The Confirmation and Denial Proofs Sample Clauses

The Confirmation and Denial Proofs. The USign algorithm defines a language L(XI) = {(m, σ) : σ = USign(xI, m)} for each public key XI. For the above signature scheme, we can write L(XI) = {(m, σ) : DL(σ, H1(m)) = DL(xI, g) in G}. In other words, L(XI) is the language of all possible message and signature pairs (m, σ) where the discrete logarithm of σ to the base H1(m) equals the discrete logarithm of XI to the base g modulo p. The family of languages L is defined as L = {L(XI) : XI ∈ G}. We can now define confirmation and denial proofs with respect to the languages L(XI). Confirmation proof: The confirmation proof requires a secure NIDV proof system C for L. Informally, C must prove the equality of two discrete logarithms (EDL). Denial proof: The denial proof requires a secure NIDV proof system D for L. Informally, D must prove the inequality of two discrete logarithms (IDL).