CFRG V. Kalos
Internet-Draft MATTR
Intended status: Informational G. Bernstein
Expires: 28 December 2026 Grotto Networking
26 June 2026
Blind BBS Signatures
draft-irtf-cfrg-bbs-blind-signatures-03
Abstract
This document defines an extension to the BBS Signature scheme that
supports blind digital signatures, i.e., signatures over messages not
known to the Signer.
Discussion Venues
This note is to be removed before publishing as an RFC.
Discussion of this document takes place on the Crypto Forum Research
Group mailing list (cfrg@ietf.org), which is archived at
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https://github.com/cfrg/draft-irtf-cfrg-bbs-blind-signatures.
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Table of Contents
1. Introduction
1.1. Blind BBS Protocol Overview
1.2. Example Blind BBS Applications
1.3. Example Committed Disclosure Applications
1.4. Terminology
1.5. Notation
2. Conventions
3. BBS Signature Scheme Operations
4. Scheme Definition
4.1. Commitment Operations
4.1.1. Commitment Computation
4.1.2. Commitment Validation and Deserialization
4.2. Blind BBS Signatures Interface
4.2.1. Blind Signature Generation
4.2.2. Blind Signature Verification
4.2.3. Proof Generation
4.2.4. Proof Verification
4.3. Core Operations
4.3.1. Core Commitment Computation
4.3.2. Core Commitment Verification
4.3.3. Finalize Blind Sign
4.3.4. Core Proof Generation
4.3.5. Core Proof Verification
5. Utilities
5.1. Calculate B value
5.2. Blind Challenge Calculation
5.3. Proof Challenge Calculation
5.4. Serialize
5.4.1. Commitment with Proof to Octets
5.4.2. Octets to Commitment with Proof
5.4.3. Proof to Octets
5.4.4. Octets to Proof
6. Privacy Considerations
6.1. Total Number and Index of Committed Messages
7. Application Considerations
7.1. Input Validity Checks
8. Security Considerations
8.1. Prover Blind Factor
8.2. Key Binding
9. Ciphersuites
10. Test Vectors
11. IANA Considerations
12. Normative References
13. Informative References
Appendix A. Document History
Authors' Addresses
1. Introduction
Blind signatures are cryptographic protocols that allow for a signer
to create a signature over content without actually knowing the
content. They form a useful cryptographic primitive particularly in
situations that are privacy sensitive. The concept has existed for
quite some time and is well explained in Chaum's 1985 popular article
"Security without identification: transaction systems to make big
brother obsolete" [Chaum85]. In [RFC9474], "RSA Blind Signatures",
the RSA signature scheme was extended to provide for blind signing.
In this document the BBS digital signature scheme, as defined in
[I-D.irtf-cfrg-bbs-signatures], is extended to provide blind BBS
signatures.
Like BBS signatures blind BBS signatures work with a three party
model of _Signer_, _Prover_, and _Verifier_. The blind BBS protocol
defined here has the following useful properties:
1. Provides a signature over an ordered set of messages from the
_Prover_ that are kept secret from the _Signer_ via a
statistically hiding cryptographic commitment.
2. The _Signer_ will produce a signature for the _Prover_, only if
the later can prove knowledge of the set of messages they choose.
This will be done through a zero-knowledge proof-of-knowledge of
the ordered set of secret _Prover_ messages. The _Signer_ will
not issue a signature without this proof of knowledge.
3. The Blind BBS signature produced is of the same size as current
BBS signatures based on the same elliptic curve.
4. In addition to the _Prover_ provided secret messages, the
_Signer_ can optionally sign over an additional ordered set of
messages of their choosing. This is sometimes know as a
"partially blind" signature.
5. Using the Blind BBS signature created by the _Signer_ the
_Prover_ can disclose any subset of both the secret _Prover_
messages or the _Signer_'s messages and prove that these were in
the signed sets.
6. Without knowledge of the ordered set of secret messages no
selective disclosure proof can be generated even solely for a
subset of the _Signer_ messages. (within the security assumptions
of the BBS signature scheme).
While the core BBS protocol allows a prover to either disclose or
withhold a message from a verifier. This specification allows for
*committed disclosure* of a message [Vision2025]. In this case, the
prover provides a commitment (computationally binding and perfectly
hiding) to the message along with proof that the commitment
corresponds to a particular message in the signature.
The idea behind this committed-disclosure extension for BBS is that
it also accommodates further zero knowledge proof (ZKP) extensions --
e.g. range proofs or different pseudonyms -- in a modular, plug-and-
play style. Such extensions are out of scope of this specification.
1.1. Blind BBS Protocol Overview
The presented protocol, compared to the scheme defined in
[I-D.irtf-cfrg-bbs-signatures], introduces an additional
communication step between the _Prover_ and the _Signer_. An overview
of the protocol is given below.
1. The _Prover_ will start by constructing a "hiding" commitment to
the ordered set of messages they want to get a signature on
(i.e., a commitment which reveals no information about the
committed values), together with a proof of correctness of that
commitment.
2. The _Prover_ will send the (commitment, proof) pair to the
_Signer_, who, upon receiving the pair, will attempt to verify
the commitment's proof of correctness.
3. If successful, they will use it in generating a blind BBS
signature over the messages committed by the _Prover_, including
the _Signer_'s own messages if any.
4. The _Signer_ will send the blind signature along with its
additional ordered messages (if any) to the _Prover_
5. The _Prover_ can choose to selectively disclose or commit to any
subset of either its own messages, kept secret from the _Signer_
and messages provided by the _Signer_ in the signature. They
also furnish a ZKP that the these disclosed messages were
included in the signature.
6. The _Verifier_ verifies the proof received from the _Prover_
based on the _Signer_'s public key.
Note: Cryptographic _commitments_ are used for two distinct purposes
in this specification. One, as a mechanism for the prover to get a
blind signature from an signer, i.e., the prover is getting a
signature over some data it is not revealing to the signer. And,
two, as mechanism to furnish less information from the prover to the
verifier by providing a commitment along with a ZKP about that
commitment. For example, instead of providing a date of birth, the
prover provides a commitment to that date of birth along with ZKP
that indicates that the provers age lies in a particular range.
Below is a basic diagram describing the main entities involved in the
scheme.
(3) Blind Sign (1) Commit
+----- +-----
| | | |
| | | |
| \ / | \ /
+----------+ +-----------+
| | | |
| | | |
| |<-(2)* Commitment + Proof of Correctness--| |
| Signer | | Prover |
| |--(4)* Send signature + msgs + coms------>| |
| | | |
| | | |
+----------+ +-----------+
|
|
|
(5)* Send proof
+
disclosed msgs
|
|
\ /
+-----------+
| |
| |
| |
| Verifier |
| |
| |
| |
+-----------+
| / \
| |
| |
+-----
(6) ProofVerify
Figure 1: Basic diagram capturing the main entities involved in
using the scheme.
*Note* The protocols implied by the items annotated by an asterisk
are out of scope for this specification
This document, in addition to defining the operation for creating and
verifying a commitment, also details a core signature generation
operation, different from the one presented in
[I-D.irtf-cfrg-bbs-signatures], meant to handle the computation of
the blind signature. The document will also define a new BBS
Interface, which is needed to handle the different inputs, i.e.,
messages committed by the _Prover_ or chosen by the Signer etc.. The
signature verification and proof generation and verification core
cryptographic operations however, will work as described in
[I-D.irtf-cfrg-bbs-signatures].
