Beaver三元组主动性生成协议研究

Research on Proactive Generation Protocol of Beaver Triples

在安全多方计算中,Beaver三元组是实现加法和乘法有效安全计算的基本技术之一,其可以将协议轮数降低至参与方个数的多项式大小。文章对移动敌手模型下Beaver三元组的安全生成协议开展研究,提出抵御半诚实移动敌手攻击的安全协议。首先,文章利用Paillier公钥系统设计了计算安全的有效两方主动性Beaver三元组生成协议,协议轮数为分享片段更新次数的2倍,每轮通信复杂度为3个Paillier密文;然后利用Shamir秘密分享等初等密码工具设计出信息论安全的有效n方Beaver三元组主动性生成协议,其中n≥3,协议发送元素总数至多为6nκ+6n个,执行轮数不多于2κ+2,其中κ为分享片段更新次数,且敌手控制参与方数不超过n-2。最后,针对恶意敌手文章给出协议设计思路。

In secure multi-party computation, Beaver triples have been one of basic technique to realize the secure computation of addition and multiplication under secret sharing, which can make the number of protocol rounds reach the polynomial of the number of participating parties.This paper studied secure generation protocol of Beaver triples in the mobile adversary model.First, a computational security, effective two-party active Beaver triple generation protocol was designed based on Paillier public key cryptosystem, whose number of rounds was twice the number of renew operations and sent three ciphertexts of Paillier cryptosystem in each round.Then the effective n-party Beaver triplet initiative generation protocol for information theory security was designed using primary cryptographic tools such as Shamir secret sharing, where n ≥ 3, the total number of elements sent by the protocol was at most 6nκ+6n, and the number of execution rounds is not more than 2κ+2, where к was the number of sharing fragment updates and the number of adversary control participants does not exceed n-2. Finally, protocol design ideas were given for malicious adversary articles.