AnonCreds Credential. This blind signature is sent to the Holder, who removes the blinding factor to retrieve a credential signature over the Credential attributes including the unblinded link secret. By using the same link secret for every Credential that is issued to the Holder, the Holder can prove the affiliation of multiple Credentials at presentation time.

Holders never present the raw signed credential data they - received from Issuers - to Verifiers for verification purposes. Instead a Verifiable Presentation is created by the Holder and sent to the Verifier. A Verifiable Presentation is a derivation of an AnonCreds Credential which allows a Holder to proof the correctness of the revealed credential data, without revealing the original raw credential signature(s). Additionally, Holders prove knowledge the link secret attribute within the Credential, without revealing this value to the Verifiers. Verifiers process Verifiable Presentations for verification of credential data.

AnonCreds allows the revocation of Credentials issued to Holders by Issuers. In case revocation is required, at least one (Revocation Registry Definition), which references the associated Public Credential Definition, has to be stored to the VDR by the Issuer in addition to the Public Credential Definition. A Revocation Registry Definition can have Revocation Status Lists. When one or more credentials have to be revoked, the Issuer stores a Revocation Status List with the updated status of the credentials in question to the VDR. Holder use these additional pieces of information in order to generate a Non-Revocation Proof. A Non-Revocation Proof proves to a Verifier, that the credential the Holder presented to the Verifier, has not been revoked. Verifiers use the information provided by a Revocation Registry Definition and associated Revocation Status Lists to verify the Holder`s Non-Revocation Proof. A Tails File supports the revocation mechanism. Each Revocation Registry Definition requires exactly one Tails File.

§ Requirements, Notation and Conventions

The key words “MUST”, “MUST NOT”, “REQUIRED”, “SHALL”, “SHALL NOT”, “SHOULD”, “SHOULD NOT”, “RECOMMENDED”, “NOT RECOMMENDED”, “MAY”, and “OPTIONAL” in this document are to be interpreted as described in BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all capitals, as shown here.

§ Terminology

Accumulator

A [cryptographic accumulator] is used in the AnonCreds v1.0 Revocation scheme as a space- and time-efficient method of proving a value membership in a set of values without revealing the individual members of the set. In AnonCreds v1, an accumulator is a core element of the verifiable credential revocation mechanism.

AnonCreds Method

AnonCreds methods specify how AnonCreds objects are written (registered) and read (resolved) on a given verifiable data registry implementation. AnonCreds was originally written to use Hyperledger Indy as its only VDR implementation, but the evolution of AnonCreds to enable storing objects on any VDR implementation means that AnonCreds methods (comparable to DID Methods from the W3C DID Core specification) are necessary. AnonCreds Methods are defined in the AnonCreds Methods Registry repository.

AnonCreds Objects

The published and shared data objects used in AnonCreds v1.0 including the published objects schema, credential definition, revocation registry definition, revocation registry entry and the shared objects credential offer, credential request, and presentation request.

BigNumber

A BigNumber is an data object which safely allows mathematical operations on numbers of any magnitude. BigNumbers are commonly used in cryptography schemes, including those underlying AnonCreds v1.0.

Blinded Secret

A cryptographic technique where a secret value (a number) is blinded before it is shared such that the sender can later prove knowledge of the secret value without sharing it. The AnonCreds v1.0 link secret mechanism is based on the use of a blinded secret.

Blinded Secrets Correctness Proof

A ZKP-based proof that can be verified to show that a blinded secret was produced correctly from an unblinded secret without exposing the secret.

Blinding Factor

A blinding factor is a random BigNumber selected from the set of integers up to the order of the RSA group, n. It is generated by the holder to blind their link secret during credential issuance. Knowledge of the blinding factor can be used to create a Blinded Secrets Correctness Proof.The blinding factor can be removed from the signature the issuer produces to retrieve a valid signature over the unblinded link secret. A blinding factor and associated Blinded Secrets Correctness Proof are similarly generated for each non-disclosed attribute during credential presentation, such that a holder can prove they know these values without revealing them to the verifier.

Call Home

Call home is a term used when evaluating the privacy characteristics of verifiable credential deployments. If a holder presenting data from a verifiable credential must always contact (“call home to”) the issuer, holder actions are open to the actual, or perception of, tracking of the holder by the issuer. Verifiable credential schemes that do not make possible the tracking of holder activities by issuers are preferred.

Claim

A claim is a part of digital identity related to a subject. A claim can be attested by the identity subject itself, or it can be asserted by another entity.

Correlatability

When a verifiable credential scheme that has the attribute of unlinkability, the data from the process of sharing a verifiable presentations with different verifiers cannot be correlated to identify the holder.

Credential

A credential is a set of claims about an identity subject. A verifiable credential is a tamper-proof credential whose authorship is cryptographically verifiable. An anonymous credential, also known as AnonCreds, is a verifiable credential that has privacy-preserving properties to enable data minimization and correlation resistance.

Credential Definition

A credential definition (also known as CRED_DEF or CLAIM_DEF) contains the public data required for credential issuances (used by the issuer) as well as credential validation data (used by holders and verifiers). Any number of credentials can be issued based on a single credential definition. A credential definition is generated by the issuer before credential any issuances and published for anyone (primarily holders and verifiers) to use. In generating the published credential definition, related private data is also generated and held as a secret by the issuer. The secret data includes the private keys necessary to generate signed verifiable credentials that can be presented and verified using the published credential definition. A credential definition can optionally be generated such that its generated credentials can be revoked.

Credential Key Correctness Proof

A proof generated during the creation of the credential definition and included in the credential offer so that the holder can verify that the issuer is in control of the private data associated with the published credential definition.

Credential Offer

A credential offer is a data object sent by an issuer to a holder offering to issue a credential. The credential offer contains the details about the claims the issuer intends to issue to the holder. A holder can reply to the issuer with a credential request. A credential offer also includes a nonce and a Credential Key Correctness Proof.

Credential Request

A credential request is a request from an holder towards a issuer to get a credential issued by the issuer. The credential request references a preceding credential offer and defines the claims the holder wants to get issued, including a Blinded Secret and associated Blinded Secrets Correctness Proof. A credential request also includes a nonce that is used in issuing the credential.

Data Minimization

An attribute of verifiable data sharing schemes that considers privacy of a scheme based on the amount of data shared in a given interaction. Ideally, the minimum amount of data is shared for the purpose of the interaction. Techniques such as selective disclosure, predicates, and unlinkability, all available in AnonCreds v1.0 support the goal of privacy-preserving, minimal data sharing.

DID

A Decentralized Identifier (DID), defined by the W3C DID Core Specification, is a type of identifier that is useful in enabling verifiable, decentralized digital identity. A DID refers to any subject (e.g., a person, organization, thing, data model, abstract entity, etc.) as determined by the controller of the DID. DIDs are not used in AnonCreds itself but there must be a verifiable identifier (usually a DID) with an enforced relationship between schema publishers and issuers and the AnonCreds objects they publish. This is outlined in a note in this specification section.

DID Method

DID methods specify how DID documents are created and resolved (read) on a given verifiable data registry implementation, allowing DIDs to be created and resolved in a wide variety of storage containers. The capabilities required by DID Methods are defined in the [DID Core specification], and the (many) DID Methods are defined in the DID Methods Registry repository.

Holder

In this specification, the holder is a software component (agent) used by an entity (person, organization, etc.) in possession of credentials issued to them. Where “holder” is used in the specification we mean the software component. In some places where required, we clearly refer to an entity using holder software as separate from the holder software component. Holders interact with issuers to obtain credentials, and derive presentations from the credentials they hold.

Issuer

An issuer is one of the three entities that interact with each other within the domain of digital identities. It can assert claims about a subject in the form of a tamper-proof credential whose origins are cryptographically verifiable.

Issuer Identifier

An issuer identifier is a unique identifier for an issuer. It is used to identify the issuer of AnonCreds objects published to a Verifiable Data Registry.

Link secret

A link secret is a unique identifier known only to the holder used in AnonCreds to bind credentials issued to a holder to that holder, and to demonstrate that all of the source verifiable credentials in a presentation are bound to the same link secret that is known to the holder. During issuance and presentation processes the holder's link secret is blinded with a blinding factor such that it is not correlatable, and a Blinded Secrets Correctness Proof is provided by the holder to demonstrate they know the link secret without revealing it.

Link secret is also known by the deprecated term master_secret in some AnonCreds source code.

Nonce

A nonce is an arbitrary unique number that is often required as an input to the generation of a cryptographic proof to ensure it is uniquely generated and once produced, cannot be replayed. Within AnonCreds, nonces are used during the issuance and presentation processes to prevent replay attacks.

Non-Revocation Proof

A non-revocation proof is a proof provided by a holder to demonstrate that a revocable credential they are presenting has not been revoked, without revealing a unique, correlatable identifier for the credential. A verifier verifies a non-revocation proof using information from the revocation registry to which the credential belongs.

Predicates

A zero-knowledge proof predicate is a boolean assertion (operators <=, <, >, >=) in an presentation about the value of an integer claim without disclosing the value of the claim.

Presentation Request

An AnonCreds presentation request is an object constructed by the verifier and sent to the holder defining the verifiable data that the verifier wants from the holder for some purpose.

Prover

A prover is a synonym for holder that is sometimes used in a holder-verifier interaction. In this specification, we use the term “holder” in all cases. However the underlying AnonCreds implementations use “prover” in code.

Revocation

A unilateral action by the issuer of a verifiable credential issued to a holder to revoke that credential for some reason. Once an issued credential has been revoked, the holder can no longer produce a non-revocation proof for the credential. Verifiers usually (but not always) are interested if a data is presented from a revoked credential.

Revocation Registry

A Revocation registry is a set of objects related to one another and a credential definition that holds information about the revocation status of a set of revocable credentials issued from the credential definition. Each revocation registry consists of a revocation registry definition and one or more revocation registry entries. There can be 0 or more revocation registries related to a credential definition, and every issued AnonCreds revocable credential is in a revocation registry.

Revocation Registry Definition

A revocation registry definition is an object with public and private information about a revocation registry. The public part is published such that it an be resolved and used by anyone, while the private part is a secret held by the issuer for use when publishing revocation registry entries that update the revocation status of one or more credentials.

Revocation Registry Entry

A revocation registry entry is an object that is published by the issuer to set/update the revocation status of one or more issued credentials that are in a revocation registry. Each revocation registry entry has an identifier (sometimes called a timestamp), a cryptographic accumulator that summarizes the revocation state of all the credentials in the revocation registry and, depending on the AnonCreds Method being used to publish the object, either the revocation state of all of the credentials in the registry, or the set of credentials whose revocation state has changed (“deltas”) since the last revocation registry entry was published.

Revocation Status List

A Revocation status list is an object that contains the revocation status (“revoked” or “not revoked”) of all credentials in a Revocation Registry at the time of a given revocation registry entry. For [[AnonCreds Methods]] that store revocation registry entries as deltas (changes to the revocation state of credentials from the previous revocation registry entry), the set of deltas from the initial publication of the revocation registry must be collected and used to calculate the full revocation state of all of the credentials.

Schema

A Schema is a object that defines the set of claims (also known as attributes) that will be populated by issuers in issuing a give type of AnonCreds verifiable credentials. Schemas have a name, version, and are published to a verifiable data registry by a schema publisher using an AnonCreds Method. Credential definitions are generated from a specific schema.

Schema Publisher

A Schema publisher is an entity that publishes a Schema to a verifiable data registry. The schema publisher could be the one issuer of a type of credential, but could also be another entity that creates a Schema to be used by many issuers to issue the same type of credential.

Selective Disclosure

Selective disclosure is the ability to minimize data the shared data from an issued credential in a presentation by revealing to a verifier only a subset of claims in the credential. The source credential is still verified by the verifier, but only the revealed values are disclosed.

Signature Correctness Proof

A ZKP-based proof that can be verified to show that a signature over a message is valid, without revealing the message or signature.

Subject

A subject, also known as an identity subject, is the entity about whom the claims in a credential are asserted. In AnonCreds, the credential subject is not formally defined in credential. Rather, the issuance of a credential is always to a specific holder. The semantics of the credential defines the relationship between the holder and the subject, with the holder frequently being the subject.

