Quantum Key Distribution(QKD) thrives to achieve perfect secrecy of One time Pad (OTP) through quantum processes. One of the crucial components of QKD are Quantum Random Number Generators(QRNG) for generation of keys. Unfortunately, these QRNG does not immediately produce usable bits rather it produces raw bits with high entropy but low uniformity which can be hardly used by any cryptographic system. A lot of pre-processing is required before the random numbers generated by QRNG to be usable. This causes a bottle neck in random number generation rate as well as QKD system relying on it. To avoid this lacuna of post-processing methods employed as a central part of Quantum Random Number Generators alternative approaches that satisfy the entropy(non determinism) and quantum security is explored. Pseudorandom generators based on quantum secure primitives could be an alternative to the post-processing problem as PRNGs are way more faster than any random number generator employing physical randomness (quantum mechanical process in QRNG) as well as it can provide uniform bits required for cryptography application. In this work we propose a pseudorandom generator based on post quantum primitives. The central theme of this random number generator is designing PRNG with non deterministic entropy generated through hard lattice problem - Learning with errors. We leverage the non determinism by Gaussian errors of LWE to construct non-deterministic PRNG satisfying the entropy requirement of QKD. Further, the paper concludes by evaluating the PRNG through Die-Harder Test.

翻译：量子密钥分发（QKD）致力于通过量子过程实现一次一密（OTP）的完美保密性。其关键组件之一是用于密钥生成的量子随机数生成器（QRNG）。然而，这类QRNG无法直接生成可用比特，而是产生具有高熵但低均匀性的原始比特，这难以被任何密码系统直接采用。在QRNG生成的随机数可用之前，需要大量预处理，这导致随机数生成速率及其依赖的QKD系统产生瓶颈。为规避作为量子随机数生成器核心环节的后处理方法存在的这一缺陷，本文探索了满足熵（非确定性）要求与量子安全性的替代方案。基于量子安全原语的伪随机生成器可作为后处理问题的替代方案，因为PRNG的速度远超任何采用物理随机性（如QRNG中的量子力学过程）的随机数生成器，同时能为密码应用提供所需的均匀比特。本文提出一种基于后量子原语的伪随机生成器。该随机数生成器的核心思想是，通过困难格问题——带误差学习（LWE）——生成具有非确定性熵的PRNG。我们利用LWE中高斯误差的非确定性构建满足QKD熵要求的非确定性PRNG。此外，本文通过Die-Harder测试对该PRNG进行了评估。