Multi-receiver Authentication Scheme for Multiple Messages Based on Linear Codes
In this paper, we construct an authentication scheme for multi-receivers and multiple messages based on a linear code C.This construction can be re garded as a generalization of the authentication scheme given by Safavi-Naini and Wang 1.Actually, we notice that the scheme of Safavi-Naini and Wang is constructed with Reed-Solomon codes.The generalization to linear codes has the similar advantages as generalizing Shamirs secret sharing scheme to linear se cret sharing sceme based on linear codes 2--6.For a fixed message base field Fq, our scheme allows arbitrarily many receivers to check the integrity of their own messages, while the scheme of Safavi-Naini and Wang has a constraint on the number of verifying receivers V ≤ q.We further introduce access structure in our scheme.Massey 4 characterized the access structure of linear secret sharing scheme by minimal codewords in the dual code whose first component is 1.We slightly modify the definition of minimal codewords in 4.Let C be a V,k linear code.For any coordinate i ∈ 1, 2,..., V, a codeword c in C is called minimal respect to i if the codeword c has component 1 at the i-th coordinate and there is no other codeword whose i-th component is 1 with support strictly contained in that of c.Then the security of receiver Ri in our authentication scheme is char acterized by the minimal codewords respect to i in the dual code C1.Finally, we illustrate our authentication scheme based on the elliptic curve codes, a special class of algebraic geometry codes.We use the group of rational points on the elliptic curve to determine all the malicious groups that can successfully make a substitution attack to any fixed receiver.
Authentication scheme linear codes secret sharing minimal code words substitution attack
Jun Zhang Xinran Li Fang-Wei Fu
Chern Institute of Mathematics and LPMC,Nankai University,Tianjin,300071,China Chern Institute of Mathematics and LPMC,Nankai University,Tianjin,300071,China; Cryptography Enginee
国际会议
福州
英文
287-301
2014-05-05（万方平台首次上网日期，不代表论文的发表时间）