一种新的基于零知识码的通信量减少的身份识别方案
A new zero-knowledge code based identification scheme with reduced communication
摘要：
本文基于伴随式译码问题，提出了一种新的渐近欺骗概率为1/2的5遍身份鉴别方案。我们的协议是相关的斯特恩识别方案，但有一个减少的通信成本相比，以前的代码为基础的零知识计划，而且我们的计划允许获得一个非常小的大小的公钥和秘密密钥。本文的贡献是双重的，首先，我们提出了一个变化的斯特恩认证计划，允许渐近降低作弊概率为1/2，而不是2/3（和非常接近1/2在实践中），但与较少的通信。我们的解决方案是基于新的挑战，通过循环移位的初始公钥综合征的秘密密钥，一个新的证明，这种情况下的合理性。其次，我们提出了一种新的方法来处理哈希承诺的零知识计划的基础上斯特恩的计划，使在通信方面，平均而言，只有一个哈希值发送，而不是两个或三个。新方案具有基于编码理论的零知识安全性证明、秘密和公钥规模小等优点（几百比特），计算复杂度小，用于认证的总通信成本为19 kb（对于$2^{16}$安全性）和长度为93 kb（11.5kB）的签名（对于$2^{80}$安全性），与先前基于编码理论的方案相比改进了40%。
英文摘要：
In this paper we present a new 5-pass identification scheme with asymptotic cheating probability 1/2 based on the syndrome decoding problem. Our protocol is related to the Stern identification scheme but has a reduced communication cost compared to previous code-based zero-knowledge schemes, moreover our scheme permits to obtain a very low size of public key and secret key. The contribution of this paper is twofold, first we propose a variation on the Stern authentication scheme which permits to decrease asymptotically the cheating probability to 1/2 rather than 2/3 (and very close to 1/2 in practice) but with less communication. Our solution is based on deriving new challenges from the secret key through cyclic shifts of the initial public key syndrome; a new proof of soundness for this case is given Secondly we propose a new way to deal with hashed commitments in zero-knowledge schemes based on Stern's scheme, so that in terms of communication, on the average, only one hash value is sent rather than two or three. Overall our new scheme has the good features of having a zero-knowledge security proof based on well known hard problem of coding theory, a small size of secret and public key (a few hundred bits), a small calculation complexity, for an overall communication cost of 19kb for authentication (for a $2^{16}$ security) and a signature of size of 93kb (11.5kB) (for security $2^{80}$), an improvement of 40% compared to previous schemes based on coding theory.
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