Pseudo Quantum Random Number Generator with Quantum Permutation Pad

Cryptographic random number generation is critical for any quantum safe encryption. Based on the natural uncertainty of some quantum processes, variety of quantum random number generators or QRNGs have been created with physical quantum processes. They generally generate random numbers with good unpredictable randomness. Of course, physical QRNGs are costic and require physical integrations with computing systems. This paper proposes a pseudo quantum random number generator with a quantum algorithm called quantum permutation pad or QPP, leveraging the high entropy of quantum permutation space its bijective transformation. Unlike the Boolean algebra where the size of information space is 2n for an n-bit system, an n-bit quantum permutation space consists of 2n! quantum permutation matrices, representing all quantum permutation gates over an n-bit computational basis. This permutation space holds an equivalent Shannon information entropy log_2(2^n!). A QPP can be used to create a pseudo QRNG or pQRNG capable integrated with any classical computing system or directly with any application for good quality deterministic random number generation. Using a QPP pad with 64 8-bit permuation matrices, pQRNG holds 107,776 bits of entropy for the pseudo random number generation, comparing with 4096 bits of entropy in Linux /dev/random. It can be used as a deterministic PRNG or entropy booster of other PRNGs. It can also be used as a whitening algorithm for any hardware random number generator including QRNG without discarding physical bias bits.