How to construct pseudorandom permutations from pseudorandom functions

Reviewer: Pradip K. Srimani

The authors' main purpose in this paper is to propose an efficient strategy for the construction of a pseudorandom invertible permutation generator from a pseudorandom function generator. By combining this strategy with the previous result that a pseudorandom function generator can be built efficiently from a pseudorandom bit generator, the authors provide a ready method for the design of a block private key cryptosystem that is secure against chosen plaintext attack. Their correctness proofs and method of construction are elegant, and their presentation is excellent and fairly self-contained. Another important contribution of this paper is a more formal and mathematical description of the concepts of the well-known data encryption standard (DES) cryptographic methodology. The reader will need a reasonable amount of mathematical maturity, as well as a familiarity with complexity theory and combinatorics, to make complete sense of this paper. The authors provide precise and formal definitions for most of the terms and concepts in the area of cryptosystems security, and they largely succeed in giving a theoretical justification for the apparent security of the DES system. Anyone interested in the security of cryptosystems would benefit from reading this paper, even if she or he is not interested in the detailed mathematical proofs.