Designs of Efficient Secure Large Hash Values

A double length hash function is a 2n-bit hash function based on an n-bit compression function. To increase the security level, designs of good double length hash functions are important. In this paper we construct a class of maximally secure double length hash functions in random oracle model based on some good permutations. This class contains recently proposed double length hash functions [16, 25]. We also propose an efficient double length hash function and study its security level in the random oracle model. We prove that any attack algorithm in the random oracle model needs Ω(2/(sn)) time complexity, where s is some parameter related to the rate of the hash function. Thus there is a trade-off between the efficiency and security. We use the notion of computable message [29] to make the security analysis of proposed hash functions. We also see that the security analysis of hash functions based on random permutations and hash functions based on random functions are very much related.