Abstract
Tillich and Zémor proposed a hashing scheme based on the group of unimodular matrices SL 2(F q) over a finite field F q of q = 2n elements. Charnes and Pieprzyk studied the security of this scheme. They showed that for n = 131 and for some irreducible polynomial P 131(x) this scheme is weak. We show that with sufficiently high probability the polynomials P n(x) can be chosen in such a way that this type of attack can be avoided. Futhermore, we generalize the Tillich-Zémor hashing scheme for any finite field F q and show that the new generalized scheme has similar properties.
This author’s research was partially funded by the Korea Science and Engineering Foundation, grant 961-0106-038-2
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References
C. Charnes and J. Pieprzyk. Attacking the SL 2 hashing scheme. In Advanced in Cryptology — Proceedings of ASIACRYPT’94 (1994). LNCS 917. Springer-Verlag pp. 322–330.
L.E. Dickson. Linear groups with an exposition of the Galois field theory. Leibzig: Teubner 1901 (New York: Dover Publ. 1958).
L. Dornhoff. Group representation theory, volume I. Marcel Dekker, Inc., New York 1971.
W. Geiselman. A note on the hash function of Tillich and Zémor. In Fast Software Encryption Workshop. LNCS 1039. Springer-Verlag pp. 51–52.
M. Suzuki. Group theory, volume I. Springer-Verlag 1982.
H.C.A. van Tilborg. An introduction to cryrtology. Klumer, 1989.
J-P. Tillich and G. Zémor. Hashing with SL 2. In Advanced in Cryptology — Proceedings of CRYPTO’94 (1994). LNCS 917. Springer-Verlag pp. 40–49.
J-P. Tillich and G. Zémor. Group-theoretic hash functions. In First French-Israeli workshop on algebraic coding (1994) LNCS 781. Springer-Verlag pp. 90–110.
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© 1998 Springer-Verlag Berlin Heidelberg
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Abdukhalikov, K.S., Kim, C. (1998). On the Security of the Hashing Scheme Based on SL 2 . In: Vaudenay, S. (eds) Fast Software Encryption. FSE 1998. Lecture Notes in Computer Science, vol 1372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69710-1_7
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DOI: https://doi.org/10.1007/3-540-69710-1_7
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