1.2. Example Blind BBS Applications
By allowing the _Prover_ to acquire a valid signature over messages
not known to the Signer, blind signatures address some limitations of
their plain digital signature counterparts. In the BBS Signature
scheme, knowledge of a valid signature and set of signed messages
allows generation of BBS proofs. As a result, a signature compromise
(for example by a Signer database leakage, a phishing attack etc.,)
can lead to impersonation of the _Prover_ by malicious actors
(especially in cases involving "long-lived" signatures, as in digital
credentials applications etc.,). Using Blind BBS Signatures on the
other hand, the _Prover_ can commit to a secret message (for example,
a private key) before issuance, guaranteeing that no one will be able
to generate a valid BBS proof without knowledge of that secret
message.
Furthermore, applications like Privacy Pass
([I-D.ietf-privacypass-protocol]) may require a signature to be
"scoped" to a specific audience or session (as to require "fresh"
signatures for different sessions etc.,). However, simply sending an
audience or session identifier to the Signer (to be included in the
signature), will compromise the privacy guarantees that these
applications try to enforce. Using blind signing, the Prover will be
able to require signatures bound to those values, without having to
reveal them to the Signer.
1.3. Example Committed Disclosure Applications
Privacy is enhanced via the *committed disclosure* mechanism along
with an external ZKP proof of some predicate. In this case rather
than selectively disclosing a signed message to the verifier the
prover provides a (computationally binding and perfectly hiding)
commitment along with a ZKP concerning some aspect (the predicate) of
the committed value. This ZKP actually comes in two parts. One part
is specified in this specification and proves that the given
commitment(s) corresponds to the corresponding messages signed by the
signer. The second part is an additional ZKP, not specified here,
that proves some predicate about the committed values.
As discussed in [Vision2025] this allows for the modular addition for
proving (1) possession of a device key, (2) range proofs and (3)
pseudonyms. While in [LegacyBinding2026] additional more efficient
proof of possession of a (hardware) device key are given. These
would all be implemented as an additional ZKP along with the ZKP
specified here.
1.4. Terminology
Terminology defined by [I-D.irtf-cfrg-bbs-signatures] applies to this
draft.
Additionally, the following terminology is used throughout this
document:
blind_signature The blind digital signature output.
commitment A point of G1, representing a Pedersen commitment ([P91])
constructed over a vector of messages, as described e.g., in
[BG18].
committed_messages A list of messages committed by the Prover to a
commitment.
commitment_proof A zero knowledge proof of correctness of a
commitment, consisting of a scalar value, a possibly empty set of
scalars (of length equal to the number of committed_messages, see
above) and another scalar, in that order.
secret_prover_blind A random scalar used to blind (i.e., randomize)
the commitment constructed by the prover.
signer_blind A random scalar used by the signer to optionally re-
blind the received commitment.
NONE An empty function input indicator, used to specify that one of
the OPTIONAL inputs of a procedure is not provided by the calling
operation.
1.5. Notation
Notation defined by [I-D.irtf-cfrg-bbs-signatures] applies to this
draft.
Additionally, the following notation and primitives are used:
list.append(elements) Append either a single element or a list of
elements to the end of a list, maintaining the same order of the
list's elements as well as the appended elements. For example,
given list = [a, b, c] and elements = [d, a], the result of
list.append(elements) will be [a, b, c, d, a].
2. 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.
3. BBS Signature Scheme Operations
This document makes use of various operations defined by the BBS
Signature Scheme document [I-D.irtf-cfrg-bbs-signatures]. For
clarity, whenever an operation will be used defined in
[I-D.irtf-cfrg-bbs-signatures], it will be prefixed by "BBS." (e.g.,
"BBS.CoreProofGen" etc.). More specifically, the operations used are
the following:
* BBS.CoreVerify: Refers to the CoreVerify operation defined in
Section 3.6.2 (https://www.ietf.org/archive/id/draft-irtf-cfrg-
bbs-signatures-05.html#name-coreverify) of
[I-D.irtf-cfrg-bbs-signatures].
* BBS.CoreProofGen: Refers to the CoreProofGen operation defined in
Section 3.6.3 (https://www.ietf.org/archive/id/draft-irtf-cfrg-
bbs-signatures-05.html#name-coreproofgen) of
[I-D.irtf-cfrg-bbs-signatures].
* BBS.create_generators: Refers to the create_generators operation
defined in Section 4.1.1 (https://www.ietf.org/archive/id/draft-
irtf-cfrg-bbs-signatures-05.html#name-generators-calculation) of
[I-D.irtf-cfrg-bbs-signatures].
* BBS.messages_to_scalars: Refers to the messages_to_scalars
operation defined in Section 4.1.2
(https://www.ietf.org/archive/id/draft-irtf-cfrg-bbs-signatures-
05.html#name-messages-to-scalars) of
[I-D.irtf-cfrg-bbs-signatures].
* BBS.calculate_random_scalars: Refers to the
calculate_random_scalars operation defined in Section 4.2.1
(https://www.ietf.org/archive/id/draft-irtf-cfrg-bbs-signatures-
05.html#name-random-scalars) of [I-D.irtf-cfrg-bbs-signatures].
* BBS.hash_to_scalar: Refers to the hash_to_scalar operation defined
in Section 4.2.2 (https://www.ietf.org/archive/id/draft-irtf-cfrg-
bbs-signatures-05.html#name-hash-to-scalar) of
[I-D.irtf-cfrg-bbs-signatures].
* BBS.calculate_domain: Refers to the calculate_domain operation
defined in Section 4.2.3 (https://www.ietf.org/archive/id/draft-
irtf-cfrg-bbs-signatures-07.html#domain-calculation) of
[I-D.irtf-cfrg-bbs-signatures].
4. Scheme Definition
4.1. Commitment Operations
4.1.1. Commitment Computation
This operation is used by the Prover to create a commitment to a set
of messages (committed_messages), that they intend to include in the
blind signature. Note that this operation returns both the
serialized combination of the commitment and its proof of correctness
(commitment_with_proof), as well as the random scalar used to blind
the commitment (secret_prover_blind).
(commitment_with_proof, secret_prover_blind) = Commit(
committed_messages,
api_id)
Inputs:
- committed_messages (OPTIONAL), a vector of octet strings. If not
supplied it defaults to the empty
array ("()").
- api_id (OPTIONAL), octet string. If not supplied it defaults to the
empty octet string ("").
Outputs:
- (commitment_with_proof, secret_prover_blind), a tuple comprising from
an octet string and a
random scalar in that
order.
Procedure:
1. committed_message_scalars = BBS.messages_to_scalars(
committed_messages, api_id)
2. blind_generators = BBS.create_generators(
length(committed_message_scalars) + 1,
"BLIND_" || api_id)
3. return CoreCommit(committed_message_scalars,
blind_generators, api_id)
4.1.2. Commitment Validation and Deserialization
The following is a helper operation used by the BlindSign procedure
(Section 4.2.1) to validate an optional commitment. If a commitment
is not supplied, or if it is the Identity_G1, the following operation
will return the Identity_G1 as the "default" commitment point, which
will be ignored by all computations during BlindSign.
commit = deserialize_and_validate_commit(commitment_with_proof,
blind_generators, api_id)
Inputs:
- commitment_with_proof (OPTIONAL), octet string. If it is not supplied
it defaults to the empty octet
string ("").
