Abstract
Recently, some collisions have been exposed for a variety of cryptographic hash functions [20,21] including some of the most widely used today. Many other hash functions using similar constructions can however still be considered secure. Nevertheless, this has drawn attention on the need for new hash function designs.
In this article is presented a family of secure hash functions, whose security is directly related to the syndrome decoding problem from the theory of error-correcting codes.
Taking into account the analysis by Coron and Joux [4] based on Wagner’s generalized birthday algorithm [19] we study the asymptotical security of our functions. We demonstrate that this attack is always exponential in terms of the length of the hash value.
We also study the work-factor of this attack, along with other attacks from coding theory, for non asymptotic range, i.e. for practical values. Accordingly, we propose a few sets of parameters giving a good security and either a faster hashing or a shorter description for the function.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Augot, D., Finiasz, M., Sendrier, N.: A fast provably secure cryptographic hash function. Cryptology ePrint Archive (2003), http://eprint.iacr.org/2003/230/
Barg, A.: Complexity issues in coding theory. In: Pless, V.S., Huffman, W.C. (eds.) Handbook of Coding theory, ch. 7, vol. I, pp. 649–754. North-Holland, Amsterdam (1998)
Berlekamp, E.R., McEliece, R.J., van Tilborg, H.C.: On the inherent intractability of certain coding problems. IEEE Transactions on Information Theory 24(3) (May 1978)
Coron, J.-S., Joux, A.: Cryptanalysis of a provably secure cryptographic hash function. Cryptology ePrint Archive (2004), http://eprint.iacr.org/2004/013/
Dai, W.: Crypto++ library, http://www.eskimo.com/~weidai/
Damgård, I.B.: A design principle for hash functions. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 416–427. Springer, Heidelberg (1990)
Gurevich, Y.: Average case completeness. Journal of Computer and System Sciences 42(3), 346–398 (1991)
Joux, A., Granboulan, L.: A practical attack against knapsack based hash functions. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 58–66. Springer, Heidelberg (1995)
Levin, L.: Average case complete problems. SIAM Journal on Computing 15(1), 285–286 (1986)
McEliece, R.J.: A public-key cryptosystem based on algebraic coding theory. In: DSN Prog. Rep., Jet Prop. Lab., California Inst. Technol., Pasadena, CA, January 1978, pp. 114–116 (1978)
Menezes, A., van Oorschot, P., Vanstone, S.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1996)
Merkle, R.C.: One way hash functions and DES. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 428–446. Springer, Heidelberg (1990)
National Insitute of Standards and Technology. FIPS Publication 180: Secure Hash Standard (1993)
Niederreiter, H.: Knapsack-type crytosystems and algebraic coding theory. Prob. Contr. Inform. Theory 15(2), 157–166 (1986)
Preneel, B.: The state of cryptographic hash functions. In: Damgård, I.B. (ed.) EEF School 1998. LNCS, vol. 1561, pp. 158–182. Springer, Heidelberg (1999)
Rivest, R.L.: The MD4 message digest algorithm. In: Menezes, A., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 303–311. Springer, Heidelberg (1991)
Rogaway, P., Shrimpton, T.: Cryptographic hash-function basics: definitions, implications, and separations for preimage resistance, second-preimage resistance, and collision resistance. In: Roy, B., Meier, W. (eds.) FSE 2004. LNCS, vol. 3017, pp. 371–388. Springer, Heidelberg (2004)
Sendrier, N.: On the security of the McEliece public-key cryptosystem. In: Blaum, M., Farrell, P.G., van Tilborg, H. (eds.) Information, Coding and Mathematics, pp. 141–163. Kluwer, Dordrecht (2002); Proceedings of Workshop honoring Prof. Bob McEliece on his 60th birthday
Wagner, D.: A generalized birthday problem. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 288–304. Springer, Heidelberg (2002)
Wang, X., Lai, X., Feng, D., Chen, H., Yu, X.: Cryptanalysis of the hash functions md4 and ripemd. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 1–18. Springer, Heidelberg (2005)
Wang, X., Yu, H.: How to break md5 and other hash functions. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 19–35. Springer, Heidelberg (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Augot, D., Finiasz, M., Sendrier, N. (2005). A Family of Fast Syndrome Based Cryptographic Hash Functions. In: Dawson, E., Vaudenay, S. (eds) Progress in Cryptology – Mycrypt 2005. Mycrypt 2005. Lecture Notes in Computer Science, vol 3715. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11554868_6
Download citation
DOI: https://doi.org/10.1007/11554868_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28938-8
Online ISBN: 978-3-540-32066-1
eBook Packages: Computer ScienceComputer Science (R0)