Entropy Transformation and Expansion with Quantum Permutation Pad for 5G Secure Networks

This paper proposes a quantum safe solution for 5G networks using a quantum permutation pad (or QPP) algorithm, originated from quantum computing logic gates or quantum permutation gates. All permutation gates form a unique permutation space, just like a classical key space. An n-bit permutation space consists of the entire 2 ⁿ ! permutation gates, or permutation matrices over its computational basis. The huge equivalent Shannon entropy of this permutation space would be a nice entropy source for information security. Kuang and Bettenburg in 2020 first proposed QPP and proved it to be the Shannon type of perfect secrecy. Here, we extend its capability of entropy transformations for distribution over the Internet to entropy expansions for 5G networks. We analyze the randomnesses following transformations and expansions with QPP, using industry randomness testing suites. Testing results confirm that QPP can maintain the original randomness of QRNG random numbers for transformations and expansions. Leveraging its strong diffusion capability, QPP may also improve the byte-level randomness of input random numbers.