ORGANIZATION OF FAST EXPONENTIATION ON GALOIS FIELDS FOR CRYPTOGRAPHIC DATA PROTECTION SYSTEMS

Abstract

The object of the research described in the article is the process of calculating the exponent on finite Galois fields when implementing cryptographic mechanisms for protecting information with a public key.

The purpose of these studies is to speed up the exponentiation operation on Galois fields, which is basic for the implementation of a wide range of cryptographic data protection protocols through the use of precomputations that depend only on the forming Galois polynomial field.

To achieve the goal, the feature of performing exponentiation on Galois fields in public key cryptography is used - the constancy of the forming Galois field polynomial, which is part of the public key. This allows you to select calculations that depend only on the generating polynomial and perform them only once, saving the results in the precalculation tables. The use of precomputations allows not only to reduce the computational complexity of the exponentiation operation on Galois fields, but also to effectively use it to speed up the combination of the processing of several bits.

The article proposes the organization of accelerated execution of the basic operation of a wide range of cryptographic algorithms with a public key - exponentiation on finite Galois fields GF(2n). Acceleration of the computational implementation of this operation is achieved by organizing the processing of several bits of the code at once during squaring on Galois fields. This organization is based on the use of polynomial squared properties, Montgomery group reduction,  and extensive use of previous calculations. Procedures for performing basic operations of exponentiation on Galois fields are developed in detail, the work of which is illustrated by numerical examples. It has been proved that the proposed organization can increase the computational speed of this operation by 2.4 times, which is significant for cryptographic applications.