Tails File

A tails file is a part of the AnonCreds v1.0 scheme that enables a holder to produce a non-revocation proof. A tails file is a static file generated as part of the creation of a revocation registry by the issuer, published, and retrieved by the holder of a credential that is in the related revocation registry. The holder must have the tails file in order to generate a non-revocation proof for a source credential they are providing in a presentation.

Unlinkability

Unlinkability is the attribute of some verifiable credentials schemes (notably AnonCreds) such that no correlatable identifiers are shared in carrying out verifiable credential issuance and presentation processes. Unlinkability requires that when the processes are repeated with the same or different parties (issuers, verifiers) no common unique identifiers are shared. Note that unlinkability may be lost if there are unique identifiers shared in the revealed claim values of presentations.

Verifiable Data Registry

DIDs, DID documents and published AnonCreds objects are stored in a verifiable data registry (VDR) such that an identifier for an object can be resolved (by anyone, in most cases), and the identified object returned. A VDR can be a distributed ledger, a blockchain, a web server, database or any other type of storage system. The process of going from the identifier to discovering and resolving the object is a DID Method (for DIDs) and AnonCreds Method (for AnonCreds objects). Resolved objects must adhere to their specified data model, regardless of the discover/resolution method used and the verifiable data registry in which the objects are stored.

Verifiable Presentation

An AnonCreds verifiable presentation is a collection of claims and predicates derived from one or more credentials with an added proof that the verifier can verifier. AnonCreds enable the holder to prove it holds a claim from a VC without revealing the VC itself. Verifying a presentation shows the issuer of the source credentials, to whom the credentials where issued, that the claims have not been tampered with, and, if applicable, that the source credentials have not been revoked. AnonCreds presentations are designed to maximize the privacy of the holder sharing the presentation.

Verifier

A verifier is an entity that verifies the information from a holder in a presentation.

Zero-knowledge proof

In cryptography, a zero-knowledge proof is a method by which an entity can prove that they know a certain value without disclosing the value itself. Zero-knowledge proofs in AnonCreds enable a number of privacy-preserving capabilities.

• Prove knowledge of the value of the link secret related to given a blinded link secret.

• Share data from multiple credentials in a single verifiable presentation without revealing to the verifier any correlatable identifiers.

• Use selective disclosure to reveal only necessary claims in a verifiable presentation.

• Use predicates to minimize the data shared by the holder, such as proving based on a date of birth claim that they are older than 18 without sharing their date of birth.

• Prove that the source credentials shared in a presentation have not been revoked without sharing unique identifiers for the credentials.

§ Cryptographic Notations

This specification contains the cryptographic calculations necessary to produce the data objects exchanged in using Hyperledger AnonCreds, and to verify the various proofs embedded in those objects. The following is information about the notations used in displaying the cryptographic calculations:

a || b : Denotes the concatenation of octet strings a and b.

I \ J : For sets I and J, denotes the difference of the two sets i.e., all the elements of I that do not appear in J, in the same order as they were in I.

X[a..b] : Denotes a slice of the array X containing all elements from and including the value at index a until and including the value at index b. Note when this syntax is applied to an octet string, each element in the array X is assumed to be a single byte.

range(a, b) : For integers a and b, with a <= b, denotes the ascending ordered list of all integers between a and b inclusive (i.e., the integers i such that a <= i <= b).

length(input) : Takes as input either an array or an octet string. If the input is an array, returns the number of elements of the array. If the input is an octet string, returns the number of bytes of the inputted octet string.

H(...) : Any hash function.

Terms specific to pairing-friendly elliptic curves are:

E1, E2 : elliptic curve groups defined over finite fields. This document assumes that E1 has a more compact representation than E2, i.e., because E1 is defined over a smaller field than E2.

G1, G2 : subgroups of E1 and E2 (respectively) having prime order r.

GT : a subgroup, of prime order r, of the multiplicative group of a field extension.

e : G1 x G2 -> GT a non-degenerate bilinear map.

r : The prime order of the G1 and G2 subgroups.

P1, P2 : points on G1 and G2 respectively. For a pairing-friendly curve, this document denotes operations in E1 and E2 in additive notation, i.e., P + Q denotes point addition and x * P denotes scalar multiplication. Operations in GT are written in multiplicative notation, i.e., a * b is field multiplication.

§ AnonCreds Setup Data Flow

The following sequence diagram summarizes the setup operations performed by a Schema Publisher, the Issuer (one required and one optional) in preparing to issue an AnonCred credential based on provided Schema, and the one setup operation performed by each Holder. On successfully completing the operations, the Issuer is able to issue credentials based on the given Schema to the Holder. The subsections below the diagram detail each of these operations.

§ Schema Publisher: Publish Schema Object

Each type of AnonCred credential is based on a Schema published to a Verifiable Data Registry (VDR), an instance of Hyperledger Indy in this version of AnonCreds. The Schema is defined and published by the Schema Publisher. Any issuer who can reference the Schema (including the Schema Publisher) MAY issue credentials of that type by creating and publishing a Credential Definition based on the Schema. This part of the specification covers the operation to create and publish a Schema. The flow of operations to publish a Schema is illustrated in the Schema Publisher: Publish Schema section of the AnonCreds Setup Data Flow sequence diagram.

The Schema is a JSON structure that can be manually constructed, containing the list of attributes (claims) that will be included in each AnonCreds credential of this type. The following is an example Schema:

{
  "issuerId": "https://example.org/issuers/74acabe2-0edc-415e-ad3d-c259bac04c15",
  "name": "Example schema",
  "version": "0.0.1",
  "attrNames": ["name", "age", "vmax"]
}

• issuerId - the Issuer Identifier of the schema. MUST adhere to Issuer Identifiers rules.
• name (string) - the name of the schema
• version (string) - the schema version as a documentation string that it’s not validated. The format is up to each implementor or publisher. For example, Indy uses Semantic Versioning
• attrNames (str[]) - an array of strings with each string being the name of an attribute of the schema

Once constructed, the Schema is published to a Verifiable Data Registry (VDR) using the Schema Publishers selected AnonCreds Objects Method. For example, see this Schema that is published on the Sovrin MainNet instance of Hyperledger Indy. The schemaId for that object is: Y6LRXGU3ZCpm7yzjVRSaGu:2:BasicIdentity:1.0.0.

The identifier for the schema is dependent on where the Schema is published and the AnonCreds method used.

§ Issuer Create and Publish Credential Definition Object

Each Issuer of credentials of a given type (e.g. based on a specific Schema) must create a Credential Definition for that credential type. The flow of operations to create and publish a Credential Definition is illustrated in the Issuer: Create, Store and Publish Credential Definition section of the AnonCreds Setup Data Flow sequence diagram.

In AnonCreds, the Credential Definition and Credential Definition identifier include the following elements.

• A link to the Issuer of the credentials via the DID used to publish the Credential Definition.
• A link to the Schema upon which the Credential Definition is based (the credential type).
• A set of public/private key pairs, one per attribute (claim) in the credential. The private keys will later be used to sign the claims when credentials to be issued are created.

• Other information necessary for the cryptographic signing of credentials.
• Information necessary for the revocation of credentials, if revocation is to be enabled by the Issuer for this type of credential.

We’ll initially cover the generation and data for a Credential Definition created without the option of revoking credentials. In the succeeding section, we describe the additions to the generation process and data structures when credential revocation is enabled for a given Credential Definition.

§ Retrieving the Schema Object

Prior to creating a Credential Definition, the Issuer must get an instance of the Schema upon which the Credential Definition will be created. If the Issuer is also the Schema Publisher, they will already have the Schema. If not, the Issuer must request that information from the VDR on which the Schema is published. In some AnonCreds Objects there is a requirement that the Schema and Credential Definition must be on the same VDR.

§ Generating a Credential Definition Without Revocation Support

The Credential Definition is a JSON structure that is generated using cryptographic primitives (described below) given the following inputs.

• A Schema and identifier for the schema for the credential type.
• A tag, an arbitrary string defined by the Issuer, enabling an Issuer to create multiple Credential Definitions for the same Schema.
• An optional flag support_revocation (default false) which if true generates some additional data in the Credential Definition to enable credential revocation. The additional data generated when this flag is true is covered in the next section of this document.

The operation produces two objects, as follows.

• The Private Credential Definition, an internally managed object that includes the private keys generated for the Credential Definition and stored securely by the issuer.
• The Credential Definition, that includes the public keys generated for the Credential Definition, returned to the calling function and then published on a VDR (currently Hyperledger Indy).

The following describes the process for generating the Credential Definition and Private Credential Definition data.

• Build a credential schema using the schema definition.
• Build a non-credential schema that contains the single attribute master_secret, that will be used to hold the holder’s blinded link secret. The non-credential schema attribute is included in all AnonCreds verifiable credentials.
• Generate random 1536-bit primes $p'$, $q'$, such that $p \leftarrow 2p'+1$ and $q \leftarrow 2q'+1$ are primes too. $p'$, $q'$, and $2p'+1$, $2q'+1$ are Sophie Germain and Safe primes.
• Compute $n \leftarrow pq$.
• Compute random $x_z, x_{R_1}, ..., x_{R_l}$ in the range of safe primes, using the non-credential and credential schema attributes.
• Compute random quadratic residue $S$ modulo $n$ (select a random number from $1$ to $n$, and square it $mod \, n$).
• Compute $Z \leftarrow S^{x_z}(mod \, n)$, and $\{R_i = S^{x_{R_i}}(mod \, n)\}_{1\leq i\leq l}$
• Credential Definition public key is $P_k = ( n, S, Z, \{R_i\}_{i\leq i\leq l} )$ and the private key is $s_k = (p, q)$

Here is the rust implementation of the above process.

The Private Credential Definition produced by the generation process has the following format:

{
  "p_key": {
    "p": "123...782",
    "q": "234...456"
  },
  "r_key": null
}

The Credential Definition has the following format (based on this example Credential Definition on the Sovrin MainNet):

{
  "issuerId": "did:indy:sovrin:SGrjRL82Y9ZZbzhUDXokvQ",
  "schemaId": "did:indy:sovrin:SGrjRL82Y9ZZbzhUDXokvQ/anoncreds/v0/SCHEMA/MemberPass/1.0",
  "type": "CL",
  "tag": "latest",
  "value": {
    "primary": {
      "n": "779...397",
      "r": {
        "birthdate": "294...298",
        "birthlocation": "533...284",
        "citizenship": "894...102",
        "expiry_date": "650...011",
        "facephoto": "870...274",
        "firstname": "656...226",
        "link_secret": "521...922",
        "name": "410...200",
        "uuid": "226...757"
      },
      "rctxt": "774...977",
      "s": "750..893",
      "z": "632...005"
    }
  }
}

The Credential Definition contains a cryptographic public key that can be used to verify CL-RSA signatures over a block of L messages m1,m2,...,mL. The Credential Definition contains a public key fragment for each message being signed by signatures generated with the respective private key. The length of the block of messages, L, being signed is defined by referencing a specific Schema with a certain number of attributes, A = a1,a2,.. and setting L to A+1. The additional message being signed as part of a credential is for a link_secret (called the link secret everywhere except in the existing open source code and data models) attribute which is included in all credentials. This value is blindly contributed to the credential during issuance and used to bind the issued credential to the entity to which it was issued.

All integers within the above Credential Definition example json are shown with ellipses (e.g. 123...789). They are 2048-bit integers represented as 617 decimal digits. These integers belong to an RSA-2048 group characterised by the n defined in the Credential Definition.