- blind_generators (OPTIONAL), vector of points of G1. If it is not
supplied it defaults to the empty set
("()").
- api_id (OPTIONAL), octet string. If not supplied it defaults to the
empty octet string ("").
Outputs:
- commit, a point of G1; or INVALID.
Procedure:
1. if commitment_with_proof is the empty string (""), return Identity_G1
2. com_res = octets_to_commitment_with_proof(commitment_with_proof)
3. if com_res is INVALID, return INVALID
4. (commit, commit_proof) = com_res
5. if length(commit_proof[1]) + 1 != length(blind_generators),
return INVALID
6. validation_res = CoreCommitVerify(commit, commit_proof,
blind_generators, api_id)
7. if validation_res is INVALID, return INVALID
8. return commit
4.2. Blind BBS Signatures Interface
The following section defines a BBS Interface for blind BBS
signatures. The identifier of the Interface is defined as
ciphersuite_id || BLIND_H2G_HM2S_, where ciphersuite_id the unique
identifier of the BBS ciphersuite used, as is defined in Section 6
(https://www.ietf.org/archive/id/draft-irtf-cfrg-bbs-signatures-
03.html#name-ciphersuites) of [I-D.irtf-cfrg-bbs-signatures]). Each
BBS Interface MUST define operations to map the input messages to
scalar values and to create the generator set, required by the core
operations. The input messages to the defined Interface will be
mapped to scalars using the messages_to_scalars operation defined in
Section 4.1.2 (https://www.ietf.org/archive/id/draft-irtf-cfrg-bbs-
signatures-05.html#name-messages-to-scalars) of
[I-D.irtf-cfrg-bbs-signatures]. The generators will be created using
the create_generators operation defined in Section 4.1.1
(https://www.ietf.org/archive/id/draft-irtf-cfrg-bbs-signatures-
05.html#name-generators-calculation) of
[I-D.irtf-cfrg-bbs-signatures].
Other than the BlindSign operation defined in Section 4.2.1, which
uses the FinalizeBlindSign procedure, defined in Section 4.3.3, all
other interface operations defined in this section use the core
operations defined in Section 3.6 (https://www.ietf.org/archive/id/
draft-irtf-cfrg-bbs-signatures-05.html#name-core-operations) of
[I-D.irtf-cfrg-bbs-signatures].
4.2.1. Blind Signature Generation
This operation returns a BBS blind signature from a secret key (SK),
over a header, a set of messages and optionally a commitment value
(see Section 1.4). If supplied, the commitment value must be
accompanied by its proof of correctness (commitment_with_proof, as
outputted by the Commit operation defined in Section 4.1.1).
The BlindSign operation makes use of the FinalizeBlindSign procedure
defined in Section 4.3.3 and the B_calculate procedure defined in
Section 5.1. The B_calculate is defined to return an array of
elements, to establish extendability of the scheme by allowing the
B_calculate operation to return more elements than just the point to
be signed.
blind_signature = BlindSign(SK, PK, commitment_with_proof, header,
messages)
Inputs:
- SK (REQUIRED), a secret key in the form outputted by the KeyGen
operation.
- PK (REQUIRED), an octet string of the form outputted by SkToPk
provided the above SK as input.
- commitment_with_proof (OPTIONAL), an octet string, representing a
serialized commitment and
commitment_proof, as the first
element outputted by the Commit
operation. If not supplied, it
defaults to the empty string ("").
- header (OPTIONAL), an octet string containing context and application
specific information. If not supplied, it defaults
to an empty string ("").
- messages (OPTIONAL), a vector of octet strings. If not supplied, it
defaults to the empty array ("()").
Parameters:
- api_id, the octet string ciphersuite_id || "BLIND_H2G_HM2S_", where
ciphersuite_id is defined by the ciphersuite and
"BLIND_H2G_HM2S_"is an ASCII string composed of 15 bytes.
- (octet_point_length, octet_scalar_length), defined by the ciphersuite.
Outputs:
- blind_signature, a blind signature encoded as an octet string; or
INVALID.
Deserialization:
1. L = length(messages)
// calculate the number of blind generators used by the commitment,
// if any.
2. M = length(commitment_with_proof)
3. if M != 0, M = M - octet_point_length - 2 * octet_scalar_length
4. M = M / octet_scalar_length
5. if M < 0, return INVALID
Procedure:
1. generators = BBS.create_generators(L + 1, api_id)
2. blind_generators = BBS.create_generators(M + 1, "BLIND_" || api_id)
3. commit = deserialize_and_validate_commit(commitment_with_proof,
blind_generators, api_id)
4. if commit is INVALID, return INVALID
5. message_scalars = BBS.messages_to_scalars(messages, api_id)
6. res = B_calculate(generators, commit, message_scalars)
7. if res is INVALID, return INVALID
8. (B) = res
9. blind_sig = FinalizeBlindSign(SK,
PK,
B,
generators,
blind_generators,
header,
api_id)
10. if blind_sig is INVALID, return INVALID
11. return blind_sig
4.2.2. Blind Signature Verification
This operation validates a blind BBS signature (signature), given the
Signer's public key (PK), a header (header), a set of messages
(messages), including first the messages chosen by the Issuer and
then the ones chosen (and committed to) by the Prover and if used,
the secret_prover_blind as returned by the Commit operation
(Section 4.1.1).
This operation makes use of the CoreVerify operation as defined in
Section 3.6.2 (https://www.ietf.org/archive/id/draft-irtf-cfrg-bbs-
signatures-05.html#name-coreverify) of
[I-D.irtf-cfrg-bbs-signatures].
result = VerifyBlindSign(PK, signature, header, messages,
issuer_known_messages_no, secret_prover_blind)
Inputs:
- PK (REQUIRED), an octet string of the form outputted by the SkToPk
operation.
- signature (REQUIRED), an octet string of the form outputted by the
Sign operation.
- header (OPTIONAL), an octet string containing context and application
specific information. If not supplied, it defaults
to an empty string.
- messages (OPTIONAL), a vector of octet strings. If not supplied, it
defaults to the empty array "()".
- issuer_known_messages_no (OPTIONAL), a non-negative integer. If not
supplied, it defaults to 0.
- secret_prover_blind (OPTIONAL), a scalar value. If not supplied it
defaults to zero "0".
Parameters:
- api_id, the octet string ciphersuite_id || "BLIND_H2G_HM2S_", where
ciphersuite_id is defined by the ciphersuite and
"BLIND_H2G_HM2S_"is an ASCII string composed of 15 bytes.
Outputs:
- result: either VALID or INVALID
Deserialization:
1. L = length(messages)
Procedure:
1. generators = BBS.create_generators(issuer_known_messages_no, api_id)
2. blind_generators = BBS.create_generators(
L - issuer_known_messages_no, "BLIND_" || api_id)
3. message_scalars = BBS.messages_to_scalars(messages, api_id)
4. res = BBS.CoreVerify(PK,
signature,
generators.append(blind_generators),
header,
message_scalars.append(secret_prover_blind),
api_id)
5. return res
4.2.3. Proof Generation
This operation creates a BBS proof, which is a zero-knowledge, proof-
of-knowledge, of a BBS signature, while optionally disclosing any
subset of the signed messages (either chosen by the Issuer or
committed by the Prover). In addition, this operation can generate
commitments to un-revealed messages and include with the BBS proof
that these commitments correspond to specific un-revealed messages.
