The Self-Shrinking Conflation Generator: A Proposed Improvement to the Self-Shrinking Generator

Abstract

The backbone of many cybersecurity applications and algorithms require random numbers.  One of the most commonly used pseudo-random number generators is the Linear Feedback Shift Register (LFSR), which is fast, computationally inexpensive, and has excellent statistical properties. Unfortunately LFSRs have a number of weaknesses, some of which were addressed by decimation-based sequence generators such as the self-shrinking generator (SSG). Regrettably, the SSG was also found to be vulnerable to attack. In this paper, we propose an improvement to the SSG called the self-shrinking conflation generator (SSCG).  Our approach is based on the observation that what is discarded during the self-shrinking process of the SSG, is from a cryptographic perspective, just as good as that which is kept.  By combining the bits the SSG would normally discard with those it retains, using the exclusive OR (XOR) operation, we create a modified SSG bitstream with several improved characteristics. To highlight these improvements, we provide some mathematical security analysis associated with this approach, apply the NIST statistical test suite to several different bitstreams created using LFSRs driven by different degree primitive polynomials, and compare our results to that of the SSG.