Synthesizers and Their Application to the Parallel Construction of Pseudo-Random Functions

A pseudo-random function is a fundamental cryptographic primitive that is essential for encryption, identification, and authentication. We present a new cryptographic primitive called pseudo-random synthesizer and show how to use it in order to get a parallel construction of a pseudo-random function. We show severalNC¹implementations of synthesizers based on concrete intractability assumptions as factoring and the Diffie–Hellman assumption. This yields the first parallel pseudo-random functions (based on standard intractability assumptions) and the only alternative to the original construction of Goldreich, Goldwasser, and Micali. In addition, we show parallel constructions of synthesizers based on other primitives such as weak pseudo-random functions or trapdoor one-way permutations. The security of all our constructions is similar to the security of the underlying assumptions. The connection with problems in computational learning theory is discussed.