A Post Quantum Light Weight Cryptographic Algorithm over Quaternion Integers

One of the discrete subgroup of Euclidean space, known as Lattices, play a crucial part in the construction of post-quantum cryptographic ciphers. Unlike classical public-key schemes vulnerable to quantum attacks, certain lattice-based constructions appear resistant to both classical and quantum adversaries. Key lattice problems, such as the Closest Vector Problem (CVP), contribute to the hardness of these constructions. On the other hand, the Quaternion integers, that have similar structure with lattices but having different operation, are not commonly used in cryptography. Nevertheless, the non-commutativity of their multiplication makes them suitable for constructing secure cryptographic modules. In this paper, we suggest a light weight post quantum symmetric cryptographic algorithm using the quaternion integers. The Learning with Error Problem (LWE), contribute to the hardness of the proposed algorithm. Moreover, the complex algebraic structures of quaternion integers add up algebraic security to the cipher against algebraic attacks. Lastly, the various analysis results show the strength of the proposed algorithm against the attacks.