Isomorphism in Multivariate Cryptography using the New Mersenne Number Transform

Emerole, KC; Boussakta, S

doi:10.1109/ICC45855.2022.9838751

Isomorphism in Multivariate Cryptography using the New Mersenne Number Transform

Lookup NU author(s): Kelechi Emerole, Professor Said Boussakta

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Abstract

Multivariate cryptosystem employs affine isomorphism to hide the structure of quadratic forms that make up the central polynomial. However, the ease of inverting the affine isomorphism and consequently finding the rank of the quadratic form of the core map has made such cryptosystem susceptible to key recovery attacks. Also, the density of the affine matrix has led to increase in the secret key size with its attendant overhead. In this paper, we study and apply the kernel function of the New Mersenne number transform to hide the structure of the core map(central polynomial) to limit the interpolation of the rank of the quadratic form by an adversary. Also, a modified Montgomery reduction is applied to carry out modulo reduction of the polynomial in degree extension field. Finally, we compare the impact of the kernel function of the New Mersenne Number Transform and the Affine transform on the key size of the HFEv signature scheme. From the result, it can be seen that their is an average of 69% reduction of secret key size using the proposed method.