• issuerId - the Issuer Identifier of the credential definition. MUST adhere to Issuer Identifiers rules.
• schemaId - (string) The identifier of the Schema on which the Credential Definition is based. The format of the identifier is dependent on the AnonCreds Objects Method used in publishing the Schema.
• type - (string) The signature type of the Credential Definition. For this version of AnonCreds the value is always CL.
• tag (string) - the tag value passed in by the Issuer to an AnonCred’s Credential Definition create and store implementation.
• value - (object) an Ursa native object with the primary and revocation fields.
  • primary is the data used for generating credentials.
    • n is a safe RSA-2048 number. A large semiprime number such that n = p.q, where p and q are safe primes. A safe prime p is a prime number such that p = 2p'+ 1, where p' is also a prime. Note: p and q are the private key for the public CL-RSA key this Credential Definition represents.
    • r is an object that defines a CL-RSA public key fragment for each attribute in the credential. Each fragment is a large number generated by computing s^{xri} where xri is a randomly selected integer between 2 and p'q'-1.
      • master_secret (also known as link secret, but kept as master_secret for backwards compatibility) is the name of an attribute that can be found in each Credential Definition. The associated private key is used for signing a blinded value given by the Holder to the Issuer during credential issuance, binding the credential to the Holder.
      • The rest of the attributes in the list are those defined in the Schema.
      • The attribute names are normalized (lower case, spaces removed) and listed in the Credential Definition in alphabetical order.
    • rctxt is equal to s^(xrctxt), where xrctxt is a randomly selected integer between 2 and p'q'-1. (I believe this is used for the commitment scheme, allowing entities to blindly contribute values to credentials.)
    • s is a randomly selected quadratic residue of n. This makes up part of the CL-RSA public key, independent of the message blocks being signed.
    • z is equal to s^(xz), where xz is a randomly selected integer between 2 and p'q'-1. This makes up part of the CL-RSA public key, independent of the message blocks being signed.

The identifier for the Credential Definition is dependent on where the Credential Definition is published and the AnonCreds method used.

§ Generating a Credential Definition With Revocation Support

The issuer enables the ability to revoke credentials produced from a Credential Definition by passing to the Credential Definition generation process the flag support_revocation as true. When using revocation in a credential, private key material is added to the Private Credential Definition to allow the issuer to revoke credentials, and public key material is added to the Credential Definition to allow a verifier to check revocation status. The following describes the fields added to the Private Credential Definition and the Credential Definition.

The revocation scheme uses a pairing-based dynamic accumulator defined as a variant of the CKS scheme but with a Type 3 elliptic curve pairing instead of a Type 1 pairing. The curve $E$ is BN254, which is defined over a 254-bit prime $p$. The pairing is an Ate pairing $e : G_1 \times G_2 \rightarrow G_T$ where $G_1 = E(\mathbb{F}_p)$, $G_2 = E(\mathbb{F}_{p^2})$, and $G_T$ is the group of $q^{\text{th}}$ roots of unity in $\mathbb{F}_{p^{12}}$ where $q=|E(\mathbb{F}_p)|$, which is another 254-bit prime.

In the amcl library used for the elliptic curve arithmetic, points are represented using projective co-ordinates, i.e. a point $(X/Z,Y/Z)$ on the curve $E$ is mapped to a projective point $(X: Y: Z)$. Additionally, the big-integer co-ordinates are strings of 64 hexadecimal characters, meaning there are up to 64 * 4 - 254 = 2 bits of ‘excess’ in each encoding. The library includes the excess number of bits as an integer (i.e. 1 or 2) before the hexadecimal string. The upshot is:

• Elements of $G_1$ are encoded as three 64-character strings of hexadecimal characters, each preceded by the excess, e.g. 1 1D1...A04 1 146...8BC 1 095...8A8.
• Elements of $G_2$ are encoded as six 64-character strings of hexadecimal characters, each preceded by the excess. 1 104...EC9 1 01A...FC2 1 226...1EB 1 234...D08 1 095...8A8 1 000...000.

§ Private Revocation Keys

A Private Credential Definition with revocation enabled has the following format. In this, the details of the p_key element are omitted, as they are the same as was covered in the section above. The implementation can be found in the anoncreds-clsignatures-rs repository.

{
  "p_key": {
    "p": "123...782",
    "q": "234...456"
  },
  "r_key": {
    "x": "332...566",
    "sk": "992...237"
  }
}

• r_key is an object defining the revocation private key for the credential.
  • x is an integer modulo $q$
  • sk is an integer modulo $q$

The value $q$ is the order of the group $G_1=E(\mathbb{F}_p)$ on the curve BN254 (see above: $q$ is a 254-bit prime). x and sk are used to generate parts of the revocation public key as described below.

§ Public Revocation Keys

A Credential Definition with revocation enabled has the following format (from this example Credential Definition on the Sovrin MainNet). In this, the details of the primary element are omitted, as they are the same as was covered above.

{
  "issuerId": "did:indy:sovrin:F72i3Y3Q4i466efjYJYCHM",
  "schemaId": "did:indy:sovrin:F72i3Y3Q4i466efjYJYCHM/anoncreds/v0/SCHEMA/state_license/4.2.0",
  "type": "CL",
  "tag": "latest",
  "value": {
    "primary": {...},
    "revocation": {
      "g": "1 154...813 1 11C...D0D 2 095..8A8",
      "g_dash": "1 1F0...3B5 1 229...41D 1 04B...F7D 1 061...8B7 2 095...8A8 1 000...000",
      "h": "1 131...0DD 1 0D5...66E 2 095...8A8",
      "h0": "1 1AF...246 1 127...361 2 095...8A8",
      "h1": "1 242...F14 1 1AC...2FF 2 095...8A8",
      "h2": "1 072...7A1 1 09E...622 2 095...8A8",
      "h_cap": "1 196...C53 1 238...38B 1 196...C7E 1 198...D31 2 095...8A8 1 000...000",
      "htilde": "1 1D5...797 1 034...232 2 095...8A8",
      "pk": "1 0E7...A88 1 007...4B8 2 095...8A8",
      "u": "1 18E...44B 1 018...F71 1 0D8...2C2 1 003...4CF 2 095...8A8 1 000...000",
      "y": "1 068...F6B 1 16C...F7E 1 01F...68A 1 1E3...9F9 2 095...8A8 1 000...000"
    }
  }
}

In the following, only the revocation item is described, as the rest of items (primary, ref, etc.) are described in the previous section of this document.

• revocation is the data used for managing the revocation status of credentials issued using this Credential Definition
  • g is a generator for the elliptic curve group $G_1$
  • g_dash is a generator for the elliptic curve group $G_2$
  • h is an elliptic curve point selected uniformly at random from $G_1$
  • h0 is an elliptic curve point selected uniformly at random from $G_1$
  • h1 is an elliptic curve point selected uniformly at random from $G_1$
  • h2 is an elliptic curve point selected uniformly at random from $G_1$
  • h_cap is an elliptic curve point selected uniformly at random from $G_2$
  • htilde is an elliptic curve point selected uniformly at random from $G_1$
  • pk is the public key in $G_1$ for the issuer with respect to this accumulator, computed as g^sk (in multiplicative notation), where sk is from r_key above
  • u is an elliptic curve point selected uniformly at random from $G_2$
  • y is the an elliptic curve point in $G_2$, computed as h_cap^x (in multiplicative notation), where x is from r_key above

§ Publishing the Credential Definition on a Verifiable Data Registry

Once constructed, the Credential Definition is published by the Issuer to a Verifiable Data Registry using the issuers preferred AnonCreds Objects.

For example, see this Credential Definition that is published in the Sovrin MainNet instance of Hyperledger Indy. Note that the contents of the Credential Definition that have are published to the Hyperledger Indy ledger, do not exactly match the Credential Definition data model. The specific AnonCreds Objects can describe how to resolve the contents stored on the ledger into the Credential Definition data model.

§ Issuer Create and Publish Revocation Registry Objects

Once the issuer has created a Credential Definition with revocation enabled, the issuer must also create and publish a Revocation Registry Definition and create and publish the first Revocation Status List for the registry.

In this section, we’ll cover the create and publish steps for each of the Revocation Registry Definition and Revocation Status List objects. The creation and publishing of the Revocation Registry Definition includes creating and publishing the TAILS_FILE for the Revocation Registry.

§ Creating the Revocation Registry Object

A secure process must be run to create the revocation registry object, taking the following input parameters.

• revocDefType: the type of revocation registry being created. This is always CL_ACCUM
• credDefId: the ID of the Credential Definition to which the Revocation Registry is to be associated
• tag: an arbitrary string defined by the [ref: issuer], enabling an [ref: issuer] to create multiple Revocation Registry Definitions for the same Credential Definition.
• maxCredNum: The capacity of the Revocation Registry, a count of the number of credentials that can be issued using the Revocation Registry.
• tailsLocation: A URL indicating where the TAILS_FILE for the Revocation Registry will be available to all holders of credential issued using this revocation registry.

Three outputs are generated from the process to generate the Revocation Registry: the Revocation Registry object itself, the TAILS_FILE content, and the Private Revocation Registry object.

§ Revocation Registry Definition Object Generation

The Revocation Registry Definition object has the following data model. This example is from this transaction on the Sovrin MainNet and instance of Hyperledger Indy.

{
  "issuerId": "did:web:example.org",
  "revocDefType": "CL_ACCUM",
  "credDefId": "Gs6cQcvrtWoZKsbBhD3dQJ:3:CL:140384:mctc",
  "tag": "MyCustomCredentialDefinition",
  "value": {
    "publicKeys": {
      "accumKey": {
        "z": "1 0BB...386"
      }
    },
    "maxCredNum": 666,
    "tailsLocation": "https://my.revocations.tails/tailsfile.txt",
    "tailsHash": "91zvq2cFmBZmHCcLqFyzv7bfehHH5rMhdAG5wTjqy2PE"
  }
}

The items within the data model are as follows:

• issuerId - the Issuer Identifier of the revocation registry. MUST adhere to Issuer Identifiers rules and MUST be the same issuerId as the Credential Definition on which the Revocation Registry is based.
• revocDefType - the type of revocation registry (This is currently always CL_ACCUM)
• credDefId - The id of the Credential Definition on which the Revocation Registry is based.
• tag - an arbitrary string defined by the [ref: issuer], enabling an [ref: issuer] to create multiple Revocation Registry Definitions for the same Credential Definition.
• value - The value of the revocation registry definition
  • publicKeys - Public keys data for signing the accumulator; the public key of a private/public key pair
    • accumKey - Accumulator key for signing the accumulator
      • z - a public key used to sign the accumulator (described further below)
  • maxCredNum - The maximum amount of Credentials that can be revoked in the Revocation Registry before a new one needs to be started
  • tailsLocation - The URL pointing to the related tails file
  • tailsHash - The hash of the tails file TAILS_FILE (see also: next section) resulting from hashing the tails file version prepended to the tails file as SHA256 and then encoded to base58.

As noted, most of the items come directly from the input parameters provided by the issuer. The z Revocation Registry accumulator public key is generated using (TODO: fill in details) algorithm. The use of the accumulator public key is discussed in the Credential Issuance section, when the publication of revocations is described. The calculation of the tailsHash is described in the next section on TAILS_FILE generation.

The identifier for the Revocation Registry is dependent on where the Revocation Registry is published and the AnonCreds method used.

§ Tails File and Tails File Generation

The second of the outcomes from creating of a Revocation Registry is a TAILS_FILE. The contents of a TAILS_FILE is an array of calculated points on curve G2, one for each credential in the registry. Thus, if the Revocation Registry has a capacity (maxCredNum) of 1000, the TAILS_FILE holds an array of 1000 G2 curve points. Each credential issued using the Revocation Registry is given its own index (1 to the capacity of the Revocation Registry) into the array, the index of the point for that credential. The contents of the TAILS_FILE is needed by the holder to produce (if possible) a “proof of non-revocation” to show their issued credential has not been revoked.

The process of generating the points that populate the TAILS_FILE are tail[index] = g_dash * (gamma ** index)

The process for hashing the TAILS_FILE is as follows:

• Append the tails file version and all the bytes of G2 curve points one by one into a hasher.
• Compute the hash digest using SHA256 hashing algorithm.

The SHA256 hash of the array of points is returned to be inserted into the tailsHash item of the Revocation Registry object (as described in the previous section). Typically, the array is streamed into a file (hence, the term “Tails File”) and published to a URL indicated by the tailsLocation input parameter provided by the issuer.

The format of a TAILS_FILE is as follows:

• First two bytes are version number(currently 0u8 2u8)
• A list of the points, one per credential in the Revocation Registry. Each point is a collection of three integers implemented as points in 3 dimensions as per ECP2. Each point is 3x4 = 12 bytes long.

