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We prove that if f is a n-bit one-way permutation, i.e., it has some hard bits, a one-way permutation with n - k provably simultaneous hard bits can be constructed with it. We apply this construction to improve the efficiency of Blum-Micali pseudo-random bit generator. Then, we apply the construction to propose a new approach for building universal one-way hash functions. This approach merges Damgard's design principle (or Merkle's meta-method) and the method proposed by Zheng, Matsumoto and Imai for the construction of hash functions for long messages.

A Construction for One Way Hash Functions and Pseudorandom Bit Generators