From stream to provably secure block ciphers based on pseudorandom matrix transformations

Highlighting the various advantages (in terms of flexibility, reliability, development time and cost, etc.) of reusability of well-designed cryptographic primitives, particularly the fast pseudorandom (PR) number generators (PRNG) used in stream ciphers, and the high sensitivity (to changes), confusion, and pseudorandomness of highly nonlinear key and data-dependent PRNG-based matrix transformations, we develop new parameterized PR functions (PRF). To get length preserving output with uniform distribution and effectively thwart propagation of linear and differential terms and leak of key information for cryptanalysis, the proposed PRFpsilas incorporate PR operations with stream ciphering/word-wise modulus additions. Founded on a complement theorem of the central limit theorem, the proposed PRFpsilas can give almost uniform probability distribution. Evoking the Luby-Rackoff construction of super-PR permutations from PRFpsilas, we then present an extended family of provably secure, parameterized, variable key/blocklength block ciphers that flexibly fit a variety of applications.