Searching for Differential Paths in MD4
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The ground-breaking results of Wang et al. have attracted a lot of attention to the collision resistance of hash functions. In their articles, Wang et al. give input differences, differential paths and the corresponding conditions that allow to find collisions with a high probability. However, Wang et al. do not explain how these paths were found. The common assumption is that they were found by hand with a great deal of intuition.
In this article, we present an algorithm that allows to find paths in an automated way. Our algorithm is successful for MD4. We have found over 1000 differential paths so far. Amongst them, there are paths that have fewer conditions in the second round than the path of Wang et al. for MD4. This makes them better suited for the message modification techniques that were also introduced by Wang et al.
Keywordscollision search differential path MD4
- [ABB+05]Augot, D., Biryukov, A., Braeken, A., Cid, C., Dobbertin, H., Englund, H., Gilbert, H., Granboulan, L., Handschuh, H., Hell, M., Johansson, T., Maximov, A., Pornin, M.P.T., Preneel, B., Robshaw, M., Ward, M.: Ongoing Research Areas in Symmetric Cryptography (January 2005)Google Scholar
- [Dau05]Daum, M.: Cryptanalysis of Hash Functions of the MD4-Family. PhD thesis, Ruhr-Universität Bochum (May 2005)Google Scholar
- [HPR04]Hawkes, P., Paddon, M., Rose, G.G.: Musings on the Wang et al. MD5 Collision. Cryptology ePrint Archive, Report 2004/264 (2004)Google Scholar
- [NSKO05]Naito, Y., Sasaki, Y., Kunihiro, N., Ohta, K.: Improved Collision Attack on MD4. Cryptology ePrint Archive, Report 2005/151 (2005), http://eprint.iacr.org/
- [Sch06]Schläffer, M.: Cryptanalysis of MD4. Master’s thesis, Institute for Applied Information Processing and Communications (IAIK), Graz University of Technology, Inffeldgasse 16a, 8010 Graz, Austria (February 2006)Google Scholar
- [WYY05a]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)Google Scholar
- [WYY05b]Wang, X., Yu, H., Yin, Y.L.: Efficient Collision Search Attacks on SHA-0. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 1–16. Springer, Heidelberg (2005)Google Scholar