LWR-based Quantum-Safe Pseudo-Random Number Generator

Abstract

Learning with Rounding (LWR) is a lattice-based cryptographically hard problem which quantum computers find difficult to solve. LWR problem is a derandomized variant of Learning with Errors (LWE) where deterministic rounding is used to generate errors efficiently. LWR can construct a secure seed for Quantum-Safe Pseudo-Random Number Generator (QSPRNG). This study is an endeavor to construct a QSPRNG to generate a stream of pseudo-random bits through a Linear Feedback Shift Register (LFSR). The proposed QSPRNG uses secure seed as an input and a Homomorphic Function for preserving the security of the internal states of LFSRs. NIST statistical tests, ENT, and DIEHARD tests are performed on constructed PRNG for randomness analysis. Also, security and speed analysis for the proposed QSPRNG has been done to illustrate its possible future utilization in cryptography.