International Association
for Cryptologic Research

<p> We introduce a novel composition method that combines linear feedback registers into larger nonlinear structures and generalizes earlier methods such as cascade connections. We prove a Chaining Period Theorem which provides the cycle structure of these register constructions. We then use this Chaining Period Theorem and a new construction we call a Product Register (PR) to introduce a flexible and scalable register family with desirable properties, which we term Composite Mersenne Product Registers (CMPRs). We provide an algorithm to estimate the linear complexity of a chosen CMPR and investigate the statistical properties and security of a CMPR-based pseudorandom generator. Finally, we propose a family of CMPR-based stream ciphers and provide comparisons with the TRIVIUM stream cipher in terms of hardware area and security. </p>