These commitments can be used in subsequent ZKPs outside the scope of
this specification .
When this operation furnishes disclosed commitment values it will
also return an additional bundle of information for use in external
ZKPs [Vision2025]. This _add_zkp_info_ includes the disclosed
commitments and the random scalars used to produce those commitments.
The _add_zkp_info_ should never be exposed, i.e., it is NOT to be
sent sent to the verifier.
The operation will accept a set of messages (messages), including
first the messages chosen by the Issuer and then the ones chosen (and
committed to) by the Prover.
Furthermore, the operation also expects the secret_prover_blind (as
returned from the Commit operation defined in Section 4.1.1) value.
If the BBS signature is generated using a commitment value, then the
secret_prover_blind returned by the Commit operation used to generate
the commitment should be provided to the ProofGen operation
(otherwise the resulting proof will be invalid).
This operation makes use of the CoreProofGen operation as defined in
Section 4.3.4.
The operation will also accept a map message_disclosures between each
message (including both the ones known by the issuer and the ones
known only by the prover) and one of the three values DISCLOSE, HIDE
and COMMIT. A {msg: DISCLOSE} (key, value) pair indicates that the
msg will be revealed to the Verifier. Correspondingly, a {msg: HIDE}
(key, value) pair indicates that the msg will not be disclosed to the
Verifier. Finally, a {msg: COMMIT} (key, value) pair indicates that
only a commitment to the msg will be disclosed to the Verifier.
An example of the message_disclosures input map is the following,
message_disclosures = {
issuer_known_msg_1: DISCLOSE,
issuer_known_msg_2: HIDE,
issuer_known_msg_3: HIDE,
issuer_known_msg_4: COMMIT,
issuer_known_msg_5: COMMIT,
issuer_known_msg_6: DISCLOSE,
prover_known_msg_1: DISCLOSE,
prover_known_msg_2: COMMIT,
prover_known_msg_3: DISCLOSE
}
[proof, add_zkp_info] = BlindProofGen(PK,
signature,
header,
ph,
messages,
issuer_known_messages_no,
message_disclosures,
secret_prover_blind)
Inputs:
- PK (REQUIRED), an octet string of the form outputted by the SkToPk
operation.
- signature (REQUIRED), an octet string of the form outputted by the
Sign operation.
- header (OPTIONAL), an octet string containing context and application
specific information. If not supplied, it defaults
to an empty string.
- ph (OPTIONAL), an octet string containing the presentation header. If
not supplied, it defaults to an empty string.
- messages (OPTIONAL), a vector of octet strings. If not supplied, it
defaults to the empty array "()".
- issuer_known_messages_no (OPTIONAL), a non-negative integer. If not
supplied, it defaults to 0.
- message_disclosures (OPTIONAL), a map between octet strings and one
of the DISCLOSE, HIDE or COMMIT
values. If not supplied, it defaults
to the empty map "{}".
- secret_prover_blind (OPTIONAL), a scalar value. If not supplied it
defaults to zero "0".
Parameters:
- api_id, the octet string ciphersuite_id || "BLIND_H2G_HM2S_", where
ciphersuite_id is defined by the ciphersuite and
"BLIND_H2G_HM2S_"is an ASCII string composed of 15 bytes.
Outputs:
- proof, an octet string; or INVALID.
- add_zkp_info, a structure containing an array of committed disclosure
commitments, and the array of random scalars used to
create those commitments.
Deserialization:
1. L = length(messages)
2. if length(message_disclosures) != L, return INVALID
3. if issuer_known_messages_no > L, return INVALID
4. let disclosed_indexes be the integers i in 0..length(messages) so
that if msg = messages[i], messagesDisclosures[msg] = disclose, in
accenting order.
5. let commit_indexes be the integers i in 0..length(messages) so
that if msg = messages[i], messagesDisclosures[msg] = commit, in
accenting order.
Procedure:
1. generators = BBS.create_generators(issuer_known_messages_no, api_id)
2. blind_generators = BBS.create_generators(
L - issuer_known_messages_no, "BLIND_" || api_id)
3. message_scalars = BBS.messages_to_scalars(messages, api_id)
4. proof = CoreProofGen(PK,
signature,
generators.append(blind_generators),
header,
ph,
message_scalars.append(secret_prover_blind),
disclosed_indexes,
commit_indexes,
api_id)
5. return proof
4.2.4. Proof Verification
The ProofVerify operation validates a BBS proof, given the Signer's
public key (PK), a header and presentation header values, two arrays
of disclosed messages (the ones provided by the Signer and the ones
committed by the prover) and two corresponding arrays of indexes that
those messages had in the original vectors of signed messages. In
addition, the BlindProofVerify operation defined in this section
accepts the integer issuer_known_messages_no, representing the total
number of signed messages known by the Signer.
This operation makes use of the CoreProofVerify operation as defined
in Section 4.3.5.
result = BlindProofVerify(PK,
proof,
header,
ph,
issuer_known_messages_no,
disclosed_messages)
Inputs:
- PK (REQUIRED), an octet string of the form outputted by the SkToPk
operation.
- proof (REQUIRED), an octet string of the form outputted by the
ProofGen operation.
- header (OPTIONAL), an optional octet string containing context and
application specific information. If not supplied,
it defaults to the empty octet string ("").
- ph (OPTIONAL), an octet string containing the presentation header. If
not supplied, it defaults to the empty octet
string ("").
- issuer_known_messages_no (OPTIONAL), a non-negative integer. If not
supplied, it defaults to 0.
- disclosed_messages (OPTIONAL), a vector of octet strings. If not
supplied, it defaults to the empty
array ("()").
Parameters:
- api_id, the octet string ciphersuite_id || "H2G_HM2S_", where
ciphersuite_id is defined by the ciphersuite and "H2G_HM2S_"is
an ASCII string comprised of 9 bytes.
- (octet_point_length, octet_scalar_length), defined by the ciphersuite.
Outputs:
- result, either VALID or INVALID.
Deserialization:
1. bbs_proof_len = OS2IP(proof[0..7])
2. undisclosed_msgs_no = bbs_proof_len
- 3 * octet_point_length
- 4 * octet_scalar_length
3. total_msgs_no = undisclosed_msgs_no + length(disclosed_messages)
Procedure:
1. generators = BBS.create_generators(issuer_known_messages_no, api_id)
2. blind_generators = BBS.create_generators(
total_msgs_no - issuer_known_messages_no,
"BLIND_" || api_id)
3. message_scalars = BBS.messages_to_scalars(disclosed_messages, api_id)
4. result = CoreProofVerify(
PK,
proof,
generators.append(blind_generators).append(Q_2),
header,
ph,
message_scalars,
api_id)
5. return result
4.3. Core Operations
4.3.1. Core Commitment Computation
(commit_with_proof, secret_prover_blind) = CoreCommit(blind_generators,
committed_message_scalars, api_id)
Inputs:
- blind_generators (REQUIRED), vector of pseudo-random points in G1.
- committed_message_scalars (OPTIONAL), a vector of scalars. If not
supplied, it defaults to the empty array ("()").
- api_id (OPTIONAL), an octet string. If not supplied it defaults to the
empty octet string ("").
