Extended signature schemes and a non-mersenne prime RNG

Abstract

Lattice based cryptography is one of the new types of cryptography. Lattice is a mathematical construct which elements are disjoint and scatter in n-dimensional space in a consistent, repetitive pattern. The cryptography is based on the hard problem of finding the shortest non-zero element inside a lattice. Lattice based cryptographic construction such as encryption schemes and signature schemes are available already. In this research, we proposed a version of lattice based linear homomorphic signature scheme which is strong context hiding. And we revisited lattice based linear homomorphic encryption scheme and demonstrated its advantage as an alternative to the more powerful and universal fully homomorphic encryption scheme.

Non-cryptographic, general purpose pseudorandom number generators (GPRNG) have been applied in different areas, such as statistic simulation. Multiplicative linear congruential generators and Tausworthe-type LFSR generators are two main types of GPRNG. Both have underlying lattice structure for the values, that is the values generated fall on discrete planes of hyper-dimensional space only. This is not a desirable behaviour. MT19937 generator is one of the quite popular GPRNG. MT and its other Linear Feedback Shift Register (LFSR) cousins are mostly implemented over GF(2). In this research, we implemented a non-GF(2) LFSR generator. And if one has to applied generators with underlying lattice structures, one may consider applying generators with various underlying lattice structures. This non-GF(2) LFSR generator is a possible choice.