Improving the Rainbow Attack by Reusing Colours

Authors:
Martin Ågren;Thomas Johansson;Martin Hell
Affiliations:
Dept. of Electrical and Information Technology, Lund University, Lund, Sweden 221 00;Dept. of Electrical and Information Technology, Lund University, Lund, Sweden 221 00;Dept. of Electrical and Information Technology, Lund University, Lund, Sweden 221 00
Venue:
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
Year:
2009

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Abstract

Hashing or encrypting a key or a password is a vital part in most network security protocols. The most practical generic attack on such schemes is a time memory trade-off attack. Such an attack inverts any one-way function using a trade-off between memory and execution time. Existing techniques include the Hellman attack and the rainbow attack, where the latter uses different reduction functions ("colours") within a table. This work investigates the possibility of reusing colours, i.e., repeating the reduction functions, in the rainbow attack. We show how this outperforms the Hellman and the rainbow attack in a model of fixed resources. We try to characterize exactly when this improvement appears and in such a case the choice of an optimal number of colours.