How to construct a family of strong one way permutations
Much effort has been spent to identify the hard bits of one way functions, such as RSA and Rabin encryption functions. These efforts have been restricted to O(log n) hard bits. In this paper, we propose practical solutions for constructing a family of strong one way permutations such that when a member is chosen uniformly at random, with a high probability we get a one way permutation m, with t<n −O(log n), the maximum number of simultaneous hard bits. We propose two schemes. In the first scheme m is constructed with O(log n) fold iteration of f o g, where f is any one way permutation, g ∈ r G and G is a strongly universal2 family of polynomials in Galois field. In the second scheme m = f o g o h, where h is a hiding permutation. We suggest a practical solution based on this scheme. The strong one way permutations can be applied as an efficient tool to build pseudorandom bit generators and universal one way hash functions.
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