Zero-knowledge proving system and method

摘要

A zero-knowledge proving system includes a proving mechanism for proving equality or inequality of two discrete logarithms and a verifying mechanism for verifying said equality or inequality. The proving mechanism stores public information including a designated operation scheme, two input numbers alpha and beta, and two predetermined bases g and h, private information x which is a discrete logarithm of alpha to the base g. After converting alpha, beta and h to produce alpha', beta' and gamma' as follows: alpha'=alpha^r; beta'=beta^r; and gamma'=h^xr, the equality of a log_alphaalpha' and log_betabeta' and the equality of log_galpha' and log_hgamma' are proved. The verifying mechanism verifies the equality of a log_alphaalpha' and log_betabeta' and the equality of log_galpha' and log_hgamma'. Then, the received beta' and gamma' are checked to determine the equality or inequality thereof, and it is determined whether the proof is acceptable, depending on the verification and the check results.