Authors: Sayan Bairagi, Sayan Singha Roy, Abir Rakshit, Anik Bhowmick
This work presents a zero-knowledge credential framework designed to enable secure and privacy-preserving attribute verification across multiple independent systems. Theframework allows a user to prove statements of the form a ≥ t,where a ∈ Zq represents a secret attribute and t denotes a public threshold, without revealing the attribute value itself. At the sametime, the framework prevents the exposure of any globally stable identifier, thereby eliminating the risk of cross-domain tracking. The construction is based on Pedersen commitments, where each attribute is encoded as C = g^ah^r ∈ G, with G ⊆ Z^∗p denoting a cyclic group of prime order q. The generators g and h are selected such that the discrete logarithm relation between them is unknown. This ensures that the commitment is computationally binding under the discrete logarithm assumption and perfectly hiding due to the use of randomness r. As a result, the committed attribute remains concealed while still allowing verification of statements about it. Predicate verification is achieved using a sigma protocol, whichenables the prover to demonstrate knowledge of valid witnesses without revealing them. In particular, the protocol proves the relation C · g−t = g^δh^r, where δ = a − t. This transformation allows the system to verify threshold conditions such as a ≥ twithout disclosing the value of a. The zero-knowledge property of the protocol ensures that the verifier learns only the validity ofthe statement and no additional information about the underlying attribute or randomness.To prevent correlation of user activity across different verification domains, the framework introduces scoped pseudonyms defined as IDS = pkH(S), where pk = g^x is a public key derivedfrom a secret key x, and H is a cryptographic hash functionmodeled as a random oracle. The scope S represents a domain specific identifier. This construction produces a unique identifierfor each domain while ensuring that identifiers generated for different scopes cannot be linked without solving the discrete logarithm problem in G. Revocation is supported through an RSA accumulator constructed under the Strong RSA assumption. For a revoked set R={ri}, the accumulator value is defined as A = g^Qri mod N,where N is an RSA modulus. The system enables efficient non membership verification using witnesses derived from B´ezout coefficients1. This mechanism allows a verifier to confirm thata credential has not been revoked, while maintaining constant verification cost that does not depend on the size of the revoked set. (Truncated by viXra Admin)
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