关键词: 秘密共享, 二元对称多项式, 欺骗者, 离散对数, 无可信中心

Abstract:

Based on symmetric bivariate polynomial, this paper proposes a new fair（t, n） threshold secret sharing scheme without trusted center. In the scheme, the symmetry of the symmetric polynomial is used to provide the verification private key to any participant, effectively preventing the fraud of the external attacker; combining the intractability of the discrete logarithm to verify the correctness of the secret while ensuring the secret will not leak. The participant selects the sub-secret, encrypts the sub-secret by constructing a symmetric polynomial, and obtains the shadow secret and discloses it. The participant can effectively verify the correctness of the public information; the distributor does not need to exist, and the fraud of the distributor is avoided. Analysis shows that the program is safe and effective.

Key words: secret sharing, symmetric bivariate polynomial, cheater, discrete logarithm problem, no trusted center