Abstract
We present new techniques for deriving preimage resistance bounds for block cipher based double-block-length, double-call hash functions. We give improved bounds on the preimage security of the three “classical” double-block-length, double-call, block cipher-based compression functions, these being Abreast-DM, Tandem-DM and Hirose’s scheme. For Hirose’s scheme, we show that an adversary must make at least 22n − 5 block cipher queries to achieve chance 0.5 of inverting a randomly chosen point in the range. For Abreast-DM and Tandem-DM we show that at least 22n − 10 queries are necessary. These bounds improve upon the previous best bounds of Ω(2n) queries, and are optimal up to a constant factor since the compression functions in question have range of size 22n.
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Armknecht, F., Fleischmann, E., Krause, M., Lee, J., Stam, M., Steinberger, J. (2011). The Preimage Security of Double-Block-Length Compression Functions. In: Lee, D.H., Wang, X. (eds) Advances in Cryptology – ASIACRYPT 2011. ASIACRYPT 2011. Lecture Notes in Computer Science, vol 7073. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25385-0_13
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