可验证多秘密共享方案的研究

发布时间：2018-05-24 15:29

  本文选题：秘密共享 + 多秘密　； 参考：《长沙理工大学》2014年硕士论文

【摘要】：秘密共享是一种用于分发、保存和恢复秘密信息的方法。秘密共享体制的提出为解决密钥管理问题提供了非常有效的途径,已成为了现代密码学和信息安全研究领域的一个重要分支。可验证秘密共享方案是一种能检测出秘密分发者和参与者之间的欺骗行为的秘密共享方案。可公开验证秘密共享是对可验证秘密共享的改进,方案中任何验证者都能公开地检验秘密份额的正确性。可验证多秘密共享方案不但能检测分发者和参与者的欺骗,而且能同时共享多个秘密。本文主要从秘密份额的可公开验证和定期更新这两个方面对可验证多秘密共享进行了深入研究,研究成果如下：研究了基于双线性对的秘密共享方案的可公开验证性问题,并结合Hermite插值多项式构造了一个双线性对上的可公开验证多秘密共享方案。该方案由Hermite插值法重构秘密多项式,突破了传统公开可验证秘密共享方案由拉格朗日插值多项式或中国剩余定理来构造的局限性,而且在一次秘密共享过程中多个秘密可以同时被重构。方案的安全性是基于椭圆曲线离散对数问题和双线性Diffie-Hellman困难问题。针对现有多秘密共享方案不能够同时满足秘密份额的公开验证和定期更新的问题,提出了一种秘密份额可更新的可公开验证多秘密共享方案。该方案利用单向散列链的安全特性构造更新多项式,从而实现秘密份额的定期更新。同时,在秘密分发和更新阶段公开一些验证信息,验证者能够根据这些公开信息来验证秘密份额和更新份额的有效性,以便于及时检测出某个或某些成员的恶意欺骗行为。本文对以上两个方案的正确性、安全性和性能均给出了详细的分析与对比。分析结果表明,本文提出的方案是正确可行的,并且具有较好的安全性和实用性。
[Abstract]:Secret sharing is a method for distributing, preserving, and restoring secret information. The secret sharing system provides a very effective way to solve the problem of key management and has become an important branch of modern cryptography and information security research field. Verifiable secret sharing scheme is a secret sharing scheme which can detect the cheating behavior between secret distributors and participants. Publicly verifiable secret sharing is an improvement on verifiable secret sharing. Any verifier in the scheme can openly verify the correctness of secret share. The verifiable multi-secret sharing scheme not only detects the spoofing of distributors and participants, but also shares multiple secrets at the same time. In this paper, we mainly study the verifiable multi-secret sharing from the aspects of publicly verifiable secret share and periodic update. The research results are as follows: the open verifiability of secret sharing scheme based on bilinear pairings is studied. A publicly verifiable multi-secret sharing scheme over bilinear pairs is constructed by using Hermite interpolation polynomials. In this scheme, the secret polynomial is reconstructed by Hermite interpolation method, which breaks through the limitation of the traditional publicly verifiable secret sharing scheme constructed by Lagrange interpolation polynomial or Chinese remainder theorem. Moreover, in a secret sharing process, multiple secrets can be reconstructed at the same time. The security of the scheme is based on the elliptic curve discrete logarithm problem and bilinear Diffie-Hellman problem. In order to solve the problem that the existing multi-secret sharing schemes can not satisfy both the public verification and periodic updating of secret share, a publicly verifiable multi-secret sharing scheme with updatable secret share is proposed. The scheme uses the security characteristics of the one-way hash chain to construct update polynomials, so that the secret share can be updated periodically. At the same time, some verification information is disclosed in the secret distribution and update stage, according to which the verifier can verify the validity of secret share and update share, so as to detect the malicious cheating of one or some members in time. In this paper, the correctness, security and performance of the two schemes are analyzed and compared in detail. The results show that the proposed scheme is correct and feasible, and has good safety and practicability.
【学位授予单位】：长沙理工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN918.4
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本文编号：1929560