Thus the total size of a Tails File is 2+ 12*Size of the Revocation Registry+6 (the L+1 entry).

While not required, the Hyperledger Indy community has created a component, the “Indy Tails Server,” which is basically a web server for tails files. Holders get the tailsLocation during the issuance process, download the TAILS_FILE (ideally) once and cache it for use when generating proofs of non-revocation when creating a presentation that uses its revocable verifiable credential. How the TAILS_FILE is used is covered elsewhere in this specification:

• in the section about the issuer publishing credential revocation state updates, and
• in the section about holders creating a proof of non-revocation.

§ Revocation Registry Definition Object Generation

In addition to generating the Revocation Registry object, a Private Revocation Registry object is generated and securely stored by the issuer. The data model and definition of the items in the Private Revocation Registry is as follows:

§ Publishing the Revocation Registry Object

Once constructed, the Revocation Registry is published by the issuer in a Verifiable Data Registry using the issuer’s AnonCreds Objects. For example, see this Revocation Registry that is published on the Sovrin MainNet instance of Hyperledger Indy. The binary TAILS_FILE associated with the Revocation Registry can be downloaded from the tailsLocation in the Revocation Registry object.

§ Creating the Initial Revocation Status List Object

Published Revocation Status List objects contain the state of the Revocation Registry at a given point in time such that holders can generate a proof of non-revocation (or not) about their specific credential and verifiers can verify that proof. An initial Revocation Status List is generated and published immediately on creation of the Revocation Registry so that it can be used immediately by holders. Over time, additional Revocation Status List objects are generated and published as the revocation status of one or more credentials within the Revocation Registry change.

A secure process must be run to create the initial Revocation Status List object, taking the following input parameters.

• revRegId: the ID of the Revocation Registry for which the initial Revocation Status List is to be generated.
  • The process uses this identifier to find the associated Private Revocation Registry to access the information within that object.
• revocationList - A bit array of length maxCredNum that indicates whether a credential is initially revoked or not. The value of 1 indicates the credential is initially revoked, the value of 0 indicates the credential is initially unrevoked.

The process collects from the identified Private Revocation Registry information to calculate the cryptographic accumulator value for the initial Revocation Status List, including:

• revocDefType: the type of revocation registry. This is currently always CL_ACCUM
• maxCredNum: The capacity of the Revocation Registry, a count of the number of credentials that can be issued using the Revocation Registry.
• tailsArray: The contents of the TAILS_FILE, the array of primes, one for each credential to be issued from the Revocation Registry.
• privateKey: The accumulator private key for the Revocation Registry.

With the collected information, the initial cryptographic accumulator for the Revocation Registry can be created. The format of the identifier for the Revocation Status List is dependent on the AnonCreds Objects Method used by the issuer.

In simple terms, the cryptographic accumulator at any given point in time is the (modulo) product of the primes for each non-revoked credential in the Revocation Registry.

If all of the credentials are initially revoked (revocationList only contains 1 values), the accumulator value is 0.

The accumulator is calculated using the following steps:

THe following is an example of an initial, published Revocation Status List object:

{
  "revRegDefId": "4xE68b6S5VRFrKMMG1U95M:4:4xE68b6S5VRFrKMMG1U95M:3:CL:59232:default:CL_ACCUM:4ae1cc6c-f6bd-486c-8057-88f2ce74e960",
  "revocationList": [0, 1, 1, 0],
  "currentAccumulator": "21 124C594B6B20E41B681E92B2C43FD165EA9E68BC3C9D63A82C8893124983CAE94 21 124C5341937827427B0A3A32113BD5E64FB7AB39BD3E5ABDD7970874501CA4897 6 5438CB6F442E2F807812FD9DC0C39AFF4A86B1E6766DBB5359E86A4D70401B0F 4 39D1CA5C4716FFC4FE0853C4FF7F081DFD8DF8D2C2CA79705211680AC77BF3A1 6 70504A5493F89C97C225B68310811A41AD9CD889301F238E93C95AD085E84191 4 39582252194D756D5D86D0EED02BF1B95CE12AED2FA5CD3C53260747D891993C",
  "timestamp": 1669640864487
}

The items in the data model are:

• revRegDefId: the identifier of the associated Revocation Registry Definition. The format of the identifier is dependent on the AnonCreds Objects Method used by the issuer.
• revocationList: Bit array defining the status of the credential in the [ref: Revocation Registry]. A value of 1 means the credential is revoked, a value of 0 means the credential is not revoked.
• currentAccumulator: the calculated cryptographic accumulator reflecting the initial state of the Revocation Registry
• timestamp: the timestamp at which the accumulator value is valid

§ Publishing the Initial Initial Revocation Status List Object

Once constructed, the initial Revocation Status List is published by the issuer in a Verifiable Data Registry using their selected AnonCreds Objects Method.

It is not required for the Verifiable Data Registry to store the revocation list as defined in this model. For example, the Indy ledger uses deltas (Revocation Registry Entries) to store the change in revoked/un-revoked indices instead of storing the entire revocation list. It is also possible to compress the revocationList entry using e.g. GZIP to reduce the size on the ledger.

§ Holder Create and Store Link Secret

To prepare to use AnonCreds credentials, the Holder must create a link secret, a unique identifier that allows credentials issued to a Holder to be bound to that Holder and presented without revealing a unique identifier, thus avoiding correlation of credentials by Verifiers. The link secret is kept private by the Holder. The link secret is used during the credential issuance process to bind the credential to the holder and in the generation of a presentation. For the latter, it allows the holder to create a zero knowledge proof that they were issued the credential.This proof demonstrates knowledge the link secret and prove that it is one of the signed credential attributes, without revealing the link secret to the verifier. The details of how the link secret is used to do this is provided in the issuance, presentation generation and verification sections of this specification.

The link secret is a sufficiently random unique identifier. For example, in the Hyperledger Indy implementation, the link secret is produced by a call to the Rust uuid Crate’s new_v4() method to achieve sufficient randomness.

Once generated, the link secret is stored locally by the Holder for use in subsequent issuance and presentation interactions. If lost, the Holder will not be able to generate a proof that the credential was issued to them. The holder generates only a single link secret, using it for all credentials the holder is issued. This allows for verifiers to verify that all of the credentials used in generating a presentation with attributes from multiple credentials were all issued to the same Holder without requiring the Holder to disclose the unique identifier (link secret) that binds these credentials together.

There is nothing to stop a Holder from generating multiple link secrets and contributing them to different credential issuance processes. However, doing so prevents the Holder from producing a presentation combining credentials issued to distinct link secrets that can be proven to have been issued to the same entity. It is up to the Verifier to require and enforce the binding between multiple credentials used in a presentation.

§ AnonCreds Issuance Data Flow

The issuance of an anonymous credential requires several steps and involves the roles issuer, holder as well as the Verifiable Data Registry (see diagram below).

The issuer prepares a Credential Offer for the holder (step 1). A Credential Offer includes a commitment about the credential (referencing a Public Credential Definition) the issuer is intending to issue to the holder. The issuer sends the Credential Offer to the holder (step 2), who evaluates the offer (step 3) and fetches data about the offer (the Public Credential Definition) from the Verifiable Data Registry (steps 4-7).

Using the data from the Credential Offer and the Public Credential Definition retrieved from the Verifiable Data Registry, the holder prepares a Credential Request (step 8), a formal request to the issuer to issue a credential based on the given Public Credential Definition to the holder. The Credential Request includes a cryptographic commitment to the holder's link secret. The holder sends the Credential Request to the issuer (step 9).

The issuer verifies and decides whether to accept the Credential Request (step 10) and if so, prepares the credential (step 11). The issuer sends the credential to the holder (step 12). The holder then removes the blinding factor from the credential (step 13), verifies the credential and (usually) securely stores it (step 14).

Details about each step in the issuance process are covered in the following sections.

§ Credential Offer

The AnonCreds issuance process begins with the issuer constructing and sending a Credential Offer to the potential holder. The Credential Offer contains the following JSON elements:

{
    "schema_id": string,
    "cred_def_id": string,
    "nonce": string,
    "key_correctness_proof" : <key_correctness_proof>
}

• schema_id: The ID of the Schema on which the Public Credential Definition for the offered Credential is based.
• cred_def_id: The ID of the Public Credential Definition on which the Credential to be issued will be based.
• nonce: A random number generated for one time use by the issuer for preventing replay attacks and authentication between protocol steps. The nonce must be present in the subsequent Credential Request from the holder.
• key_correctness_proof: The Fiat-Shamir transformation challenge value in the non-interactive mode of Schnorr Protocol. It is calculated by the issuer as the proof of knowledge of the private key used to create the Credential Definition. This is verified by the holder during the creation of Credential Request.

The JSON content of the key_correctness_proof is:

"key_correctness_proof": {
    "c": "103...961",
    "xz_cap": "563...205",
    "xr_cap": [
        [
            "<attribute 1>",
            "821...452"
        ],
        [
            "master_secret",
            "156...104"
        ],
        [
            "<attribute 1>",
            "196...694"
        ]
    ]
}

The values in the proof are generated as follows:

• c: (a BigNumber) can be viewed as the committed value derived from the hash of the concatenated byte values in the process of creating the Credential Definition.

$$c = H(z || {r_i} || \tilde{z} ||\tilde{r_i})$$

where

• $z = s ^ {x_z}\ Mod\ n$ where $z$, $s$ and $n$ are values in the Public Credential Definition

• $r_i$ are the values in the $r$ map in Public Credential Definition, individual attribute public keys

• $\tilde{z}$ is similar to $z$ which equals to $s^{\tilde{x_z}}\ mod\ n$, where $\tilde{x_z}$ is a randomly selected integer between $2$ and $p'q'-1$

• $\tilde{r_i}$ is similar to $r$, which equal to $s^{\tilde{x_i}}\ mod\ n$, where $\tilde{x_i}$ are randomly selected integers between $2$ and $p'q'-1$

• xz_cap: $\hat{x_z} = c x_z + \tilde{x_z}$

• xr_cap: $\{ (attribute_i, cr_i + \tilde{r_i}) \}_{1 < i < L}$ for $L$ attributes

Both xz_cap and the second element in the tuple of the xr_cap vector are BigNumbers.

The issuer sends the Credential Offer to the holder.

§ Credential Request

A Credential Request is a formal request from a holder to an issuer to get a credential based on the Credential (and the referenced Public Credential Definition) sent by the issuer to the holder.

On receipt of the Credential Offer, the holder retrieves the referenced Public Credential Definition from a Verifiable Data. The holder MAY want to retrieve the Schema referenced in the Credential Offer and verify the consistency between the list of attributes in the Schema and in the Public Credential.

In addition, the holder also requires access to their link.

The nonce of the Credential Offer is used to generate the proof of correctness for blinded credential secrets, where it is hashed with the blinded secrets to create the proof which is sent to the issuer.

§ Verifying the Key Correctness Proof

The holder must first verify the key_correctness_proof in the Credential Offer using data from the referenced Public Credential Definition. The key_correctness_proof data is described in the previous section about the Credential Offer.

The key_correctness_proof verification is as follows:

1. Check that all attributes in Public Credential Definition and master_secret (an attribute that will be related to the link secret) are included in xr_cap.
2. Compute $c'$, where $c' = H(z || {r_i} || \hat{z'} ||\hat{r_i'})$.
3. If $\hat{z'} == \tilde{z}$ and $\hat{r_i'} == \tilde{r_i}$, then $c' == c$. The proof is accepted.

For $\hat{z'}$, we first find the multiplicative inverse of $z$

$$z^{-1}z = 1\ (Mod\ n)$$

Then

$$\hat{z'} = z^{-c} s^{\hat{x_z}} \ (Mod\ n)$$

$$= z^{-c} s^{cx_z + \tilde{x_z}}\ (Mod\ n)$$

$$= z^{-c} z^{c} s^{\tilde{x_z}}\ (Mod\ n)$$

$$\hat{z'} = \tilde{z}$$

The same can be derived for all $\hat{r_i'}$ by finding the multiplicative inverse of $r_i$, where {1 < i < L} for $L$ attributes.

