Luby-Rackoff Theorems

Abstract

In this chapter we will give complete proofs of the two results of Michael Luby and Charles Rackoff published in their important paper of 1988 (Luby and Rackoff, SIAM J. Comput. 17:373–386, 1988). These two results are: 1. A three (or more) rounds Feistel scheme with random round functions (or with pseudo-random round functions) will give us an invertible pseudo-random permutation generator. This means that we have a cryptosystem which is secure against chosen plaintext attacks. 2. A four (or more) rounds Feistel scheme with random round functions (or with pseudo-random round functions) will give us an invertible super pseudo-random permutation generator. This means that we have a cryptosystem which is secure against chosen plaintext and chosen ciphertext attacks.