What are BBS+ signatures and how do they differ from standard ECDSA/Ed25519?

Standard digital signatures like ECDSA, Ed25519, and RSA sign a single monolithic message digest. To present a signed credential, the holder must reveal the entire signed payload and the signature itself, allowing verifiers to correlate users and inspect private fields. BBS+ (Boneh-Boyen-Shacham with Camenisch-Lysyanskaya extensions) operates on pairing-friendly elliptic curves (such as BLS12-381) to sign a vector of distinct messages (m_1, m_2, ..., m_L) under a single short signature (A, e, s).

How does Selective Disclosure work without breaking signature validity?

When presenting a BBS+ signed credential, the holder can reveal only a subset of attributes D (e.g., age >= 21) while completely blinding the remaining hidden attributes U (e.g., social security number, full home address, credit score). The holder randomizes the signature point A into A' using fresh random blinding scalars (r_1, r_2, r_3) and generates a Zero-Knowledge Proof of Knowledge (ZKP-PoK) demonstrating that they hold a valid signature over both revealed and hidden messages, without leaking the hidden values or the original signature.

Why are BBS+ presentations cryptographically unlinkable across verifiers?

Because every time a holder creates a presentation proof, fresh random blinding factors (r_1, r_2, r_3) are sampled from the scalar field Fr, the resulting proof components (A', Abar, d) are completely re-randomized. Even if a user presents the exact same credential to ten different verifiers (or the same verifier ten times), each proof is indistinguishable from random curve points. Cross-verifier tracking and collusion are mathematically prevented.

What role do bilinear pairings play in BBS+ signature verification?

BBS+ relies on a bilinear pairing e: G1 x G2 -> GT where e(aP, bQ) = e(P, Q)^(ab). The signature satisfies the algebraic relation e(A, W * g2^e) = e(g1 * h0^s * prod(h_i^m_i), g2), where W = g2^x is the issuer public key. This non-degenerate bilinear map allows the verifier to check mathematical consistency in target group GT across group G1 and G2 elements without requiring knowledge of the secret key x or the blinded scalar factors.

BBS+ Signatures & Selective Disclosure Zero-Knowledge Proofs Studio

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BBS+ Signatures & Selective Disclosure Studio

Pairing-based cryptographic simulator modeling BLS12-381 BBS+ multi-message signatures, selective attribute disclosure, and unlinkable zero-knowledge proof generation.

BLS12-381 / W3C VC

1. Issuer Multi-Message Vector (m₁ .. m₅)

Disclosed Attributes

2 / 5

age, country

Zero-Knowledge Blinded

3 / 5

ssn, name, score

Unlinkability Guarantee

100% Blinded

Fresh r1, r2, r3 per presentation

Pairing Check e(A', W)

VALID (True)

BLS12-381 GT identity match

Bilinear Group Mapping & Blinded Proof Representation e: G₁ × G₂ → G_T

Disclosed Verifiable Presentation (JSON-LD)

BBS+ Verification Equations & Proof Math

BBS+ Signatures & Selective Disclosure Studio

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