Pseudorandom Functions and Factoring

The computational hardness of factoring integers is the most established assumption on which cryptographic primitives are based. This work presents an efficient construction of pseudorandom functions whose security is based on the intractability of factoring. In particular, we are able to construct efficient length-preserving pseudorandom functions, where each evaluation requires only a (small) constant number of modular multiplications per output bit. This is substantially more efficient than any previous construction of pseudorandom functions based on factoring and matches (up to a constant factor) the efficiency of the best-known factoring-based pseudorandom bit generators.

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