This paper characterizes collision preserving padding rules and provides variants of Merkle-Damgård (MD) which are having less or no overhead costs due to length. We first show that suffix-free property of padding rule is necessary as well as sufficient to preserve the collision security of MD hash... See full abstract

This paper characterizes collision preserving padding rules and provides variants of Merkle-Damgård (MD) which are having less or no overhead costs due to length. We first show that suffix-free property of padding rule is necessary as well as sufficient to preserve the collision security of MD hash function for an arbitrary domain {0,1}*. Knowing this, we propose a simple suffix-free padding rule padding only log|M| bits for a message M, which is less than that of Damgard’s and Sarkar’s padding rules. We also prove that the length-padding is not absolutely necessary. We show that a simple variant of MD with 10^d -padding (or any injective padding) is collision resistant provided that the underlying compression function is collision resistant after chopping the last-bit. Finally, we design another variant of MD hash function preserving all three basic security notions of hash functions, namely collision and (2nd) preimage, which is an improvement over a recently designed (SAC-08) three-property preserving hash function.
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