An Improved Security Bound for HCTR

HCTR was proposed by Wang, Feng and Wu in 2005. It is a mode of operation which provides a tweakable strong pseudorandom permutation. Though HCTR is quite an efficient mode, the authors showed a cubic security bound for HCTR which makes it unsuitable for applications where tweakable strong pseudorandom permutations are required. In this paper we show that HCTR has a better security bound than what the authors showed. We prove that the distinguishing advantage of an adversary in distinguishing HCTR and its inverse from a random permutation and its inverse is bounded above by 4.5 i¾?2/2n, where nis the block-length of the block-cipher and i¾?is the number of n-block queries made by the adversary (including the tweak).

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