§ Constructing the Credential Request

The holder constructs the following Credential Request JSON structure:

{
    "prover_did": "BZpdQDGp2ifid3u3Up17MG",
    "cred_def_id": "GvLGiRogTJubmj5B36qhYz:3:CL:8:faber.agent.degree_schema",
    "blinded_ms": {
        # Structure detailed below
    },
    "blinded_ms_correctness_proof": {
        # Structure detailed below
    },
    "nonce": "604812518357657692681285"
}

• entropy: a required string.
  • Called prover_did in earlier AnonCreds implementations, and called prover_id in Ursa, entropy is a random alphanumeric string generated by the holder and used by the issuer to add entropy in generating the credential signature. The value is combined by the issuer with the credential revocation index (cred_idx) if the credential is revocable, and the resulting string is hashed to create the credential_context, an input to the credential signing process. The credential_context is the m2 item in the issued verifiable credential signature.
  • Historically in Aries agent implementations, the prover_did was populated by the holder with a DID they hold, usually the DIDComm peer-to-peer DID shared by the the holder to the issuer. However, the item is not verified by the issuer as a DID nor as an identifier for the holder, and as such an random string is sufficient.
  • The holder can verify the provide entropy value was used by the [[ref: issuer] in generating the signature by combining entropy with the cred_idx value from the issuer (if the credential is revocable), hashing the resulting string and checking that the hash matches m2 in the credential signature.
• cred_def_id: The ID of the Public Credential Definition on which the Credential to be issued will be based.
• blinded_ms: The link secret in its blinded form. Described in detail in the section Blinding the Link Secret (below).
• blinded_ms_correctness_proof: The Blinded Secrets Correctness Proof of the blinded link secret. Described in detail in the section The Blinded Link Secret Correctness Proof (below).
• nonce: Used for preventing replay attacks and authentication between protocol steps. The holder creates an 80 bit nonce in the request which is a randomly generated number.

Once constructed, the holder sends the Credential Request to the issuer, who then can reply to the holder by sending an issued credential.

§ Blinding the Link Secret

The holder generates a blinding factor and uses this to create a cryptographic commitment to their link secret. This is the blinded_ms (blinded link secret) in the Credential Request. The blinded_ms will be signed by the issuer along with the rest of the credential attributes to create a blinded Signature. The holder removes the blinding factor from the blinded Signature to retrieve the Credential Signature over their unblinded link secret and the credential attributes.

During presentations, the holder can prove knowledge of the link secret within credential or set of credentials being presented, without revealing the link secret itself. This is the capability that enables the binding of the credentials to each other and to the holder without revealing a correlatable identifier.

The blinding factor is a secret generated by the holder for blinding the link secret before sending it to the issuer. The blinding factor, $v$ is created by selecting a random integer that is less than the order of the RSA group, n.

The process of blinding the link secret uses the issuer's CredentialPrimaryPublicKey, $P$, which is included in the Public Credential Definition, and contains z, r, s and n (described here). While r contains the public keys for all of the attributes to be signed, the only one of interest in this process is $r_{link_secret}$

The link secret, $A_l$ is blinded by

$A_{bl} = r_{link secret}^{A_l}\ Mod\ n$

$A_{bl}$ is multiplied by the blinding factor, $v'$,

$(s^{v'} \times A_{bl})\ Mod\ n$

The resulting blinded link secret data structure inserted into the Credential Offer is defined as follows:

"blinded_ms": {
    "u": "331...544",
    "ur": null,  # Populated when the credential definition supports revoation
    "hidden_attributes": [
        "master_secret"
    ],
    "committed_attributes": {}
}

Where:

• u: $u = (s^{v'} \times A_{bl})\ Mod\ n$
• ur: is null if revocation is not active for the [[ref: Public Credential Definition], and if revocation is active $u_r = h_2^{s'_r}$ where $s'_r$ is randomly selected quadratic residue of order of the bilinear groups q and $h_2$ is part of the revocation public key.
• hidden_attributes: is an array of hidden attributes from the list of [[ref: Public Credential Definition]. For AnonCreds v1.0, it is always a single entry of link_secret.
  • The holder's blinded link secret is a default hidden attribute in AnonCreds, meaning it is not explicitly defined in the Schema list of attributes but is included in both the Public Credential Definition and all issued credentials. Whilst it is cryptographically possible to have multiple hidden attributes, in this version of AnonCreds, only link secret is used.
• committed_attributes: An empty list of attributes in this version of AnonCreds.

§ The Blinded Link Secret Correctness Proof

In addition to creating the blinded link secret, the holder also creates a blinded link secret correctness proof and inserts it into the Credential Request. The data structure for the blinded link secret correctness proof is as follows:

"blinded_ms_correctness_proof": {
    "c": "702...737",
    "v_dash_cap": "202...924",
    "m_caps": {
        "master_secret": "907...913"
    },
    "r_caps": {}
}

The values in the proof are generated as follows:

• c: (a BigNumber) can be viewed as the committed value derived from the hash of the concatenated byte values in the process of creating the Credential Definition and the nonce value .

$$c = H(u || \tilde{u} || n_0)$$

where

• $u$ is described above.
• $\tilde{u} = s^{\tilde{v}'} \times r_{linksecret}^{\tilde{A_l}}\ mod\ n$ where $\tilde{v}'$ is randomly selected 3488-bit value and $\tilde{A_l}$ is 593-bit value by reference Anonymous credentials with type-3 revocation by Dmitry Khovratovisch, Michael Lodder and Cam Parra
• $n_0$ is the nonce value.
• v_dash_cap: $\hat{v'} \leftarrow \tilde{v'} + cv'$, where $v'$ is the blinding factor and $\tilde{v'}$ is a 3488-bit random number.
• m_caps: $\{\hat{m_i} \leftarrow \tilde{m_i} + cm_i\}_{i \in A_h}$, where $A_h$ is the set of all hidden attributes.
• r_caps: is an empty structure in this version of AnonCreds.

§ Issue Credential

After the issuer receives the Credential Request from the holder, the issuer processes the Credential Request and decides whether to issue the credential as requested in the Credential Request to the holder. In this section, we’ll cover issuing a credential that cannot be revoked, and then cover the additional steps/data elements in issuing a credential that can be revoked.

§ Verifying the Credential Request

Before deciding to issue the credential, the issuer must first verify the Credential Request from the holder by using the nonce from credential offer ($n_0$) to verify the blinded link secret correctness proof.

The blinded_ms_correctness_proof is verified by issuer. The blinded_ms_correctness_proof verification is as follows:

1. Compute $c'$, where $c' = H(u || \hat{u} || n_0)$.
2. If $\hat{u} == \tilde{u}$, then $c' == c$. The proof is accepted.

For $\hat{u}$, we first find the multiplicative inverse of $u$

$$u^{-1}u = 1\ (Mod\ n)$$

Then

$$\hat{u} = u^{-c} \times r_{linksecret}^{\hat{m} } \times s^{\hat{v'}} \ (Mod\ n)$$

$$= u^{-c} \times r_{linksecret}^{\tilde{A_l}+ cA_l } \times s^{ \tilde{v'} + cv'}\ (Mod\ n)$$

$$= u^{-c} \times u^{c} \times r_{linksecret}^{\tilde{A_l}} \times s^{\tilde{v'}}\ (Mod\ n)$$

$$\hat{u} = \tilde{u}$$

Once the Credential Request is verified and if the issuer decides to proceed with issuing the credential, the credential creation process is performed.

§ Encoding Attribute Data

The Anoncreds signature is not applied on the data attributes themselves, but rather on 32-byte integers encoded from the data attribute values. In the current version of AnonCreds, the process of encoding the attributes (also known as canonicalization) is a task performed by the issuer, who should do the encoding in a manner understood by all potential verifiers such that any verifier can confirm that the revealed raw attributes in the presentation produce the encoded value signed by the issuer. To enable the broadest possible interoperability, the Hyperledger Aries community formalized the following encoding rules for the raw attribute values in an AnonCreds credential, and those rules are adopted into this specification, as follows:

• keep any integer as is
• convert any string integer (e.g. “1234”) to be an integer (e.g. 1234)
• for data of any other type:
  • convert to string (use string “None” for null)
  • encode via utf-8 to bytes
  • apply SHA-256 to digest the bytes
  • convert the resulting digest bytes, big-endian, to integer
  • stringify the integer as a decimal.

An example implementation in Python of these rules can be found here.

A gist of test value pairs can be found here.

§ Constructing a Credential

To construct a non-revocable credential, the issuer must have available:

• The identifiers for the schema and Public Credential Definition.
• The Private Credential Definition data to be used in signing the credential.
• The raw value for each attribute to be included in the credential.
• The encoded value derived from each raw value using the encoding attribute data rules (above).
• The blinded link secret from the holder's Credential Request.

Additional data is needed for issuing a revocable credential, as described in the section Supporting Revocation in a Credential.

The JSON of a generated AnonCreds credential is as follows:

{
    "schema_id": string,
    "cred_def_id": string,
    "rev_reg_id": null,
    "values": {
        "first_name": {
            "raw": "Alice",
            "encoded": "113...335"
        },
        "last_name": {
            "raw": "Garcia",
            "encoded": "532...452"
        },
        "birthdate_dateint": {
            "raw": "19981119",
            "encoded": "19981119"
        }
    },
    "signature": {
        "p_credential": {
            "m_2": "992...312",
            "a": "548...252",
            "e": "259...199",
            "v": "977...597"
        },
        "r_credential": null
    },
    "signature_correctness_proof": {
        "se": "898...935",
        "c": "935...598"
    },
    "rev_reg": null,
    "witness": null
}

• schema_id: is the ID of the Schema upon which the Public Credential Definition was generated.
• cred_def_id: is the ID for the Public Credential Definition on which the Credential issued is based.
• rev_reg_id is null if the credential is not revocable. A description of the element when the credential is revocable is in the section Supporting Revocation in a Credential.
• values is the list of attributes in the credential, including for each:
  • the name of the attribute (in this case first_name, last_name, and birth_dateint),
  • the raw data for the attribute, and
  • the encoded data for the attribute, derived from the raw value has defined in the encoding attribute data rules.
• signature is the cryptographic signature generated for the credential.
  • A description of the p_signature elements and generation process are in the section The Credential Signature.
  • r_credential is null if the credential is not revocable. A description of the r_signature elements and generation process when the credential is revocable are in the section Supporting Revocation in a Credential.
• signature_correctness_proof is the Signature Correctness Proof generated for the credential. A description of the elements and generation process are in the section The Credential Signature Correctness Proof.
• rev_reg is null if the credential is not revocable. A description of the element and generation process when the credential is revocable are in the section Supporting Revocation in a Credential.
• witness is null if the credential is not revocable. A description of the element and generation process when the credential is revocable are in the section Supporting Revocation in a Credential.

Once constructed, the issuer sends the credential to the holder for verification and storage.

"r_credential": {
    "sigma": "1 14C...8A8",
    "c": "12A...BB6",
    "vr_prime_prime": "0F3...FC4",
    "witness_signature": {
        "sigma_i": "1 1D72...000",
        "u_i": "1 0B3...000",
        "g_i": "1 10D...8A8"
    },
    "g_i": "1 10D7...8A8",
    "i": 1,
    "m2": "FDC...283"
}

"rev_reg": {
    "accum": "21 118...1FB"
}

"witness": {
    "omega": "21 124...AC8"
}

§ Create Presentation Request

The verifier starts the presentation process in step 1 of the AnonCreds Presentation Data Flow by creating and sending a presentation to the holder.

The presentation request provides information about the attributes and predicates the verifier is asking the the holder to reveal, restrictions on what verifiable credentials can be the sources for the attributes and predicates, and limitations on the freshness of the credential revocation status. Presentation requests are defined at the “business logic” layer, with any cryptographic processing applied. The verification process includes verifications that the presentation satisfies the request. The verifier SHOULD validate that the presentation satisfies the business requirements for which the presentation was provided.

In reading this section, the term attribute is used in two ways, and readers should be aware of the context of each use. A presentation request has **requested attributes that are to be included in the presentation provided from the holder. Those requested attributes in turn reference attribute names and values from source verifiable credentials held by the holder.

