Abstract
In this paper, we study the recently proposed encryption scheme MST 3, focusing on a concrete instantiation using Suzuki-2-groups. In a passive scenario, we argue that the one wayness of this scheme may not, as claimed, be proven without the assumption that factoring group elements with respect to random covers for a subset of the group is hard. As a result, we conclude that for the proposed Suzuki 2-groups instantiation, impractical key sizes should be used in order to prevent more or less straightforward factorization attacks.
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Bellare M., Desai A., Pointcheval D., Rogaway P.: Relations among notions of security for public-key encryption schemes. In: CRYPTO’98: Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology, pp. 26–45. Springer-Verlag, London, UK (1998).
Blackburn S.R., Cid C., Mullan C.: Cryptanalysis of the MST 3 Public Key Cryptosystem. Cryptology ePrint Archive: Report 2009/248. At the time of writing available electronically at http://www.eprint.iacr.org/2009/248 (2009).
Bohli J.M., González Vasco M.I., Martínez C., Steinwandt R.: Weak keys in MST 1. Des. Codes Cryptogr. 37, 509–524 (2005)
ElGamal T.: A public key cryptosystem and a signature scheme based on discrete logarithm. IEEE Trans. Info. Theory 31, 469–472 (1985)
The GAP Group: GAP—Groups, Algorithms, and Programming, Version 4.4.10 http://www.gap-system.org (2007).
González Vasco M.I., Steinwandt R.: Obstacles in two public-key cryptosystems based on group factorizations. In: Nemoga, K., Grošek, O. (eds.) Cryptology, pp. 23–37. Tatra Mountains Mathematical Publications, Slovakia (2002).
Huppert B., Blackburn N.: Finite Groups II. Springer, Berlin (1982)
Lempken W., Magliveras S.S., van Trung T., Wei W.: A public key cryptosystem based on non-abelian finite groups. J. Cryptol. 22, 62–74 (2009)
Magliveras S.S.: A cryptosystem from logarithmic signatures of finite groups. In: Proceedings of the 29th Midwest Symposium on Circuits and Systems, pp. 972–975. Elsevier Publishing Company, Amsterdam (1986).
Magliveras S.S., Memon N.D.: Linear complexity profile analysis of the PGM cryptosystem. Congresus Numerantium, Utilitas Mathematica 72, 51–60 (1989)
Magliveras S.S., Memon N.D.: Properties of cryptosystem PGM. In: Advances in Cryptology. Proceedings of CRYPTO 1989, Lecture Notes on Computer Science, pp. 447–460. Springer-Verlag, Berlin (1989).
Magliveras S.S., Memon N.D.: Complexity tests for cryptosystem PGM. Congressus Numerantium, Utilitas Mathematica 79, 61–68 (1990)
Magliveras S.S., Memon N.D.: Algebraic properties of cryptosystem PGM. J. Cryptol. 5, 167–183 (1992)
Magliveras S.S., Stinson D.R., van Trung T.: New approaches to designing public key cryptosystems using one-way functions and trap-doors in finite groups. J. Cryptol. 15, 285–297 (2002)
Magliveras S.S., Svaba P., van Trung T., Zajac P.: On the security of a realization of cryptosystem MST 3. Tatra Mt. Math. Publ. 41, 1–13 (2008)
Motwani R., Raghavan P.: Randomized Algorithms. Cambridge University Press, Cambridge (1995)
Svaba P., Van Trung T.: On generation of random covers for finite groups. Tatra Mt. Math. Publ. 37, 105–112 (2007)
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Communicated by Ron Mullin / Rainer Steinwandt.
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Vasco, M.I.G., del Pozo, A.L.P. & Duarte, P.T. A note on the security of MST 3 . Des. Codes Cryptogr. 55, 189–200 (2010). https://doi.org/10.1007/s10623-010-9373-0
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DOI: https://doi.org/10.1007/s10623-010-9373-0