Abstract
Random covers for finite groups have been introduced in Magliveras et al. (J Cryptol 15:285–297, 2002), Lempken et al. (J Cryptol 22:62–74, 2009), and Svaba and van Trung (J Math Cryptol 4:271–315, 2010) for constructing public key cryptosystems. In this article we describe a new approach for constructing pseudorandom number generators using random covers for large finite groups. We focus, in particular, on the class of elementary abelian 2-groups and study the randomness of binary sequences generated from these generators. We successfully carry out an extensive test of the generators by using the NIST Statistical Test Suite and the Diehard battery of tests. Moreover, the article presents argumentation showing that the generators are suitable for cryptographic applications. Finally, we include performance data of the generators and propose a method of using them in practice.
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References
Blum L., Blum M., Shub M.: A simple unpredictable pseudo-random number generator. SIAM J. Comput. 15, 364–383 (1986)
Knuth D.E.: The Art of Computer Programming, Volume 2: Seminumerical Algorithms, 3rd edn. Addison-Wesley, Reading (1998)
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., Oberg B.A., Surkan A.J.: A new random number generator from permutation groups. In: Rend. del Sem. Matemat. e Fis. di Milano, vol. 54, pp. 203–223 (1984).
Magliveras S.S.: A cryptosystem from logarithmic signatures of finite groups. In: Proceedings of the 29’th Midwest Symposium on Circuits and Systems, pp. 972–975. Elsevier, Amsterdam (1986).
Magliveras S.S., Memon N.D.: Random Permutations from Logarithmic Signatures. In: Computing in the 90’s, First Great Lakes Comp. Sc. Conf. Lecture Notes in Computer Science, vol. 507, pp. 91–97. Springer-Verlag, New York (1989).
Magliveras S.S., Stinson D.R., van Trung T.: New approaches to designing public key cryptosystems using one-way functions and trapdoors in finite groups. J. Cryptol. 15, 285–297 (2002)
Marsaglia G.: DIEHARD: a battery of test of randomness (1995). http://stat.fsu.edu/~geo/diehard.html.
Matsumoto M., Nishimura T.: Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Model. Comput. Simul. 8(1), 3–30 (1998)
Menezes A., van Oorschot P., Vanstone S.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1997)
Rukhin A., et al.: Statistical test suite for random and pseudorandom number generators for cryptographic applications. NIST Special Publication 800-22, Revised April 2010, National Institute of Standards and Technology (2010). http://csrc.nist.gov/rng.
Rivest R.L.: The RC4 Encryption Algorithm. RAS Data Security, Inc. (1992), unpublished.
Svaba P., van Trung T.: On generation of random covers for finite groups. Tatra Mt. Math. Publ. 37, 105–112 (2007)
Svaba P., van Trung T.: Public key cryptosystem MST 3: cryptanalysis and realization. J. Math. Cryptol. 4, 271–315 (2010)
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This is one of several papers published together in Designs, Codes and Cryptography on the special topic: “Geometry, Combinatorial Designs & Cryptology”.
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Marquardt, P., Svaba, P. & van Trung, T. Pseudorandom number generators based on random covers for finite groups. Des. Codes Cryptogr. 64, 209–220 (2012). https://doi.org/10.1007/s10623-011-9485-1
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DOI: https://doi.org/10.1007/s10623-011-9485-1