基于GF(qN)上秩距離碼的校驗(yàn)矩陣的驗(yàn)證方案
AN IDENTIFICATION SCHEME BASED ON PARITY CHECK MATRIX OF RANK DISTANCE CODES OVER GF(qN)
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摘要: J.Stern(1996)在公鑰驗(yàn)證的一個(gè)新范例中基于GF(2)上糾錯(cuò)碼的校驗(yàn)矩陣提出了一驗(yàn)證方案。該文基于GF(qN)(q為素?cái)?shù))上秩距離碼的校驗(yàn)矩陣提出一新的驗(yàn)證方案,將J.Stern的方案中對(duì)秘密數(shù)據(jù)s的重量限制改為對(duì)s的秩的限制;證明了在隨機(jī)預(yù)言模型中給出的協(xié)議是零知識(shí)交互證明,并顯示出通過(guò)參數(shù)的適當(dāng)選取,此方案比J.Stern的方案更安全。
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關(guān)鍵詞:
- 驗(yàn)證方案; 校驗(yàn)矩陣; 秩距離碼; 零知識(shí)
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. -
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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