Deserialization:
1. M = length(committed_messages)
2. if length(blind_generators) != M + 1, return INVALID
3. (Q_2, J_1, ..., J_M) = blind_generators
4. (msg_1, ..., msg_M) = committed_message_scalars
Procedure:
1. (secret_prover_blind, s~, m~_1, ..., m~_M)
= BBS.calculate_random_scalars(M + 2)
2. C = J_1 * msg_1 + ... + J_M * msg_M + Q_2 * secret_prover_blind
3. Cbar = J_1 * m~_1 + ... + J_M * m~_M + Q_2 * s~
4. challenge = calculate_blind_challenge(C, Cbar, blind_generators,
api_id)
5. s^ = s~ + secret_prover_blind * challenge
6. for i in (1, 2, ..., M): m^_i = m~_i + msg_i * challenge
7. proof = (s^, (m^_1, ..., m^_M), challenge)
8. commit_with_proof = commitment_with_proof_to_octets(C, proof)
9. return (commit_with_proof, secret_prover_blind)
4.3.2. Core Commitment Verification
This operation is used by the Signer to verify the correctness of a
commitment_proof for a supplied commitment, over a list of points of
G1 called the blind_generators, used to compute that commitment.
result = CoreCommitVerify(commitment, commitment_proof,
blind_generators, api_id)
Inputs:
- commitment (REQUIRED), a commitment (see (#terminology)).
- commitment_proof (REQUIRED), a commitment_proof (see (#terminology)).
- blind_generators (REQUIRED), vector of pseudo-random points in G1.
- api_id (OPTIONAL), octet string. If not supplied it defaults to the
empty octet string ("").
Outputs:
- result: either VALID or INVALID
Deserialization:
1. (s^, commitments, cp) = commitment_proof
2. M = length(commitments)
3. (m^_1, ..., m^_M) = commitments
4. if length(blind_generators) != M, return INVALID
5. (Q_2, J_1, ..., J_M) = blind_generators
Procedure:
1. Cbar = J_1 * m^_1 + ... + J_M * m^_M + Q_2 * s^ + commitment * (-cp)
2. cv = calculate_blind_challenge(commitment, Cbar, blind_generators,
api_id)
3. if cv != cp, return INVALID
4. return VALID
4.3.3. Finalize Blind Sign
This operation computes a blind BBS signature, from a secret key
(SK), a set of generators (points of G1), a supplied commitment with
its proof of correctness (commitment_with_proof), a header (header)
and a set of messages (messages). The operation also accepts the
identifier of the BBS Interface, calling this core operation.
blind_signature = FinalizeBlindSign(SK,
PK,
B,
generators,
blind_generators,
header,
api_id)
Inputs:
- SK (REQUIRED), a secret key in the form outputted by the KeyGen
operation.
- PK (REQUIRED), an octet string of the form outputted by SkToPk
provided the above SK as input.
- B (REQUIRED), a point of G1, different than Identity_G1.
- generators (REQUIRED), vector of pseudo-random points in G1.
- blind_generators (OPTIONAL), vector of pseudo-random points in G1. If
not supplied it defaults to the empty
array.
- header (OPTIONAL), an octet string containing context and application
specific information. If not supplied, it defaults
to an empty string.
- api_id (OPTIONAL), an octet string. If not supplied it defaults to the
empty octet string ("").
Outputs:
- blind_signature, a blind signature encoded as an octet string; or
INVALID.
Definitions:
1. signature_dst, an octet string representing the domain separation
tag: api_id || "H2S_" where "H2S_" is an ASCII string
composed of 4 bytes.
Deserialization:
1. L = length(generators) - 1
2. M = length(blind_generators) - 1
3. if L <= 0 or M <=0, return INVALID
4. (Q_1, H_1, ..., H_L) = generators
5. (Q_2, J_1, ..., J_M) = blind_generators
Procedure:
1. domain = BBS.calculate_domain(PK, Q_1,
(H_1, ..., H_L, Q_2, J_1, ..., J_M), header, api_id)
2. e_octs = BBS.serialize((SK, B, domain))
3. e = BBS.hash_to_scalar(e_octs, signature_dst)
4. A = B * (1 / (SK + e))
5. return BBS.signature_to_octets((A, e))
4.3.4. Core Proof Generation
The Proof Generation with extension, combines the BBS Proof
Generation operations (i.e., BBS.ProofInit and BBS.ProofFinalize)
with a proof of correctness of commitments over some of the signed
messages. The commitments proof of correctness will similarly
constitute of a initialization and finalization phase. The two proof
protocols will use a common challenge, returned by the
ProofChallengeCalculate operation described in Section 5.3. The
result of the commitments proof of correctness initialization process
will be an object of the following form
CommitInitRes = {
commits: (REQUIRED) Array of points in G1,
commits_proofs: (REQUIRED) Array of Scalars,
indexes: (REQUIRED) Array of numbers
}
Following, we describe the Proof Generation Procedure.
proof = CoreProofGen(PK, signature, generators, header, ph, messages,
disclosed_indexes, commits_indexes, api_id)
Inputs:
- PK (REQUIRED), an octet string of the form outputted by the SkToPk
operation.
- signature (REQUIRED), an octet string of the form outputted by the
Sign operation.
- generators (REQUIRED), vector of pseudo-random points in G1.
- header (OPTIONAL), an octet string containing context and application
specific information. If not supplied, it defaults
to the empty octet string ("").
- ph (OPTIONAL), an octet string containing the presentation_header. If
not supplied, it defaults to the empty octet
string ("").
- messages (OPTIONAL), a vector of scalars representing the messages.
If not supplied, it defaults to the empty
array ("()").
- disclosed_indexes (OPTIONAL), vector of non-negative integers in
ascending order. Indexes of disclosed
messages. If not supplied, it defaults
to the empty array ("()").
- commits_indexes (OPTIONAL), vector of non-negative integers in
ascending order. Indexes of disclosed
messages. If not supplied, it defaults
to the empty array ("()").
- api_id (OPTIONAL), an octet string. If not supplied it defaults to the
empty octet string ("").
Parameters:
- Y_0 and Y_1, fixed points of G1 computed as
(Y_0, Y_1) = BBS.create_generators(2, "COM_DIS_" || api_id)
Outputs:
- proof, an octet string; or INVALID.
Deserialization:
1. signature_result = octets_to_signature(signature)
2. if signature_result is INVALID, return INVALID
3*. if commits_indexes is not a list of integers from 0 to L in
accenting order, return INVALID
4*. if disclosed_indexes is not a list of integers from 0 to L in
accenting order, return INVALID
Procedure:
1. init_res = BBS.ProofInit(PK,
signature_result,
generators,
header,
messages,
disclosed_indexes,
api_id)
2. if init_res is INVALID, return INVALID
// Calculate the commitments and initiate the correctness proof
3. N = length(commits_indexes)
4. (s_1, ..., s_N, s~_1, ..., s~_N) = calculate_random_scalars(2*N)
5. init_random_scalars = init_res.random_scalars
6. for i in 1...N,
7. idx = commits_indexes[i]
8. C_i = Y_0 * s_i + Y_1 * messages[idx]
9. C~_i = Y_0 * s~_i + Y_1 * init_random_scalars[idx + 5]
10. commit_init_res = {commits: (C_1, ..., C_N),
commits_proofs: (C~_1, ...,C~_N)
indexes: commits_indexes}
11. challenge = ProofChallengeCalculate(init_res, commit_init_res,
ph, api_id)
12. if challenge is INVALID, return INVALID
13. bbs_proof = BBS.ProofFinalize(init_res, challenge)
// Finalize the commitment correctness proof
14. for i in 1...N, s^_i =
s~_i + challenge * s_i
15. commits_proof = ((C_1, ..., C_N), (s^_1, ..., s^N))
16. proof = proof_to_octets(length(bbs_proof), bbs_proof,
length(disclosed_indexes), disclosed_indexes,
length(commits_proof), commits_proof
length(commits_indexes), commits_indexes)
17. add_zkp_info = {commits: (C_1, ..., C_N),
commit_rands: (s_1, ..., s_N)}
18. return [proof, add_zkp_info]
4.3.5. Core Proof Verification
result = CoreProofVerify(PK, proof, generators, header, ph,
disclosed_messages, api_id)
Inputs:
- PK (REQUIRED), an octet string of the form outputted by the SkToPk
operation.
