Binary Field Arithmetic using GMP Library in C Procedural Programming

Abstract

Almost all cryptographic algorithms involve the construction of integer arithmetic operations. The operations is referred to huge operation to an integer value in order to support the level of security of a cryptosystem. Related to this, the arithmetic operations in binary field is needed to construct various cryptographic algorithms. Binary field arithmetic implementation starts with the representation of its members, who then will be done by operating the addition, multiplication, reduction, and inversion. Each operation is simulated in 1024 bit length or more. Unlike the addition of polynomial operations that are directly applicable in the binary field , multiplication operations require reduction step necessary to build . Through experiments conducted for three types of reduction each Trinomial, Pentanomial, and Full Polynomial, apparently Full Polynomials provide the most high-speed reduction.