Abstract
This paper presents a new public key cryptosystem that uses noncommutative groups as platform group. The underlying hard problem of the proposed cryptosystem is a combination of discrete log problem and conjugacy search problem. Due to use of noncommutative platform groups, it is expected that the presented cryptosystem provides higher levels of security against known attacks. Some important issues regarding the choice of platform and parameters of this cryptosystem are addressed. Further, a brief analysis of security aspects is also presented.
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References
Anshel I, Anshel M, Goldfeld D (1999) An algebraic method for public key cryptography. Math Res Lett 6:287–291
Barker E, Roginsky A (2015) Recommendation for transitioning the use of cryptographic algorithms and key lengths
Charalambos M, Koupparis C (2012) Non-commutative cryptography: Diffie-Hellman and CCA secure cryptosystems using matrices over group rings and digital signatures, ProQuest LLC, Ann Arbor, Thesis (Ph.D.), City University of New York
Diffie W, Hellman M (1976) New directions in cryptography. IEEE Trans Inf Theory 22:644–654
ElGamal T (1985) A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans Inf Theory 31:469–472
Gu L, Wang L, Ota K, Dong M, Cao Z, Yang Y (2013) New public key cryptosystems based on non-Abelian factorization problems. Secur Commun Netw 6(7):912–922
Hofheinz D, Steinwandt R (2003) A practical attack on some braid group based cryptographic primitives, public key cryptography PKC. Springer, Berlin
Kahrobaei D, Koupparis C, Shpilrain V (2013) Public key exchange using matrices over group rings. Groups Complex Cryptol 5(1):97–115
Ko KH, Lee SJ, Cheon JH, Han JH, Kang JS, Park C (2000) New public-key cryptosystems using Braid groups, Advances in Cryptography, In: Proceedings of Crypto 2000, Lecture Notes in Computer Science 1880, 166–183
Lee SJ, Lee E (2002) Potential weaknesses of the commutator key agreement protocol based on braid groups. In: Knudsen L (ed) Advances in cryptology EUROCRYPT. Springer, Berlin, pp 14–28
Magyarik R, Wagner NR (1985) A public key cryptosystem based on the word problem, advances in cryptology–CRYPTO 1984, Lecture Notes in Computer Science 196, 19–36. Springer, Berlin
Menezes A, Wu Y (1997) The discrete logarithm problem in GL(n, q). Ars Combinatorica 47:23–32
Mullan C (2012) Some Results in Group-Based Cryptography, Thesis submitted to the University of London for the Degree of Doctor of Philosophy
Myasnikov AD, Ushakov A (2009) Cryptanalysis of the Anshel-Anshel-Goldfeld-Lemieux key agreement protocol. Groups Complex Cryptol 1:63–75
Myasnikov AG, Shpilrain V, Ushakov A (2007) Group-based cryptography, advanced courses in mathematics. CRM Barcelona, Spain
Rivest R, Shamir A, Adleman L (1978) A method for obtaining digital signatures and public-key cryptosystems. Commun ACM 21(2):120–126
Rotman J (1965) The theory of groups. Allyn and Bacon, Boston
Shpilrain V (2008) Cryptanalysis of Stickel’s key exchange scheme. Proc Comput Sci Russia 5010:283–288
Sramka M On the security of Stickels key exchange scheme, available at http://crises-deim.urv.cat/msramka/pubs/sramka-stickelkesecurity
Stickel E (2005) A new method for exchanging secret keys. In: Proceedings of the Thirteenth International Conference on Information Technology and Applications, (ICITA 2005) 2:426–430
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Kanwal, S., Ali, R. A cryptosystem with noncommutative platform groups. Neural Comput & Applic 29, 1273–1278 (2018). https://doi.org/10.1007/s00521-016-2723-8
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DOI: https://doi.org/10.1007/s00521-016-2723-8