On the Design of Secure and Fast Double Block Length Hash Functions

In this work the security of the rate-1 double block length hash functions, which based on a block cipher with a block length of n-bit and a key length of 2n-bit, is reconsidered. Counter-examples and new attacks are presented on this general class of double block length hash functions with rate 1, which disclose uncovered flaws in the necessary conditions given by Satoh et al. and Hirose. Preimage and second preimage attacks are presented on Hirose’s two examples which were left as an open problem. Therefore, although all the rate-1 hash functions in this general class are failed to be optimally (second) preimage resistant, the necessary conditions are refined for ensuring this general class of the rate-1 hash functions to be optimally secure against the collision attack. In particular, two typical examples, which designed under the refined conditions, are proven to be indifferentiable from the random oracle in the ideal cipher model. The security results are extended to a new class of double block length hash functions with rate 1, where one block cipher used in the compression function has the key length is equal to the block length, while the other is doubled.