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

摘要：

基于二元对称多项式，提出一个新的无可信中心的（t，n）门限秘密共享方案。方案中，利用对称多项式的对称性，为任意对参与者提供验证私钥，有效地预防外部攻击者的欺诈行为；结合离散对数的难解性，对秘密的正确性进行验证，同时确保秘密不会泄露。参与者选取子秘密，通过构造对称多项式，对子秘密加密，得出影子秘密并公开，参与者可以对公开的信息的正确性进行有效验证；不需要分发者的存在，避免了分发者的欺诈。分析结果表明，该方案是安全有效的。

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