Аннотации:
he S-box is a key component of modern ciphers, determining the quality and
performance of the cryptographic algorithms in which it is applied. Many constructions for
synthesizing high-quality S-boxes have been established, and those based on Galois fields
theory—for example, the Nyberg construction applied in the AES cryptographic algorithm—
are particularly important. An integral component of the Nyberg construction is the affine
transformation, which is used to improve the avalanche and correlation properties of the
S-box. In this paper, a new approach is adopted for synthesizing affine transformations
for S-boxes based on the quaternary matrices over the Galois field GF(4). We describe
four basic structures that serve as the foundation for synthesizing a complete class of
648 affine transformation matrices of order n = 3 and a class of 7776 matrices of order n = 4
and introduce a recurrent structure to facilitate the synthesis of matrices for higher orders.
Using these matrices in combination with the Nyberg construction, it is possible to construct
bijective S-boxes that outperform the original Nyberg construction and many other known
S-boxes in terms of strict avalanche criterion (SAC) and bit independence criterion strict
avalanche criterion (BIC SAC) values, while maintaining a maximal level of nonlinearity
and good cryptographic properties. We also propose modified GF(4) affine transformations
that can be applied to specialized S-boxes which already satisfy the SAC for both component
Boolean and 4-functions, as well as the criterion of minimal correlation between input and
output, allowing us to enhance their nonlinearity to the value of Nf = 96. We integrate the
synthesized S-boxes into the AES algorithm and evaluate their practical performance. The
encryption outputs successfully pass the NIST statistical test suite in 96 out of 100 cases,
outperforming both the original AES S-box and other reference constructions, confirming
the practical strength of the proposed method.
