  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.
