ИСТИНА

Every automaton (a letter-to-letter transducer) whose input/output alphabets consist of p symbols produces a 1-Lipschitz map from p-adic integers to p-adic integers; and vice versa, every that map can be performed by a suitable automaton. Accordingly, straight line programs which are combined from arithmetic and/or bitwise logical instructions can be regarded as 1-Lipschitz 2-adic maps. That approach has been successfully applied applied to construct various cryptographic primitives (e.g., T-functions, cipher combiners, Latin squares, etc.) as well as pseudorandom generators and stream ciphers. Mathematically, these results can be considered as an application of algebraic (namely, p-adic) dynamics, especially of the p-adic ergodic theory. In the talk, recent advances in that area will be considered.