The value of the function is the tuple ( v( y 1), вЂ¦, v( y m)), in which output y j, 1 в‰¤ j в‰¤ m, contributes the jth bit of the output. It is easy for the prover to convince the verifier that the k bit strings encrypted by z 1, z 2,вЂ¦, z k and zвЂІ 1, zвЂІ 2,вЂ¦, zвЂІ k are identical without providing the verifier with any additional information by the following string equality protocol.ДefinitionВ 2.11 (String Equality Protocol) For each i, 1В в‰¤ iВ в‰¤ k, the prover gives the verifier some x iВ в€€ в„¤ в‹‰ вЃЋ ( denoting the set of integers relatively prime to n between 1 and nВ в€’В 1) so that z i z i вЂІВ в‰Ў x i 2( modВ n).ДefinitionВ 2.12 (Boolean Computation Protocol) Consider any Boolean function B : obtained by applying П„( v) to the value( s) of the vertices incoming to v.

For each 1В в‰¤ iВ в‰¤ k, let z i and zвЂІ i be the two encryptions of b i randomly chosen by the prover. Let uВ = b 1, b 2,вЂ¦, b k be a k bit string of the prover. At the end of the protocol, if the final output of the circuit is 1, then the circuit is satisfiable, but nothing else. is through the simulation of an arbitrary Boolean circuit without disclosing the inputs or any intermediary results. Under the assumption of quadratic residuosity that two states are computationally indistinguishable through the calculation of the quadratic residues modulo n, a protocol for satisfiability (SAT) is suggested that directly simulates a circuit that evaluates given instances of SAT. The quadratic residuosity problem is the question of distinguishing by calculating the quadratic residues modulo n, where n is a composite number of two odd primes p and q. LiFeng, Bruce McMillin, in Advances in Computers, 2014 4.6 ZKP Sketch for SAT

Truth table calculator