APPLICATION OF MATHEMATICAL ELEMENTS IN CRYPTOGRAPHY
Keywords:
Discrete mathematic, modular arithmetic, prime number theory, discrete logarithm, elliptic curves, finite fields, combinatorics, probability theoryAbstract
Discrete mathematics is one of the most important scientific areas that form the theoretical basis of modern cryptography. Discrete areas such as prime number theory, modular arithmetic, finite fields, combinatorics, probability theory, graph structures, lattice theory, logical algebra, and algorithm theory form the internal mechanisms of modern encryption algorithms. Each mathematical operation used in the encryption process consists of bounded, discrete arithmetic performed on bits, and it is this discreteness that ensures that cryptosystems are deterministic, reliable, and secure. This article provides a comprehensive analysis of the role of discrete mathematics in various areas of cryptography.
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