O-GGH: THE GGH PUBLIC KEY CRYPTOSYSTEM VIA OCTONION ALGEBRA AND POLYNOMIAL RINGS

Designing new and improving existing lattice-based public key cryptosystem have attracted attentions in the literature. The Goldreich, Goldwasser and Halevi (GGH) was one of those first proposed lattice based encryption algorithms. The closest vector problem (CVP) and the shortest vector problem (SVP) are considered for lattice complexity and difficulty. Although, the GGH cryptosystem is known as broken for dimensions of 400, however, proposing improvements can make resistance against lattice reductions. In this study, a novel approach for improving GGH cryptosystem is presented by taking advantage of octonion algebra (known as non-commutative and non-associative algebra) and polynomial rings to tackle with the shortcomings of the original GGH and its variants. The new proposed O-GGH increases the security and complexity of GGH. The key generation, encryption, and decryption procedures of O-GGH have been discussed in details. And, it has been shown that O-GGH is resistant to lattice based attacks at even lower values of dimensions (i.e., 50).