- bbs_proof (REQUIRED), an array with four octet strings of the form
outputted by the ProofGen operation.
- commits_proof (REQUIRED), an tuple consisting from an array of points
in G1 and an array of scalars of the same
length. Both arrays can be empty.
- generators (REQUIRED), vector of pseudo-random points in G1.
- header (OPTIONAL), an optional octet string containing context and
application specific information. If not supplied,
it defaults to the empty octet string ("").
- ph (OPTIONAL), an octet string containing the presentation_header. If
not supplied, it defaults to the empty octet
string ("").
- disclosed_messages (OPTIONAL), a vector of scalars representing the
messages. If not supplied, it defaults
to the empty array ("()").
- api_id (OPTIONAL), an octet string. If not supplied it defaults to the
empty octet string ("").
Parameters:
- P1, fixed point of G1, defined by the ciphersuite.
Outputs:
- result, either VALID or INVALID.
Deserialization:
1. W = octets_to_pubkey(PK)
2. if W is INVALID, return INVALID
3. proof_res = octets_to_proof(proof)
4. if proof_res is INVALID, return INVALID
5. (bbs_proof_res, disclosed_indexes,
commits_proof_res, commits_indexes) = proof_res
6. (Abar, Bbar, D, e^, r1^, r3^, hats, cp) = bbs_proof_res
7. (commits, commits_proof) = commits_proof_res
8. if length(commits) != length(commits_proof) or
if length(commits) != length(commits_indexes) return INVALID
9. L = length(generators)
10. if commits_indexes is not a list of integers from 0 to L in
accenting order, return INVALID
11. if disclosed_indexes is not a list of integers from 0 to L in
accenting order, return INVALID
12. (C_1, ... C_N) = commits
13. (s^_1, ..., s^_N) = commits_proof
Procedure:
1. init_res = ProofVerifyInit(PK, proof_result, generators, header,
disclosed_messages,
disclosed_indexes,
api_id)
2. if init_res is INVALID, return INVALID
3. for i in 1...length(commits),
4. idx = commit_indexes[i]
5. C^_i = Y_0 * s^_i + Y_1 * hats[idx] - C_i * cp
6. commit_init_res = {commits: (C_1, ..., C_N),
commits_proofs: (C^_1, ...,C^_N)
indexes: commit_indexes}
7. challenge = ProofChallengeCalculate(init_res, commit_init_res,
ph, api_id)
8. if challenge is INVALID, return INVALID
9. if cp != challenge, return INVALID
10. if h(Abar, W) * h(Bbar, -BP2) != Identity_GT, return INVALID
11. return VALID
5. Utilities
5.1. Calculate B value
res = B_calculate(generators, commitment, message_scalars)
Inputs:
- generators (REQUIRED), an array of at least one point from the
G1 group.
- commitment (OPTIONAL), a point from the G1 group. If not supplied it
defaults to the Identity_G1 point.
- message_scalars (OPTIONAL), an array of scalar values. If not
supplied, it defaults to the empty
array ("()").
Outputs:
- res, an array of a single element from the G1 subgroup, or INVALID.
Deserialization:
1. L = length(message_scalars)
2. if length(generators) != L + 1, return INVALID
3. (Q_1, H_1, ..., H_L) = generators
4. (msg_1, ..., msg_L) = message_scalars
Procedure:
1. B = P1 + Q_1 * domain + H_1 * msg_1 + ... + H_L * msg_L + commitment
2. if B is Identity_G1, return INVALID
3. return (B)
5.2. Blind Challenge Calculation
challenge = calculate_blind_challenge(C, Cbar, generators, api_id)
Inputs:
- C (REQUIRED), a point of G1.
- Cbar (REQUIRED), a point of G1.
- generators (REQUIRED), an array of points from G1, of length at
least 1.
- api_id (OPTIONAL), octet string. If not supplied it defaults to the
empty octet string ("").
Definition:
- blind_challenge_dst, an octet string representing the domain
separation tag: api_id || "H2S_" where
ciphersuite_id is defined by the ciphersuite and
"H2S_" is an ASCII string composed of 4 bytes.
Deserialization:
1. if length(generators) == 0, return INVALID
2. M = length(generators) - 1
Procedure:
1. c_arr = (M)
2. c_arr.append(generators)
3. c_octs = BBS.serialize(c_arr.append(C, Cbar))
4. return BBS.hash_to_scalar(c_octs, blind_challenge_dst)
5.3. Proof Challenge Calculation
challenge = ProofChallengeCalculate(bbs_init_res, commit_init_res,
ph, api_id)
Inputs:
- init_res (REQUIRED), a ProofInitRes object representing the value
returned after initializing the proof generation
or verification operations.
- commit_init_res (REQUIRED), a CommitInitRes representing the value
returned after initializing the commits
proof of correctness generation or
verification.
- ph (OPTIONAL), an octet string. If not supplied, it must default to
the empty octet string ("").
- api_id (OPTIONAL), an octet string. If not supplied it defaults to the
empty octet string ("").
Outputs:
- challenge, a scalar.
Definitions:
1. hash_to_scalar_dst, an octet string representing the domain
separation tag: api_id || "H2S_" where "H2S_" is
an ASCII string comprised of 4 bytes.
Deserialization:
1. if validate_init_res(init_res) returns INVALID, return INVALID
2. (Abar, Bbar, D, T1, T2, domain) = (init_res.Abar,
init_res.Bbar,
init_res.D,
init_res.T1,
init_res.T2,
init_res.domain)
3. R = length(init_res.disclosed_indexes)
4. (i1, ..., iR) = init_res.disclosed_indexes
5. (msg_i1, ..., msg_iR) = init_res.disclosed_messages
6. N = length(commit_init_res.commits)
7. if length(commit_init_res.commits_proofs) != N, return INVALID
8. if length(commit_init_res.commits_indexes) != N, return INVALID
9. (C_1, ..., C_N) = commit_init_res.commits
10. (C~_1, ...,C~_N) = commit_init_res.commits_proofs
11. (i_1, ..., i_N) = commit_init_res.commits_indexes
ABORT if:
1. R > 2^64 - 1
2. length(ph) > 2^64 - 1
Procedure:
1. c_arr = (R, i1, msg_i1, i2, msg_i2, ..., iR, msg_iR, Abar, Bbar,
D, T1, T2, domain)
2. c_octs = serialize(c_arr)
3. c_octs = c_octs || serialize(N, i_1, C_1, C~_1, ..., i_N, C_N, C~_N)
5. c_octs = c_octs || I2OSP(length(ph), 8) || ph
6. return hash_to_scalar(c_octs, hash_to_scalar_dst)
5.4. Serialize
5.4.1. Commitment with Proof to Octets
commitment_octets = commitment_with_proof_to_octets(commitment, proof)
Inputs:
- commitment (REQUIRED), a point of G1.
