基于GF(qN)上秩距离码的校验矩阵的验证方案
AN IDENTIFICATION SCHEME BASED ON PARITY CHECK MATRIX OF RANK DISTANCE CODES OVER GF(qN)
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摘要: J.Stern(1996)在公钥验证的一个新范例中基于GF(2)上纠错码的校验矩阵提出了一验证方案。该文基于GF(qN)(q为素数)上秩距离码的校验矩阵提出一新的验证方案,将J.Stern的方案中对秘密数据s的重量限制改为对s的秩的限制;证明了在随机预言模型中给出的协议是零知识交互证明,并显示出通过参数的适当选取,此方案比J.Stern的方案更安全。Abstract: An identification scheme based on parity check matrix of error-correcting codes over GF(2) was proposed in the paper A New Paradigm for Public Key Identification by J. Stern(1996), a new identification scheme based on parity check matrix of rank distance codes over GF(qN) (q is a prime) is proposed in this paper, the limitation on the weight of mysterious datum s is changed into the limitation on the rank of s. It is proved that the given protocol is a zero-knowledge interactive proof in the random oracle model, and it is shown that the scheme is more secure than the scheme of J. Stern when parameters are selected properly.
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S. Goldwasser, S. Micali, C. Rackoff, The knowledge complexity of interactive proof-systems,SIAM Journal on Computing, 1989, 18(1), 186-208.[2]J. Stern, A new paradigm for public key identification, IEEE Trans. on Information Theory,1996, 42(6), 1757-1768.[3]E.M. Gabidulin, Theory of codes with maximum rank distance, Problems of Information Transmission, 1985, 21(1), 1-12.[4]U. Feige, A. Fiat, A. Shamir, Zero knowledge proofs of identity. Journal of Cryptology, 1988,1(2), 77 94.[5]F. Chabaud.[J].J. Stern, The cryptographic security of the syndrome decoding problem for rank distance codes, Advances in Cryptology-Asiacrypt96 (K.Kim, T. Matsumoto, eds.), Lecture Notes in Computer Science, Vol.1163, Berlin, Springer-Verlag.1996,:- -
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