The presentation request is created by the verifier in JSON format, as follows:

{
    "name": string,
    "version": string,
    "nonce": string,
    "requested_attributes": {
        "<attr_referent>": <attr_info>,
        ...,
    },
    "requested_predicates": {
        "<predicate_referent>": <predicate_info>,
        ...,
     },
    "non_revoked": Optional<non_revoc_interval>,
    "ver": Optional<str>
}

• name is a string set by the verifier, a name for the presentation request.
• version is a string set by the verifier, the version of the presentation request
• nonce is a string, a decimal, 80-bit number generated by the verifier that SHOULD be unique per presentation request. The nonce is included in the request to prevent replay attacks through its use in creating and verifying the presentation.
• requested_attributes specify the set of requested attributes
  • attr_referent is a verifier-defined identifier for the requested attribute(s) to be revealed.
  • attr_info describes a requested attribute. See attr_info
• requested_predicates specify the set of requested predicates
  • predicate_referent is a verifier-defined identifier for the requested predicate.
  • predicate_info describes a requested predicate. See predicate_info
• non_revoked specifies an optional non-revocation interval non_revoc_interval. See the Request Non-Revocation Proofs section.
• ver is an optional string, specifying the presentation request version.
  • If omitted, “1.0” is used by default.
  • “1.0” to use unqualified identifiers for restrictions
  • “2.0” to use fully qualified identifiers for restrictions

attr_info has the following format:

{
    "name": <string>,
    "names": <[string, string]>,
    "restrictions": <restrictions>,
    "non_revoked": <non_revoc_interval>,
}

All of the items are optional, but one of name or names MUST be included, and not both.

• name is a string, the name of an attribute from a source credential.
  • The name is case insensitive with spaces ignored.
• names is a array of strings, the names of attributes from a source credential
  • The names are case insensitive with spaces ignored.
  • The attribute names MUST be sourced from a single credential.
• restrictions is a condition on the source credential that can be used to satisfy this attribute request.
  • See restrictions for details about supported restrictions.
  • Omitting restrictions implies that:
    • The holder MAY provide self-attested attributes for the request in the presentation, or
    • that the name(s) of the requested attributes match the name(s) of the claim(s) in the source verifiable credential.
• non_revoked specifies a non-revocation interval non_revoc_interval for this requested attribute.
  • See Request Non-Revocation Proofs section.
  • If non_revoked is defined at the outer level of the JSON and is not defined at the attr_info level, the out level data applies to the attribute.
  • If non_revoked is defined at the outer level of the JSON AND at the attr_info layer, the attr_info data applies to the attribute.

predicate_info has the following format:

{
    "name": string,
    "p_type": string,
    "p_value": int,
    "restrictions": <restrictions>,
    "non_revoked": <non_revoc_interval>,
}

• name (required) is a string, the name of an attribute from a source credential to use in the predicate expression.
  • The name is case insensitive and spaces are ignored.
  • To be useful, the attribute in the source credential MUST be an integer, but that requirement cannot be enforced. The verifier MUST understand how the attribute value is set by the issuer(s) in the expected source credentials.
• p_type is a string, the type of the predicate. Possible type values are [“>=”, “>”, “<=”, “<”].
• p_value is an integer value.
  • The boolean expression that is to proven in zero knowledge is evaluated as: “<name> <p_type> <p_value>.” For example, to check an “older than” based on date of birth, the expression might be “birth_dateint <= 20020116”
• restrictions is a condition on the source credential that can be used to satisfy this predicate request.
  • See restrictions for details about supported restrictions.
  • If omitted, the only restriction on the requested predicate is that the name matches the attribute name in the source credential used to satisfy the predicate.
• non_revoked specifies a non-revocation interval non_revoc_interval for this predicate attribute.
  • See Request Non-Revocation Proofs section.

§ Restrictions

The restrictions item on attributes (optional) and predicates (required) is a JSON structure that forms a logical expression involving properties of the source verifiable credential. The holder must use source verifiable credentials that satisfy the restrictions expression for each attribute/predicate entry. Each element of the logic expression is a property of source credentials and a value to be matched for that property. The following properties can be specified in the JSON. All except the marker property is specified with a value that must match the property. For the marker property, the value is always 1.

• schema_id - the identifier of the schema upon which the source credential is based.
• schema_issuer_did - the identifier, usually a DID, of the publisher of the schema upon which the source credential is based.
• schema_name - the name property of the schema upon which the source credential is based.
• schema_version - the version property of the schema upon which the source credential is based.
• issuer_did - the identifier, usually a DID, of the [[re: issuer]] of the source credential.
• cred_def_id - the identifier of the Credential Definition of the source credential.
• attr::<attribute-name>::marker - an attribute <attribute-name> must exist in the source credential.
  • When used, the value of the JSON item must be “1”.
• attr::<attribute-name>::<attribute-value> - the attribute <attribute-name> must be found in the source credential with a value of <attribute-value>.
  • When this property is used, the verifer MUST request that the <attribute-name> be revealed as otherwise there is no way to be sure the restriction has been satisfied.

A boolean expression is formed by ORing and ANDing the source credential properties. The following JSON is an example. Any of the source credential properties listed above can be used in the expression components:

      "restrictions": [
        {
          "issuer_did": "<did>",
          "schema_id": "id"
        },
        {
          "cred_def_id" : "<id>",
          "attr::color::marker": "1",
          "attr::color::value" : "red"
        }
      ]

The properties in each list item are AND’d together, and the array elements are OR’d together. As such, the example above defines the logical expression:

The attributes must come from a source verifiable credential such that:
   issuer_did = <did> AND
     schema_id = <id>
   OR
   cred_def_id = <id> AND
      the credential must contain an attribute name "color" AND
      the credential must contain an attribute name "color" with the attribute value "red"

§ Request Non-Revocation Proofs

The presentation request JSON item non_revoked allows the verifier to define an acceptable non-revocation interval for a requested attribute(s) / predicate(s), as follows:

{
    "from": Optional<int>,
    "to": Optional<int>,
}

• from is an unsigned long long value, the Unix Time timestamp of the interval beginning.
• to is an unsigned long long value, the Unix Time timestamp of the interval end.

As noted in the presentation request specification above, a non-revoked item be may at the outer level of the presentation request such that it applies to all requested attributes and predicates, and/or at the attribute/predicate level, applying only to specific requested attributes and/or predicates and overriding the outer layer item.

The non-revoked items apply only to requested attributes/predicates in a presentation that derive from revocable credentials. No proof of non-revocation is needed (or possible) from credentials that cannot be revoked. Verifiers should be aware that different issuers of the same credential type (same schemaId) may or may not use revocation for the credentials they issue.

The use of a “non-revoke interval” was designed to have the semantic meaning that the verifier will accept a non-revocation Proof (NRP) from any point in the from to to interval. The intention is that by being as flexible as the business rules allow, the holder and/or verifier may have cached VDR revocation data such that they don’t have to go to the VDR to get additional RevRegEntry data. The verification of the provided non-revocation interval in a presentation request is limited. For additional details, see the Verify Non-Revocation Proof section of this specification.

In practice, the use of the interval is not well understood and tends to cause confusion amongst those building presentation requests. The AnonCreds community recommends using matching from and to values as outlined in the Aries RFC 0441 Present Proof Best Practices. The verifier can then use business rules (outside of AnonCreds) to decide if the revocation is sufficiently up to date.

While one might expect the to value to always be the current time (“Prove the credential is not revoked now”), its inclusion allows the verifier to ask for a non-revocation proof sometime in the past. This addresses use cases such as “Prove that your car insurance policy was not revoked on June 12, 2021 when the accident occurred.”

§ Presentation Request Example

The following is an example of a full presentation request for a presentation for a set of revealed attribute names from a single source credential, a self-attested attribute, and a predicate.

{
   "nonce":"168240505120030101",
   "name":"Proof of Education",
   "version":"1.0",
   "requested_attributes":{
      "0_degree_uuid":{
         "names":[
            "name",
            "date",
            "degree"
         ],
         "restrictions":[
            {
               "schema_name":"degree schema"
            }
         ]
      },
      "0_self_attested_thing_uuid":{
         "name":"self_attested_thing"
      },
      "non_revoked": {
        "from": 1673885735,
        "to": 1673885735,
      }
   },
   "requested_predicates":{
      "0_age_GE_uuid":{
         "name":"birthdate_dateint",
         "p_type":"<=",
         "p_value":20030101,
         "restrictions":[
            {
               "schema_name":"degree schema"
            }
         ]
      }
   }
}

In step 2 of the AnonCreds Presentation Data Flow, the verifier sends the presentation request to the holder.

§ Generate Presentation

In step 3, 4, and 5 of the AnonCreds Presentation Data Flow, the holder collects the required information to create the verifiable presentation according to the presentation request received from the verifier.

Each attribute and predicate in the presentation request must be satisfied by a source credential held by the holder that meets the associated restrictions item in the presentation request. The same source credential MAY be used to satisfy multiple attributes and predicates. Each attribute in the presentation request may specify (using the names item) that multiple claims from the source credential must be shared. If there is no restrictions item in the presentation request, the holder MAY satisfy the presentation request with self-attested attributes.

The verifier may specify in the presentation request that if some or all of the attributes/predicates are to be satisfied by revocable credentials, the holder must accompany the verifiable credential proofs with non-revocation proofs (NRPs) for the source credentials. The generation of NRPs is described in the generate non-revocation proofs section of the specification.

§ Collecting the Source Verifiable Credential Data

Before the holder can generate the presentation to satisfy a request, the source verifiable credentials that will be used in the presentation must be collected.

The source verifiable credentials found for use in generating a presentation must meet the following requirements:

• All of the source credentials MUST have been issued to the same link secret.
• The source credential for each presentation request attribute and predicate must satisfy the attribute’s or predicate’s associated restrictions item, and must include claim names that match the attribute’s name or names item, or claim name that match the requested predicate.

The mechanism to find the credentials in the holder’s wallet that satisfy a presentation request is outside the scope of this specification. As such, the remainder of this section covering how this process is done in Hyperledger Aries implementations is non-normative.

Aries implementations have historically used a mechanism called Wallet Query Language (WQL) to find the source credentials in the holder agent’s storage. Agents iterate through the presentation request attributes and predicates, converting the restrictions item from each into a corresponding WQL query, and calling an Aries key management service, such as Aries Askar, to return the credentials in the wallet that satisfy the query.

Completing the process results in a list of 0 or more source verifiable credentials that satisfy each attribute and predicate. If there is not a source verifiable credential for each, a business process must be invoked to decide if or how to proceed. For example, if some of the attributes or predicates cannot be satisfied with a credential already in the holder's storage, a process to get the necessary additional verifiable credentials may be initiated. If more than one verifiable credential satisfy any of the restrictions items, the holder software might select one to use by default, such as the most recently issued, non-revoked of the credentials, and/or might invoke a user interface to allow the entity that controls the holder software to select from the set of possible credentials to use.

In order to proceed to the presentation generation step, there must be one credential selected for each attribute and predicate in the presentation request.

§ Prepare Inputs to Presentation Generator

The next step of the process to create a presentation is to prepare the inputs to a call to AnonCreds to generate the presentation. The following are the inputs to the generation process (implementation). The holder must prepare each of the inputs by getting data either from local storage or, in the case of public data, retrieving it from the appropriate verifiable data registry(ies). AnonCreds implementations may provide functions to help in preparing some of the data.

• pres_req – The presentation request from the verifier.
• credentials – The list of credentials chosen by the holder for use in the presentation, including the request attributes and predicates to be populated from the each of the credentials. See note below.
• self_attested - A Hash Map containing each attribute to be satisfied with a self-attested response. Each entry includes the name of a presentation request attribute, and the self-attested value for that attribute.
• link_secret - The link secret for the credentials in the presentation.
• schemas_json - A Hash Map containing the SchemaId and complete Schema for the schemas of the credentials in the presentation.
• credential_defs_json - A Hash Map containing the CredentialDefinitionId and the complete CredentialDefinition for the credential definitions of the credentials in the presentation. Included in the CredentialDefintion are the revocation related values of the CredentialDefinition.