- proof (REQUIRED), a vector comprising of a scalar, a possibly empty
vector of scalars and another scalar in that order.
Outputs:
- commitment_octets, an octet string or INVALID.
Procedure:
1. commitment_octs = BBS.serialize((commitment))
2. if commitment_octs is INVALID, return INVALID
3. (s^, (m^_1, ..., m^_M), challenge) = proof
4. proof_octs = BBS.serialize((s^, m^_1, ..., m^_M, challenge))
5. if proof_octs is INVALID, return INVALID
6. return commitment_octs || proof_octs
5.4.2. Octets to Commitment with Proof
commitment = octets_to_commitment_with_proof(commitment_octs)
Inputs:
- commitment_octs (REQUIRED), an octet string in the form outputted from
the commitment_to_octets operation.
Parameters:
- (octet_point_length, octet_scalar_length), defined by the ciphersuite.
Outputs:
- commitment, a commitment in the form (C, proof), where C a point of G1
and a proof vector comprising of a scalar, a possibly
empty vector of scalars and another scalar in that order.
Procedure:
1. commit_len_floor = octet_point_length + 2 * octet_scalar_length
2. if length(commitment_octs) < commit_len_floor, return INVALID
3. C_octets = commitment_octs[0..(octet_point_length - 1)]
4. C = octets_to_point_E1(C_octets)
5. if C is INVALID, return INVALID
6. if C == Identity_G1, return INVALID
7. j = 0
8. index = octet_point_length
9. while index < length(commitment_octs):
10. end_index = index + octet_scalar_length - 1
11. s_j = OS2IP(commitment_octs[index..end_index])
12. if s_j = 0 or if s_j >= r, return INVALID
13. index += octet_scalar_length
14. j += 1
15. if index != length(commitment_octs), return INVALID
16. if j < 2, return INVALID
17. msg_commitments = ()
18. if j >= 3, set msg_commitments = (s_1, ..., s_(j-1))
19. return (C, (s_0, msg_commitments, s_j))
5.4.3. Proof to Octets
proof_octets = proof_to_octets(bbs_proof_len, bbs_proof,
disclosed_indexes_len, disclosed_indexes
commits_proof_len, commits_proof,
commits_indexes_len, commits_indexes)
Inputs:
- bbs_proof_len (REQUIRED), a non negative integer.
- bbs_proof (REQUIRED), an array comprising from 3 points in G1,
3 Scalars, an array of scalars and one
additional Scalar at the end.
- disclosed_indexes_len (REQUIRED), a non negative integer.
- disclosed_indexes (REQUIRED), an array of non negative integers.
- commits_proof_len (REQUIRED), a non negative integer.
- commits_proof (REQUIRED), a tuple with two arrays, the first with
points in G1 and the second with Scalars
- commits_indexes_len (REQUIRED), a non negative integer.
- commits_indexes (REQUIRED), an array of non negative integers.
Outputs:
- proof_octets, an octet string.
Procedure:
1. oct = I2OSP(bbs_proof_len) || serialize(bbs_proof) ||
I2OSP(disclosed_indexes_len) || serialize(disclosed_indexes) ||
I2OSP(commits_proof_len) || serialize(commits_proof) ||
I2OSP(commits_indexes_len) || serialize(commits_indexes)
2. return oct
5.4.4. Octets to Proof
The octets_to_proof procedure, on input an octet string will return a
BBS with commits proof comprised from the following elements
1. A BBS Proof
2. The indexes that the disclosed messages have in the list of
signed messages (both known to the issuer and known only to the
prover)
3. A tuple with two arrays. One array of points in G1,
corresponding to the message commits and one array with scalars,
corresponding to the proof of correctness of the previous
commitments.
4. The indexes that the committed messages have in the list of
signed messages (both known to the issuer and known only to the
prover)
proof = octets_to_proof(proof_octets)
- proof_octets (REQUIRED), an octet string of the form outputted from
the proof_to_octets operation.
Parameters:
- int_octet_length = 8. The number of octets of encoded integers.
- r, non-negative integer. The prime order of the G1 and G2 groups,
defined by the ciphersuite.
- octet_scalar_length, non-negative integer. The length of a scalar
octet representation, defined by the ciphersuite.
- octet_point_length, non-negative integer. The length of a point in G1
octet representation, defined by the ciphersuite.
- subgroup_check_G1, operation that on input a point P returns VALID if
P is a valid point of the G1 subgroup, otherwise it
returns INVALID (see (#notation)).
Outputs:
- proof, a proof value in the form described above or INVALID
Procedure:
1. sidx = 0
2. eidx = int_octet_length - 1
3. if length(proof_octets) < eidx, return INVALID
4. bbs_proof_len = OS2IP(proof_octets[sidx..eidx])
5. sidx = eidx + 1
6. eidx = sidx + bbs_proof_len
7. if length(proof_octets) < eidx, return INVALID
8. bbs_proof_octs = proof_octets[sidx..eidx]
9. bbs_proof = BBS.octets_to_proof(bbs_proof_octs)
10. if bbs_proof is INVALID, return INVALID
// Deserialize disclosed_indexes
11. sidx = eidx + 1
12. eidx = sidx + int_octet_length
13. if length(proof_octets) < eidx, return INVALID
14. U = OS2IP(proof_octets[sidx..eidx]) // disclosed_indexes len
15. if length(proof_octets) < eidx + U * int_octet_length,
return INVALID
16. for i in (1...U)
17. sidx = eidx + 1
18. eidx = sidx + int_octet_length
19. idx_i = OS2IP(proof_octets[sidx..eidx])
20. disclosed_indexes = (idx_1, ..., idx_U)
// Deserialize commits_proof
21. sidx = eidx + 1
22. eidx = sidx + int_octet_length
23. if length(proof_octets) < eidx, return INVALID
24. N = OS2IP(proof_octets[sidx..eidx]) // commits_proof len
25. len_floor = eidx + N * (octet_point_length + octet_scalar_length)
26. if length(proof_octets) < len_floor, return INVALID
27. for i in (1..N)
28. sidx = eidx + 1
29. eidx = sidx + octet_point_length
30. C_i = BBS.octets_to_point_E1(proof_octets[sidx..eidx])
31. if C_i is INVALID or Identity_G1, return INVALID
32. if subgroup_check_G1(C_i) returns INVALID, return INVALID
33. for i in (1..N)
34. sidx = eidx + 1
35. eidx + octet_scalar_length
36. s_i = OS2IP(proof_octetss[sidx..eidx])
37. if s_i = 0 or if s_i >= r, return INVALID
38. commits_proof = ((C_1, ..., C_N), (s_1, ..., s_N))
// Desirialize commits_indexes
39. sidx = eidx + 1
40. eidx = sidx + int_octet_length
41. if length(proof_octets) < eidx, return INVALID
42. N' = OS2IP(proof_octets[sidx..eidx]) // commits_indexes len
43. if length(proof_octets) < eidx + N' * int_octet_length,
return INVALID
44. for i in (1...N')
45. sidx = eidx + 1
46. eidx = sidx + int_octet_length
47. cidx_i = OS2IP(proof_octets[sidx..eidx])
48. commits_indexes = (cidx_1, ..., cidx_N')
49. if N' not equal to N, return INVALID
50. if length(proof) not equal to eidx, return INVALID
51. return (bbs_proof, disclosed_indexes,
commits_proof, commits_indexes)
6. Privacy Considerations
The privacy considerations discussed in Section 5
(https://www.ietf.org/archive/id/draft-irtf-cfrg-bbs-signatures-
09.html#name-privacy-considerations) of
[I-D.irtf-cfrg-bbs-signatures] apply to this draft as well.
