Abstract
Recently, a new generic method to find near-collisions for cryptographic hash functions in a memoryless way has been proposed. This method is based on classical cycle-finding techniques and covering codes. This paper contributes to the coding theory aspect of this method by giving the optimal solution to a problem which arises when constructing a suitable code as the direct sum of Hamming and trivial codes.
Chapter PDF
Similar content being viewed by others
Keywords
References
Biham, E., Chen, R.: Near-Collisions of SHA-0. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 290–305. Springer, Heidelberg (2004)
Brent, R.P.: An improved Monte Carlo factorization algorithm. BIT 20(2), 176–184 (1980)
Chabaud, F., Joux, A.: Differential Collisions in SHA-0. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 56–71. Springer, Heidelberg (1998)
Cohen, G., Honkala, I., Litsyn, S., Lobstein, A.: Covering codes. North-Holland Mathematical Library, vol. 54. North-Holland Publishing Co., Amsterdam (1997)
De Cannière, C., Mendel, F., Rechberger, C.: Collisions for 70-Step SHA-1: On the Full Cost of Collision Search. In: Adams, C., Miri, A., Wiener, M. (eds.) SAC 2007. LNCS, vol. 4876, pp. 56–73. Springer, Heidelberg (2007)
De Cannière, C., Rechberger, C.: Finding SHA-1 Characteristics: General Results and Applications. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 1–20. Springer, Heidelberg (2006)
Dobbertin, H.: Cryptanalysis of MD4. J. Cryptology 11(4), 253–271 (1998)
Feller, W.: An introduction to probability theory and its applications, 3rd edn., vol. I. John Wiley & Sons Inc., New York (1968)
Kéri, G.: Tables for bounds on covering codes, http://www.sztaki.hu/~keri/codes/ (accessed May 17, 2010)
Gordon, D., Miller, V., Ostapenko, P.: Optimal hash functions for approximate matches on the n-cube. IEEE Trans. Inform. Theory 56(3), 984–991 (2010)
Graham, R.L., Sloane, N.J.A.: On the covering radius of codes. IEEE Trans. Inform. Theory 31(3), 385–401 (1985)
Knuth, D.E.: The art of computer programming. Seminumerical algorithms, Addison-Wesley Series in Computer Science and Information Processing, vol. 2. Addison-Wesley Publishing Co., Reading (1997)
Lamberger, M., Mendel, F., Rijmen, V., Simoens, K.: Memoryless Near-Collisions via Coding Theory (December 2009), http://asiacrypt2009.cipher.risk.tsukuba.ac.jp/rump/slides/13_NC-talk.pdf , (short talk) presented at the ASIACRYPT 2009 rump session
Mendel, F., Schläffer, M.: On Free-Start Collisions and Collisions for TIB3. In: Samarati, P., Yung, M., Martinelli, F., Ardagna, C.A. (eds.) ISC 2009. LNCS, vol. 5735, pp. 95–106. Springer, Heidelberg (2009)
Menezes, A., van Oorschot, P.C., Vanstone, S.A.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1996)
National Institute of Standards and Technology (NIST). Cryptographic Hash Project (2007), http://www.nist.gov/hash-competition
Nivasch, G.: Cycle detection using a stack. Inf. Process. Lett. 90(3), 135–140 (2004)
Pramstaller, N., Rechberger, C., Rijmen, V.: Exploiting Coding Theory for Collision Attacks on SHA-1. In: Smart, N.P. (ed.) Cryptography and Coding 2005. LNCS, vol. 3796, pp. 78–95. Springer, Heidelberg (2005)
Struik, R.: An improvement of the Van Wee bound for binary linear covering codes. IEEE Transactions on Information Theory 40(4), 1280–1284 (1994)
van Oorschot, P.C., Wiener, M.J.: Parallel Collision Search with Cryptanalytic Applications. J. Cryptology 12(1), 1–28 (1999)
van Wee, G.J.M.: Improved sphere bounds on the covering radius of codes. IEEE Transactions on Information Theory 34(2), 237–245 (1988)
Wang, X., Yin, Y.L., Yu, H.: Finding Collisions in the Full SHA-1. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 17–36. 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)
Yuval, G.: How to swindle Rabin? Cryptologia 3(3), 187–191 (1979)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lamberger, M., Rijmen, V. (2011). Optimal Covering Codes for Finding Near-Collisions. In: Biryukov, A., Gong, G., Stinson, D.R. (eds) Selected Areas in Cryptography. SAC 2010. Lecture Notes in Computer Science, vol 6544. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19574-7_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-19574-7_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-19573-0
Online ISBN: 978-3-642-19574-7
eBook Packages: Computer ScienceComputer Science (R0)