A Fast Stream Cipher with Huge State Space and Quasigroup Filter for Software

Recent personal computers have high-spec CPUs and plenty of memory. The motivation of this study is to take these advantages in designing a tough and fast key-stream generator. Natural controversies on using a large state space for a generator are (1) effectiveness is unclear, (2) slower generation speed, (3) expensive initialization, and (4) costs in a hardware implementation. Our proposal is to combine a linear feedback shift register (LFSR) and a uniform quasigroup filter with memory of wordsize. We prove theorems which assure the period and the distribution property of such generators, answering to (1). As for (2), the generation speed of a LFSR is independent of the state size. In addition, we propose a filter based on integer multiplication, which is rather fast in modern CPUs. We analyze the algebraic degree of such filters. We answer to (3) by a simple trick to use another small generator to initialize LFSR while outputting. We have no answer to (4), but comment that recent hardwares tend to have larger memory and sophisticated instructions. As a concrete example, we propose CryptMT stream generator with period (no less than) 219937−1, 1241-dimensional equidistribution property, which is sometimes faster than SNOW2.0 in modern CPUs.