Abstract: Existing (n,t,n) secret sharing scheme can guarantee the main share of strong t consistency,but they can not verify the authenticity of subshare or prevent fraud appeared in the process of secret reconstructing.This paper designs a publicly verifiable strong (n,t,n) secret sharing scheme without trusted center using the assumption about the difficulty of computing discrete logarithm,public-key encryption algorithms and key agreement thought,which reduces the cost needed by establishing private channel.In addition,the participator needs only public information to finish verification,without interactive group communication,which can resist deceits of other schemes.Performance analysis shows that the proposed scheme not only has less computational overhead and communication cost,but also has strong t consistency and public verifiability,compared with existing (n,t,n) secret sharing scheme.

Key words: discrete logarithm, (n,t,n) secret sharing, strong t consistency, homomorphic sum;public verifiability, public key encryption

摘要： 现有(n,t,n)秘密共享方案能够保证主份额满足强t一致性,但不能验证子份额的正确性,而且不能防止秘密重构过程中出现欺骗行为。为此,利用离散对数困难假设、公钥加密算法以及密钥协商思想,设计一个可公开验证的无可信中心的强(n,t,n)秘密共享方案。参与者在验证过程中只需利用公开信息便可验证,无需进行交互式通信,从而能够抵抗秘密重构过程中出现的欺骗行为,并在一定程度上减少建立私有信道所需的成本开销。性能分析结果表明,与现有(n,t,n)秘密共享方案相比,该方案具有较少的计算开销和通信开销,并且在强t一致性和可公开验证性方面更具优势。

关键词: 离散对数, (n, t, n)秘密共享, 强t一致性, 同态加, 可公开验证, 公钥加密

CLC Number: 

• TP309