A Non-commutative Cryptosystem Based on Quaternion Algebras
This work addresses the need for faster and more secure cryptosystems in cryptography, though it appears incremental as it builds upon existing NTRU-like methods.
The authors tackled the problem of improving the efficiency and security of NTRU-like cryptosystems by proposing BQTRU, a non-commutative cryptosystem based on quaternion algebras, which achieves approximately 16/7 times faster key generation and encryption than NTRU while offering higher resistance to attacks and allowing smaller key sizes for equivalent security.
We propose BQTRU, a non-commutative NTRU-like cryptosystem over quaternion algebras. This cryptosystem uses bivariate polynomials as the underling ring. The multiplication operation in our cryptosystem can be performed with high speed using quaternions algebras over finite rings. As a consequence, the key generation and encryption process of our cryptosystem is faster than NTRU in comparable parameters. Typically using Strassen's method, the key generation and encryption process is approximately $16/7$ times faster than NTRU for an equivalent parameter set. Moreover, the BQTRU lattice has a hybrid structure that makes inefficient standard lattice attacks on the private key. This entails a higher computational complexity for attackers providing the opportunity of having smaller key sizes. Consequently, in this sense, BQTRU is more resistant than NTRU against known attacks at an equivalent parameter set. Moreover, message protection is feasible through larger polynomials and this allows us to obtain the same security level as other NTRU-like cryptosystems but using lower dimensions.