6.1. Total Number and Index of Committed Messages
When a Prover submits a commitment to the Signer, the Prover's
committed messages are "perfectly" (statistically) hidden from the
Signer. However, the proof of the committed messages, which is also
sent from the Prover to the Signer, contains the number of committed
messages.
In the proof sent from the Prover to the Verifier the number of
committed messages can be inferred. In addition, indexes of
disclosed committed messages are revealed to the Verifier. In
Section 5.2 (https://www.ietf.org/archive/id/draft-irtf-cfrg-bbs-
signatures-09.html#name-total-number-and-index-of-s) of
[I-D.irtf-cfrg-bbs-signatures] the threats to unlinkability and
mitigations for this information with respect to Signer messages is
discussed. These threats and mitigations apply to the Prover total
number of committed messages and the disclosed committed indexes as
well.
7. Application Considerations
7.1. Input Validity Checks
Applications using CoreProofGen (as defined in Section 4.3.4) only as
a subroutine of BlindProofGen (as defined in Section 4.2.3), can skip
the checks of the commits_indexes and disclosed_indexes inputs,
performed at step 3* and 4* of the Deserialization section of that
operation, since the inputs provided by the calling operation (i.e.,
BlindProofGen) will always have the correct form. However, if
applications intend to use CoreProofGen in different contexts (and
not necesearily only call it from BlindProofGen), those checks must
be applied.
8. Security Considerations
Security considerations detailed in Section 6
(https://www.ietf.org/archive/id/draft-irtf-cfrg-bbs-signatures-
09.html#name-security-considerations) of
[I-D.irtf-cfrg-bbs-signatures] apply to this draft as well.
8.1. Prover Blind Factor
The random scalar value secret_prover_blind calculated and returned
by the Commit operation is responsible for "hiding" the committed
messages (otherwise, in many practical applications, the Signer may
be able to retrieve them). Furthermore, it guarantees that the
entity generating the BBS proof (see BlindProofGen defined in
Section 4.2.3) has knowledge of that factor. As a result, the
secret_prover_blind MUST remain private by the Prover and it MUST be
generated using a cryptographically secure pseudo-random number
generator. See Section 6.7 (https://www.ietf.org/archive/id/draft-
irtf-cfrg-bbs-signatures-09.html#name-randomness-requirements) of
[I-D.irtf-cfrg-bbs-signatures] on recommendations and requirements
for implementing the BBS.calculate_random_scalars operation (which is
used to calculate the secret_prover_blind value).
8.2. Key Binding
One natural use case for the blind signatures extension of the BBS
scheme is key binding. In the context of BBS Signatures, key binding
guarantees that only entities in control of a specific private key
can compute BBS proofs. This can be achieved by committing to the
private key prior to issuance, resulting in a BBS signature that
includes that key as one of the signed messages. Creating a BBS
proof from that signature will then require knowledge of that key
(similar to any signed message). The Prover MUST NOT disclose that
key as part of a proof generation procedure. Note also that the
secret_prover_blind value returned by the Commit operation defined in
Section 4.1.1 (see Section 8.1), has a similar property, i.e., it's
knowledge is required to generate a proof from a blind signature.
Many applications however, requiring key binding, mandate that the
same private key is used among multiple signatures, whereas the
secret_prover_blind is uniquely generated for each blind signature
issuance request. In those cases, a commitment to a private key must
be used, as described above.
9. Ciphersuites
This document uses the BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_ and
BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_ defined in Section 7.2.1
(https://identity.foundation/bbs-signature/draft-irtf-cfrg-bbs-
signatures.html#name-bls12-381-shake-256) and Section 7.2.2
(https://identity.foundation/bbs-signature/draft-irtf-cfrg-bbs-
signatures.html#name-bls12-381-sha-256) correspondingly, of
[I-D.irtf-cfrg-bbs-signatures].
10. Test Vectors
Test vectors are being revised to include new committed disclosure
functionality.
11. IANA Considerations
This document does not make any requests of IANA.
12. Normative References
[I-D.irtf-cfrg-bbs-signatures]
Looker, T., Kalos, V., Whitehead, A., and M. Lodder, "The
BBS Signature Scheme", Work in Progress, Internet-Draft,
draft-irtf-cfrg-bbs-signatures-10, 8 January 2026,
<https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-
bbs-signatures-10>.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
<https://www.rfc-editor.org/info/rfc2119>.
[RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
May 2017, <https://www.rfc-editor.org/info/rfc8174>.
[RFC9474] Denis, F., Jacobs, F., and C. A. Wood, "RSA Blind
Signatures", RFC 9474, DOI 10.17487/RFC9474, October 2023,
<https://www.rfc-editor.org/info/rfc9474>.
13. Informative References
[BG18] Bootle, J. and J. Groth, "Efficient Batch Zero-Knowledge
Arguments for Low Degree Polynomials", In CRYPTO, 2018,
<https://link.springer.com/
chapter/10.1007/978-3-319-76581-5_19>.
[Chaum85] Chaum, D., "Security without identification: transaction
systems to make big brother obsolete", In Commun. ACM,
vol 10, pages 1030-1044, 1985,
<https://dl.acm.org/doi/pdf/10.1145/4372.4373>.
[I-D.ietf-privacypass-protocol]
Celi, S., Davidson, A., Valdez, S., and C. A. Wood,
"Privacy Pass Issuance Protocol", Work in Progress,
Internet-Draft, draft-ietf-privacypass-protocol-16, 3
October 2023, <https://datatracker.ietf.org/doc/html/
draft-ietf-privacypass-protocol-16>.
[LegacyBinding2026]
Celi, S., Lehmann, A., Levin, S., and A. Zacharakis,
"Device Binding for Anonymous Credentials on Legacy
Phones", 2026, <https://eprint.iacr.org/2026/965>.
[P91] Pedersen, T., "Non-Interactive and Information-Theoretic
Secure Verifiable Secret Sharing", In CRYPTO, 1991,
<https://ia.cr/2023/275>.
[Vision2025]
Lehmann, A., Sidorenko, A., and A. Zacharakis, "Vision: A
Modular Framework for Anonymous Credential Systems", 2025,
<https://eprint.iacr.org/2025/1981>.
Appendix A. Document History
-00
* Initial Version
-01
* Change committed_messages to committed_scalars in CoreCommit
* Added explanatory text
* Added test vectors
-02
* Expanded privacy and security considerations
* Updated the introduction
-03
* Add committed disclosure functionality and explanatory text
* Editorial fixes
Authors' Addresses
Vasilis Kalos
MATTR
Email: vasilis.kalos@mattr.global
Greg M. Bernstein
Grotto Networking
Email: gregb@grotto-networking.com
Datatracker
draft-irtf-cfrg-bbs-blind-signatures-03
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| Intended RFC status | Informational | ||
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