The credentials data structure contains for each listed credential:

• The complete credential data structure, as received from the issuer.
• A list of the presentation request attributes and predicates that will be populated from the credential.
  • For each of the source credential claim to be included in a request attribute, an indicator if the credential is to be revealed or not (true/false) in the presentation.
• The timestamp for the selected RevRegEntry that will be used to produce the non-revocation proof, if required.
• The witness for the credential based on the RevRegEntry being used to produce the non-revocation proof, if needed.

If the credential is not revocable, the latter two inputs are null, and are not used. See the later section on generating a presentation for a revocable credential for details about populating the timestamp and witness data elements.

The indicator of whether a claim is to be revealed or not in AnonCreds 1.0 must be carefully understood by verifiers. While a verifer requests a set of claims from the prover, the prover may choose to not reveal the raw value of some of those claims. If the prover does not reveal all of the requested claims, AnonCreds treats the presentation as cryptographically verified. It is then up to the verifier to decide, after cryptographic verification, if a presentation with unrevealed values is acceptable for the business purpose of the presentation.

§ Generate the Presentation

From the inputs, the presentation data is generated and put into the following data structure:

• presentation_request – The presentation request from the verifier.
• presentation – The set of proofs generated to satisfy the presentation request, including:
  • For each source credential, a primary eq_proof of the issuer signature across all of the claims in the credentials.
  • For each source credential that is revocable and for which the verifier has requested proof of non-revocation, a non-revocation proof, non_revoc_proof.
    • See the specification section on non-revocation-proof generation for details on this data structure.
  • For each requested predicate, a primary ge_proof (predicate) proof based on the requested claim from a source credential, the boolean operator (one of <=, <, >, >=), and the comparison value in the presentation request predicate.
  • One aggregate proof, aggregated_proof, across all of the source credentials that proves that the same link secret was used in the issuance of all of the credentials.
  • The mapping from each of the requested attributes and predicates to the primary proofs that satisfies the request.
    • A mapping for the requested attributes of the raw and encoded values from each revealed source credential claim.
    • A list of the self-attested attributes provided for the requested attributes that permit self-attested attributes.
    • A list of the unrevealed attributes.
    • A mapping of the requested predicates to the ge_proof that satisfies the request.
  • An array identifiers containing the schemaId and credDefId for each source credential in the presentation.
    • Also included for each source credentials for which a non-revocation proof is provided is the revRegDefId and the timestamp of the Revocation Registry Entry used in the non-revocation proof.

The following is an example of a multi-credential presentation without revocation.

{
  "presentation_request": {
    "nonce": "182453895158932070575246",
    "name": "Step 3 Send your Health Information",
    "version": "1.0",
    "requested_attributes": {
      "biomarker_attrs_0": {
        "names": [
          "name",
          "concentration",
          "unit",
          "range",
          "collected_on",
          "biomarker_id",
          "researcher_share"
        ],
        "restrictions": [
          {
            "schema_name": "MYCO Biomarker",
            "attr::name::value": "Iron"
          }
        ]
      },
      "consent_attrs": {
        "restrictions": [
          {
            "schema_name": "MYCO Consent Enablement",
            "schema_version": "0.1.0",
            "attr::jti_unique_identifier::value": "205b1ea0-7848-48d4-b52b-339122d84f62"
          }
        ],
        "name": "jti_unique_identifier"
      }
    },
    "requested_predicates": {}
  },
  "presentation": {
    "proof": {
      "proofs": [
        {
          "primary_proof": {
            "eq_proof": {
              "revealed_attrs": {
                "biomarker_id": "33034450023603237719386825060766757598085121996569112944281451290292212516012",
                "collected_on": "92231735610070911075924224447204218356256133056723930517696107260511721601349",
                "concentration": "10",
                "name": "85547618788485118809771015708850341281587970912661276233439574555663751388073",
                "range": "106828626115908025842177441696860557581575579893927923198365300598359723920768",
                "researcher_share": "101264834079306301897660576123112461042861436742738894013248454492965796383403",
                "unit": "38351211041892038382023569421847544683371072212679556578649761181279472893849"
              },
              "a_prime": "80156520245352052628208149565161465200964633377479145197038408116901327106468493831807000641577246417448908134495822028339761705905365398613527463662816881507291787145610182891716009505407072490691097943029471835157968113065071523597746984296197661560454442163361095634052138951650373193896962906203169809352467024247772052836999799731422581068645748537557874869718897034120634529002420631012358510111427944993245065350416694516913472010105229188198167306183788520891926236449848811955646933539477960935319919207451858981065765523367984374104834278565184338252025155136368869580505679884921590811310587077071610172673",
              "e": "115602723672843258810892161808995599340414281260248127600708536325470178701996999306086286379312077726886107268519700961209712187789855371",
              "v": "1250383260306407741656763352595256748825474237767244783206569756476708112785930898966696687140808011529311298553822794830872826226191807175199015541611342880032928005827271961840046208463350458298210749103878893742434685172894883857423865293195542824393317226300133796527531436931435189766065404966370796699897584860421160155369018136946091524266742514828667575397735892093187106092545876795688095293610064164136737808333322708435913545499149948994191514980395955519036106660001526586674248282052492138917987323789012051794441548696998993861159018178474063785171288325900474499496141522583368982451169653258746506425495702762445790848698570457196767532483566475068200091609719957656394696938689265240025099424248587121592521826940348286940172887963179718337593603053496022182071613592070622825622277436966372346642772481567879001423472517233061740522533372490151585309457871632521280719357505751796940152868034526426510835",
              "m": {
                "master_secret": "3455871040557234123393960708120725061759594951341120214330342075748561632734634451036095543889895409812764789858455375956895105746442946098665140470124325622343440794421325163223",
                "client_share": "4233663763294709836704307308997831519311512039775169744174375585917035614714239153287862168426091336550799195245481707264207548331415960277065672755643752404180562900805493953484"
              },
              "m2": "12942698897200869280316481431207639453433287089474860040781378232999349549981799159560238504559317917040820580596635945161264308025301203452846862479261473387068350544024561412435"
            },
            "ge_proofs": []
          }
        },
        {
          "primary_proof": {
            "eq_proof": {
              "revealed_attrs": {
                "jti_unique_identifier": "46414468020333259158238797309781111434265856695713363124410805958145233348633"
              },
              "a_prime": "52825780315318905340996188008133401356826233601375100674436798295026172087388431332751168238882607201020021795967828258295811342078457860422414605408183505911891895360825745994390769724939582542658347473498091021796952186290990181881158576706521445646669342676592451422000320708168877298354804819261007033664223006892049856834172427934815827786052257552492013807885418893279908149441273603109213847535482251568996326545234910687135167595657148526602160452192374611721411569543183642580629352619161783646990187905911781524203367796090408992624211661598980626941053749241077719601278347846928693650092940416717449494816",
              "e": "40342480172543061520030194979861449480343743039487113094246205723322643070249538229638327935935486373873622430409109409257546971244601965",
              "v": "217871997575635857881367472262154388060800564043554848081521162883333745687724235201324121915821236796357195214089699645741515836727882126142579489701412861659136426497703162695983681701205672924385915403141611021784136285588350763399255203187442277784718461565122805239422370067600654500115262174706580098147603414365915243447789285877195068031630371954678432401446457453517813298670236942253026249413255471803997869331683293818651006043399070308083119054618677128448043841313844695654424369871669436628257531643623230026240200330490039607166147891705813033761093730859310423856156850596341547950105490585959768382544221555877471751940512766452511773683786023245283041103270102119125303027835868565240336923422734962345750992898991606841120358203160628015844345063465293475128118937815965000466081345494616126511595974927544434058100817176268040385848789013718618727873445834393897904247054897801708217939187593785671914",
              "m": {
                "iat_consent_timestamp": "7919242808448912829024078929834347184203169048480606699350973804205285806978474375691141504249426249676222104091995582731720654507393708298132400435805626192291975477967402460279",
                "master_secret": "3455871040557234123393960708120725061759594951341120214330342075748561632734634451036095543889895409812764789858455375956895105746442946098665140470124325622343440794421325163223",
                "data_controller": "16070549690575784944224634793654539357398383214512772967411296056738507137421264813779497172425030465490587794790393434847583852932544021088761347641812155158324233253206392974293",
                "notice": "2790610958721083178459621377821800672322230987466716467063649577108407884592339521820875278264969393963213925568888672412150769438560815981777952572004955362915245795447078373509",
                "sensitive": "13552814315985495030467505807226704038231487014593307078913973520081443107274508887651839292151852713782653522711975492131914644109941607616672243509214979259100892541150351227883",
                "services": "14860984314279608355643170908802532226194914773406547259519961082467311361623076451869406343140860447342041426195737612897540117192702117380288330928866665314831926780606136352645",
                "sub_subject_identifier": "11736177517163751882849070942823049196298287414132249166618760803125435466270948777194044507635346721244111946358927525083691171695431736819244809221351813271261283779276670885101",
                "moc_method_of_collection": "10026360820367693771310999595495505533281326977349798360729122862705999157070660881611421445424239119786180921960380892002204780026072600494332540208429642332890963846523547470729",
                "jurisdiction_data_processing": "15829143141425514118932461858094583045441924952665872659029333578019676797278419825311275014912077620757631693167948665554731430154156737419706553672424812320891308795411687679270",
                "iss_internet_processing_uri": "6900796243066434651671715348976599009606292569990892886896520779618011026060325075822786686418461731663661832508437549373109822105600719490952253743950241384782222356411498407620",
                "version_consent_specification": "7796257942256624260327966366702213561879098947042014532961291550019706546662478888172243088973621029223408695289700984802154645011280488167967047321149956253054269901250137513345",
                "policy_url": "12241676508867847022708464707584814145889660003604359058532137895063826021524887759921830911553663255421852525705197991376264187781979066233701110706958983099645275940668404311601"
              },
              "m2": "6509130065158989037891281073557909501783443634141673890142284302459280804904096303151728187237486991775852971807701594247754409108836089746736345158069365449802597798950172729241"
            },
            "ge_proofs": []
          }
        }
      ],
      "aggregated_proof": {
        "c_hash": "81763443376178433216866153835042672285397553441148068557996780431098922863180",
        "c_list": [
          [
            2,
            122,
            246,
            66,
            85,
            35,
            17,
            213,
            1
          ],
          [
            1,
            162,
            117,
            246,
            95,
            154,
            129,
            32
          ]
        ]
      }
    },
    "requested_proof": {
      "revealed_attrs": {
        "consent_attrs": {
          "sub_proof_index": 1,
          "raw": "205b1ea0-7848-48d4-b52b-339122d84f62",
          "encoded": "46414468020333259158238797309781111434265856695713363124410805958145233348633"
        }
      },
      "revealed_attr_groups": {
        "biomarker_attrs_0": {
          "sub_proof_index": 0,
          "values": {
            "researcher_share": {
              "raw": "bf712cb328a92862b57f0dc806dec12a",
              "encoded": "101264834079306301897660576123112461042861436742738894013248454492965796383403"
            },
            "unit": {
              "raw": "μM",
              "encoded": "38351211041892038382023569421847544683371072212679556578649761181279472893849"
            },
            "concentration": {
              "raw": "10",
              "encoded": "10"
            },
            "name": {
              "raw": "Iron",
              "encoded": "85547618788485118809771015708850341281587970912661276233439574555663751388073"
            },
            "range": {
              "raw": "9.00-30.0",
              "encoded": "106828626115908025842177441696860557581575579893927923198365300598359723920768"
            },
            "collected_on": {
              "raw": "2020-07-05",
              "encoded": "92231735610070911075924224447204218356256133056723930517696107260511721601349"
            },
            "biomarker_id": {
              "raw": "c9ace7dc-0485-4f3f-b466-16a27a80acf1",
              "encoded": "33034450023603237719386825060766757598085121996569112944281451290292212516012"
            }
          }
        }
      },
      "self_attested_attrs": {},
      "unrevealed_attrs": {},
      "predicates": {}
    },
    "identifiers": [
      {
        "schema_id": "CsQY9MGeD3CQP4EyuVFo5m:2:MYCO Biomarker:0.0.3",
        "cred_def_id": "CsQY9MGeD3CQP4EyuVFo5m:3:CL:14951:MYCO_Biomarker"
      },
      {
        "schema_id": "FbozHyf7j5q7TDn2s8MXZN:2:MYCO Consent Enablement:0.1.0",
        "cred_def_id": "TUku9MDGa7QALbAJX4oAww:3:CL:531757:MYCO_Consent_Enablement"
      }
    ]
  }
}

Once the presentation data structure is generated, it is sent to the verifier for processing.

