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New Preimage Attacks Against Reduced SHA-1

Simon Knellwolf and Dmitry Khovratovich

This paper shows preimage attacks against reduced SHA-1 up to 57 steps. The best previous attack has been presented at CRYPTO 2009 and was for 48 steps finding a two-block preimage with incorrect padding at the cost of $2^{159.3}$ evaluations of the compression function. For the same variant our attacks find a one-block preimage at 2150.6 and a correctly padded two-block preimage at $2^{151.1}$ evaluations of the compression function. The improved results come out of a differential view on the meet-in-the-middle technique originally developed by Aoki and Sasaki. The new framework closely relates meet-in-the-middle attacks to differential cryptanalysis which turns out to be particularly useful for hash functions with linear message expansion and weak diffusion properties.