YC: A Luby-Rackoff ciphers family driven by pseudorandom vector/matrix transformations

We first propose pseudorandom (PR) vector and matrix transformations-based family of parameterized PR functions (PRF) with matrices constructed using a highly nonlinear key and data dependent PR number generator. Presenting complement theorems of the central limit theorem, we base the uniformity of the PRFpsilas probability distribution functions on them. We then develop a family of parameterized Luby-Rackoff ciphers, named YC, with new modes of operations. The high nonlinearity, confusion, diffusion and pseudorandomness of its underlying PRFpsilas effectively resist propagation of linear/differential terms and leak of key information for cryptanalysis. YCpsilas are not practically vulnerable to known, chosen, adaptive plaintext/ciphertext, brute force and dictionary attacks. Extensive NIST statistical tests of the YCpsilas demonstrate their effectiveness. The flexibility of the YCpsilas makes them suitable for a wide range of applications and SW/HW implementation choices.