Key Distribution and Agreement Diffie - Hellman Over Polynomial Rings with Two Cyclomic Cossets
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Abstract
In this paper, we introduce a D-H key distribution protocol over polynomial rings. These protocols use some polynomials with two cyclomic cosets in the center of the ring as part of the private keys. We give some examples over the polynomial rings Zp. where p is a prime number. We also give a security analysis of the proposed protocols and conclude that the only possible attack is by brute force. In this paper, D-H key distribution and agreement protocols are also described in PR with two cyclotomic cosets based on DLP. DLP over number rings is important problem in public-key cryptography. This DLP is studied in the case of polynomial rings with two cyclotomic coset.
Keywords
key distribution, authentication, discrete logarithm problem, polynomial rings, cyclotomic coset
Article Details
References
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[3]. R. Alvarez, L. Tortosa, J. Vicent and A. Zamora. "A non-abelian group based on block upper triangular matrices with cryptographic applications". In M. Bras-Amoros and T. Hoholdt (editors), Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes, volume 5527 of Lecture Notes in Computer Science, pages 117-126. Springer-Verlag, Berlin, 2009.
[4]. J.-J. Climent, P. R. Navarro and L. Tortosa. "Key exchange protocols over noncommutative rings". The case End(Zp×Zp2). In J. Vigo Aguiar (editor), Proceedings of the 11th International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE 2011), pages 357-364. 2011.
[5]. W. D. Diffie and M. E. Hellman. "New directions in cryptography". IEEE Transactions on Information Theory, 22(6): 644 (654 (1976).
[6]. A. J. Menezes, P. C. van Oorschot and S. A. Vanstone. Handbook of Applied Cryptography. CRC Press, Boca Raton, FL, 1996.
[7]. B. Schneier. Applied Cryptography. John Wiley & Sons, New York, NY, second edition, 1996.
[8]. D. R. Stinson. Cryptography. Theory and Practice. CRC Press, Boca Raton, FL, 1995.
[9]. D. Boneh and R. J. Lipton, "Quantum cryptanalysis of hidden linear functions". In D. Coppersmith (editor), Advances in Cryptology, CRYPTO '95, volume 963 of Lecture Notes in Computer Science, pages 424-437. Springer-Verlag, Berlin, 1995.
[10]. P. W. Shor. "Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer". SIAM Journal on Computing, 26(5): 1484-1509 (1997).
[11]. Nguyen Trung Hieu, Nguyen Van Tung. Nguyen Binh, "A classification of Linear Codes based on Algebraic Structures and LCC", Proceeding of ATC 2014