A Luby-Rackoff cipher is a Feistel cipher where in each round the nonlinear function used is assumed to be chosen uniformly at random from the set of all such functions. These ciphers are mainly of theoretical interest.

In their paper, Luby and Rackoff show how to construct 2n-bit Pseudorandom Permutations from n-bit random functions. The constructions use three and four rounds in Feistel networks with randomly chosen functions in the round functions. Let L and R be the left, respectively, the right n-bit halves of a 2n-bit input. Then one round of a Feistel network is defined as F(L,R)=(R,L XOR f(R)), where f:{0,1}n→{0,1}n is a randomly chosen function.

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