high performance computing on graphics processing units: hgpu.org

Random covers for finite groups have been introduced in [5, 9], and [18], and used for constructing public key cryptosystems. The primer [10] introduces a new approach for constructing pseudorandom number generators, called MSTg, based on random covers for large finite groups. In particular, on the class of elementary abelian 2-groups they allow a very efficient realization. The crucial point that makes random covers useful for group based cryptography is the fact, that the problem of finding a factorization with respect to a randomly generated cover is presumed intractable. In other words, random covers induce functions which possess the features of one-way functions. These in addition, as shown by results of statistical tests, behave randomly. We extend the preliminary tests done in [10] and investigate the statistical properties of the output sequences generated by MSTg on proposed class of groups and with different parameters, in particular the block size. We investigate the security of the system and claim that MSTg generators are suitable for cryptographic applications. Finally, we study the possibilities of parallelization of the generator algorithm and propose a method of using MSTg in practice.