SYND: a Fast Code-Based Stream Cipher with a Security Reduction

Abstract

In this note we reconsider the code-based pseudorandom generator proposed by Fischer and Stern. This generator is proven as secure as the syndrome decoding problem but has two main drawbacks: it is slow (3000 bits/s) and a large size of memory is needed (88 kiloBytes). We propose a variation on the scheme which avoid them: the use of regular words speeds the system up and the use of quasi-cyclic codes allows a decrease of the memory requirements. We eventually obtain a generator as fast as AES in counter mode using only about 8000 bits of memory. We also give a more precise security reduction.