How to Construct Pseudorandom Permutations from Pseudorandom Functions

TLDR

Goldreich, Goldwasser, and Micali introduced the concept of a pseudorandom function generator and showed how to build one from a pseudorandom bit generator. The paper demonstrates how to efficiently construct a pseudorandom invertible permutation generator from a pseudorandom function generator. The construction uses ideas from the Data Encryption Standard to transform a pseudorandom function generator into a pseudorandom invertible permutation generator. The result implies that any pseudorandom bit generator can be used to build a block‑private‑key cryptosystem secure against chosen‑plaintext attacks.

Abstract

We show how to efficiently construct a pseudorandom invertible permutation generator from a pseudorandom function generator. Goldreich, Goldwasser and Micali ["How to construct random functions," Proc. 25th Annual Symposium on Foundations of Computer Science, October 24–26, 1984.] introduce the notion of a pseudorandom function generator and show how to efficiently construct a pseudorandom function generator from a pseudorandom bit generator. We use some of the ideas behind the design of the Data Encryption Standard for our construction. A practical implication of our result is that any pseudorandom bit generator can be used to construct a block private key cryptosystem which is secure against chosen plaintext attack, which is one of the strongest known attacks against a cryptosystem.