Analysis of ways to increase stability of cryptographic algorithms on algebraic lattices against time attacks

Abstract

The aim of this work is to study the algorithms, the stability of which is based on the search for a short lattice vector, as well as to obtain time-resistant parameters of these algorithms. Existing methods for generating keys and choosing parameters for cryptographic transformations on algebraic lattices resistant to time attacks are considered. It is shown that the uniform distribution of coefficients for generating the NTRU algorithm keys has certain shortages, namely, a limited number of parameters suitable for use in cryptographical transformations. This is due to the vulnerability of this algorithm to time attacks. The possibility of using a discrete normal (Gaussian) distribution to form a key pair, which will prevent the sensitivity of the algorithm to time attacks, is considered. This method of generation requires checking the obtained sample for compliance with the properties of the normal distribution. The usage of SAGA tests has been proposed. They make it possible to check the Gaussian samples obtained using the discrete normal distribution. The verification result shows whether or not the sample has properties that are inherent in the normal distribution. The application of the SAGA statistical tests to the NTRU cryptographic transformation polynomials allowed us to conclude that the discrete Gaussian sample makes it possible to generate time-resistant parameters using the norm or the length of the short basis (vector) of the lattice as the mean-square deviation.