Computer Engineering and Applications ›› 2016, Vol. 52 ›› Issue (13): 38-42.

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Fair secret sharing scheme based on symmetric bivariate polynomial

GU Weiyu, MIAO Fuyou, HE Xiaoting   

  1. School of Computer Science and Technology, University of Science and Technology of China, Hefei 230027, China
  • Online:2016-07-01 Published:2016-07-15



  1. 中国科学技术大学 计算机科学与技术学院,合肥 230027

Abstract: Based on symmetric bivariate polynomial, this paper proposes a new fair [(t,n)] threshold secret sharing scheme, which can guarantee that each participant can recover the correct secret if all participants are legal and honest; when there is a cheater, all participants are unable to recover the correct secret. In the proposed scheme, a symmetric bivariate polynomial is used to generate session key for any two participants; moreover, combined with discrete logarithm, the symmetric bivariate polynomial enables the scheme to choose a sufficiently long sequence of secrets to guarantee the fairness while each participant holds a small number of shares. Additionally, the scheme also can achieve fair secret recovery in asynchronous environment. Compared with Harn’s scheme, the proposed scheme is fairer and more flexible.

Key words: secret sharing, cheater, symmetric bivariate polynomial, fairness

摘要: 基于二元对称多项式,提出一种新的公平[(t,n)]门限秘密共享方案,能够确保:所有参与者都合法且诚实时,均能恢复正确的秘密;存在欺骗者时,所有参与者都无法恢复正确的秘密。该方案利用二元对称多项式不仅为任意两个参与者提供会话密钥;结合离散对数,在确保每个share持有者拥有较少share的情况下,使得Dealer可以选取足够长的秘密序列,从而确保方案的公平性。此外,方案在异步环境下也能实现公平秘密恢复。与Harn方案相比,该方案更加公平和灵活。

关键词: 秘密共享, 欺骗者, 二元对称多项式, 公平性