Abstract:

Secure multi-party computation (SMC) is a research hotspot in cryptography in recent years, and is also a key technology for information security protection. The interval secure multi-party computation problems have important theoretical significance in cryptography. Previous studies rarely involve secret interval, that is, interval is generated by two-party or multi-party, and any one knows nothing about the interval information. The secret interval problems have important practical significance in real life. This paper mainly studies the privacy-preserving determination of secret interval and threshold. Firstly, for the secret interval is generated by two-party, based on Paillier’s homomorphic encryption, this paper proposes a protocol. Secondly, for the secret interval is generated by multi-party, this paper proposes an optimization protocol that uses the coding principle combined with Lifted ElGamal homomorphic encryption. Thirdly, this paper proves the protocols can resist collusion attacks, and proves they are safe by using the simulation paradigm. Finally, many practical application problems can be solved by using the protocols proposed in this paper.

Key words: secure multi-party computation, secret interval and threshold, homomorphic encryption, threshold decryption

摘要：

安全多方计算（SMC）是密码学领域近年来的研究热点，是信息安全保护的关键技术。区间安全多方计算问题在密码学中具有重要的理论意义。之前的研究很少涉及到秘密区间，即区间是由两方或多方合作生成的，任何人对区间信息一无所知。秘密区间问题在现实生活中有很重要的实际意义。主要研究的是秘密区间与阈值的保密判定问题，针对两方合作生成秘密区间，基于Paillier同态加密算法设计了一个协议；针对多方合作生成秘密区间，利用编码原理并结合Lifted ElGamal同态加密算法，提出了优化协议。所设计的安全多方计算协议均能抵抗合谋攻击，并利用模拟范例证明了协议的安全性。利用所设计的协议可以解决很多实际应用问题。

关键词: 安全多方计算, 秘密区间与阈值, 同态加密, 门限解密