Quantum permutation pad for quantum secure symmetric and asymmetric cryptography Randy Kuang* [1]

https://www.academia.edu/3064-979X/2/1/10.20935/AcadQuant7457 This review delves into the latest advancements in quantum-secure cryptography, focusing on the quantum permutation pad (QPP), a pivotal innovation proposed by Kuang et al. QPP harnesses the non-commutativity and generalized uncertainty derived from the Galois permutation group, making it highly suitable for cryptographic applications. The review underscores QPP’s versatility across both symmetric and asymmetric cryptography through three core representations: matrix-based for classical encryption, quantum gates for quantum-native encryption, and arithmetic-based for multivariate public key systems such as Merkle–Hellman cryptosystems, multivariate public key cryptography (MPKC), and the most recent homomorphic polynomial public key (HPPK). In particular, QPP strengthens the security of HPPK’s key encapsulation mechanism (KEM) and digital signature (DS) schemes, thus offering robust quantum resistance. This work further examines QPP’s integration with various encryption techniques for enhancing resilience against quantum attacks. By addressing challenges in cryptographic complexity, key size optimization, and security enhancement, the review presents a thorough evaluation of QPP’s role in fortifying cryptographic protocols for ensuring strong security foundations in the quantum computing era.