The following describes the data structures listed above, including the process of generating the data of the various types of proofs.

The Presentation Request

The presentation_request is a copy of the presentation_request data structure from the verifier, as described earlier in the specification.

Presentation

The presentation contains:

• Proofs of the source credentials.
• An aggregated proof across all of the source credentials.
• A mapping of how the requested attributes and predicates are satisfied.
• A list of the identifiers related to each of the source credentials in the proof.

The presentation data structure is as follows. As noted in the JSON comments included, details for each section of the presentation is provided below.

  "presentation": {
    "proof": {
      "proofs": [
        {
          "primary_proof": {
            "eq_proof": {
              # Described in detail below
            },
            "ge_proofs": [
              # Described in detail below
            ]
          }
        }
      ],
      "aggregated_proof": {
        # Described in detail below
      }
    },
    "requested_proof": {
      # Described in detail below
    }
    "identifiers": {
      # Described in details below
    }
  }

The proofs array contains an entry for each source verifiable credential. For each is a primary_proof covering the claims in the source credential called the eq_proof, and a ge_proof for each of the predicate proofs sourced from the verifiable credential.

Generating the Challenge Hash

For this step the holder follows the following steps:

• Generate a random 592-bit number $\tilde{m_j}$ for each $j \in \mathcal{A_{\bar{r}}}$ (unrevealed attributes)

• For each credential $C_p = (\{m_j\}, A, e, v)$ and issuer’s public key $pk$:

  • Choose random 3152-bit $r$.
  • Take $n, S$ from $pk$ and compute:

  $$A' \leftarrow AS^r \mod n$$

  $$v' \leftarrow v - e.r$$

  and add them to $\mathcal{C}$.

  • Compute $e' \leftarrow e-2^{596}$.
  • Generate random 456-bit $\tilde{e}$ and random 3748-bit number $\tilde{v}$.
  • Hide the unrevealed attributes using:

  $$T \leftarrow (A')^{\tilde{e}}(\prod_{j \in \mathcal{A_{\bar{r}}}} R_j^{\tilde{m_j}})(S^{\tilde{v}})\ (mod\ n)$$

  and add them to $\mathcal{T}$

• Load $Z, S$ from issuer’s public key

• For each predicate $p$ where operator * is one of $\gt, \ge, \lt, \le$:

  • Calculate $\Delta$ such that

  $$\Delta \leftarrow \left\{ \begin{array}{ll} z_j-m_j & * \equiv\ \le \\ z_j-m_j-1 & * \equiv\ \lt \\ m_j-z_j & * \equiv\ \ge \\ m_j-z_j-1 & * \equiv\ \gt \\ \end{array} \right.$$

  • Calculate $a$ such that :

  $$a \leftarrow \left\{ \begin{array}{ll} -1 & * \equiv\ \le or \lt \\ 1 & * \equiv\ \ge or \gt \\ \end{array} \right.$$

  • Find (by exhaustive search) $u_1, u_2, u_3, u_4$ such that:

  $$\Delta = (u_1)^2+(u_2)^2+(u_3)^2+(u_4)^2$$

  • Generate random 2128-bit numbers $r_1, r_2, r_3, r_4, r_{\Delta}$.

  • Blind values of $\Delta$ and $u_i$ by computing:

  $$\{ T_i \leftarrow Z^{u_i}S^{r_i}\ (mod\ n) \}_{1 \le i \le 4}$$

  $$T_{\Delta} \leftarrow Z^{\Delta}S^{r_{\Delta}}\ (mod\ n)$$

  and add these values to $\mathcal{C}$ in the order $T_1, T_2, T_3, T_4, T_{\Delta}$.

  • Generate random 592-bit numbers $\tilde{u_1}, \tilde{u_2}, \tilde{u_3}, \tilde{u_4}$, random 672-bit numbers $\tilde{r_1}, \tilde{r_2}, \tilde{r_3}, \tilde{r_4}, \tilde{r_{\Delta}}$, and random 2787-bit $\tilde{\alpha}$.

  • Compute:

  $$\{ \bar{T_i} \leftarrow Z^{\tilde{u_i}}S^{\tilde{r_i}}\ (mod\ n) \}_{1 \le i \le 4}$$

  $$\bar{T_{\Delta}} \leftarrow Z^{\tilde{m_j}}S^{a\tilde{r_{\Delta}}}\ (mod\ n)$$

  $$Q \leftarrow (S^{\tilde{\alpha}}) \prod_{i=1}^{4} T_i^{\tilde{u_i}}\ (mod\ n)$$

  and add these values to $\mathcal{T}$ in order $\bar{T_1}, \bar{T_2}, \bar{T_3}, \bar{T_4}, \bar{T_{\Delta}}, Q$.

• Finally, the holder computes the Fiat-Shamir challenge hash($c_H$):

$$c_H \leftarrow H(\mathcal{T}, \mathcal{C}, n_1)$$

where $n_1$ is the nonce sent by verifier in proof request.

Each primary eq_proof is generated as follows:

• For primary credential $C_p$ compute:

  $$e \leftarrow \tilde{e} + c_He'$$

  $$v \leftarrow \tilde{v} + c_Hv'$$

  $$\{ \hat{m_j} \leftarrow \tilde{m_j} + c_Hm_j \}_{j \in \mathcal{A_{\bar{r}}}}$$

  where $\mathcal{A_{\bar{r}}}$ is the set of unrevealed attributes.
• Compute $\hat{m_2} \leftarrow \tilde{m_2}+c_Hm_2\ (mod\ q)$
• Data attributes in eq_proof are:

"eq_proof": {
  "revealed_attrs": {
    "jti_unique_identifier": "46414468020333259158238797309781111434265856695713363124410805958145233348633"
  },
  "a_prime": "52825780315318905340996188008133401356826233601375100674436798295026172087388431332751168238882607201020021795967828258295811342078457860422414605408183505911891895360825745994390769724939582542658347473498091021796952186290990181881158576706521445646669342676592451422000320708168877298354804819261007033664223006892049856834172427934815827786052257552492013807885418893279908149441273603109213847535482251568996326545234910687135167595657148526602160452192374611721411569543183642580629352619161783646990187905911781524203367796090408992624211661598980626941053749241077719601278347846928693650092940416717449494816",
  "e": "40342480172543061520030194979861449480343743039487113094246205723322643070249538229638327935935486373873622430409109409257546971244601965",
  "v": "217871997575635857881367472262154388060800564043554848081521162883333745687724235201324121915821236796357195214089699645741515836727882126142579489701412861659136426497703162695983681701205672924385915403141611021784136285588350763399255203187442277784718461565122805239422370067600654500115262174706580098147603414365915243447789285877195068031630371954678432401446457453517813298670236942253026249413255471803997869331683293818651006043399070308083119054618677128448043841313844695654424369871669436628257531643623230026240200330490039607166147891705813033761093730859310423856156850596341547950105490585959768382544221555877471751940512766452511773683786023245283041103270102119125303027835868565240336923422734962345750992898991606841120358203160628015844345063465293475128118937815965000466081345494616126511595974927544434058100817176268040385848789013718618727873445834393897904247054897801708217939187593785671914",
  "m": {
    "iat_consent_timestamp": "7919242808448912829024078929834347184203169048480606699350973804205285806978474375691141504249426249676222104091995582731720654507393708298132400435805626192291975477967402460279",
    "master_secret": "3455871040557234123393960708120725061759594951341120214330342075748561632734634451036095543889895409812764789858455375956895105746442946098665140470124325622343440794421325163223",
    "data_controller": "16070549690575784944224634793654539357398383214512772967411296056738507137421264813779497172425030465490587794790393434847583852932544021088761347641812155158324233253206392974293",
    "notice": "2790610958721083178459621377821800672322230987466716467063649577108407884592339521820875278264969393963213925568888672412150769438560815981777952572004955362915245795447078373509",
    "sensitive": "13552814315985495030467505807226704038231487014593307078913973520081443107274508887651839292151852713782653522711975492131914644109941607616672243509214979259100892541150351227883",
    "services": "14860984314279608355643170908802532226194914773406547259519961082467311361623076451869406343140860447342041426195737612897540117192702117380288330928866665314831926780606136352645",
    "sub_subject_identifier": "11736177517163751882849070942823049196298287414132249166618760803125435466270948777194044507635346721244111946358927525083691171695431736819244809221351813271261283779276670885101",
    "moc_method_of_collection": "10026360820367693771310999595495505533281326977349798360729122862705999157070660881611421445424239119786180921960380892002204780026072600494332540208429642332890963846523547470729",
    "jurisdiction_data_processing": "15829143141425514118932461858094583045441924952665872659029333578019676797278419825311275014912077620757631693167948665554731430154156737419706553672424812320891308795411687679270",
    "iss_internet_processing_uri": "6900796243066434651671715348976599009606292569990892886896520779618011026060325075822786686418461731663661832508437549373109822105600719490952253743950241384782222356411498407620",
    "version_consent_specification": "7796257942256624260327966366702213561879098947042014532961291550019706546662478888172243088973621029223408695289700984802154645011280488167967047321149956253054269901250137513345",
    "policy_url": "12241676508867847022708464707584814145889660003604359058532137895063826021524887759921830911553663255421852525705197991376264187781979066233701110706958983099645275940668404311601"
  },
  "m2": "6509130065158989037891281073557909501783443634141673890142284302459280804904096303151728187237486991775852971807701594247754409108836089746736345158069365449802597798950172729241"
},

• revealed_attrs: The mapping of revealed attributes with their values.
• a_prime: This is the value generated during init proof and challenge hash calculation
• e: The value of $e$ in the proof.
• v: The value of $v$ in the proof.
• m: The hashmap containing hidden attribute name with calculated $\hat{m_j}$ value.
• m2: The value of $\hat{m_2}$ in the proof.

Each primary ge_proof is generated as follows:

• For each predicate $p$ compute:

  $$\{ \hat{u_i} \leftarrow \tilde{u_i} + c_Hu_i \}_{1 \le i \le 4}$$

  $$\{ \hat{r_i} \leftarrow \tilde{r_i} + c_Hr_i \}_{1 \le i \le 4}$$

  $$\hat{r_{\Delta}} \leftarrow \tilde{r_{\Delta}}+c_Hr_{\Delta}$$

  $$\hat{\alpha} \leftarrow \tilde{\alpha} + c_H(r_{\Delta} - u_1r_1 - u_2r_2 - u_3r_3 - u_4r_4)$$

• Data attributes in ge_proof are:

ge_proofs: [
  {
    u,
    r,
    mj,
    alpha,
    t,
    predicate
  }
]

• u: The hashmap containing values of $\hat{u_i}$ in the proof.
• r: The hashmap containing values of $\hat{r_i}$, and $\hat{r_{\Delta}}$ in the proof.
• mj: $\hat{m_j}$ of the concerned predicate obtained from the equality proof.
• alpha: The value of $\hat{\alpha}$ in the proof.
• t: The hashmap containing values of $\bar{T_i}$, and $\bar{T_{\Delta}}$ from the init proof.
• predicate: The concerned predicate from the proof request.

The aggregated_proof proves that the same linked secret was used to issue all of the source verifiable credentials in the presentation.

The aggregated_proof structure is as follows:

"aggregated_proof": {
        "c_hash": "base10string",
        "c_list": [ ["base10string"] ]
}

Here is an example:

"aggregated_proof": {
        "c_hash": "81763443376178433216866153835042672285397553441148068557996780431098922863180",
        "c_list": [
          [
            2,
            122,
            246,
            66,
            85,
            35,
            17,
            213,
            1
          ],
          [
            1,
            162,
            117,
            246,
            95,
            154,
            129,
            32
          ]
        ]
      }