Number-Theoretic Algorithms in Cryptography

O. N. Vasilenko



Algorithmic number theory is a rapidly developing branch of number theory, which, in addition to its mathematical importance, has substantial applications in computer science and cryptography. Among the algorithms used in cryptography, the following are especially important:

• algorithms for primality testing;
• factorization algorithms for integers and for polynomials in one variable;
• applications of the theory of elliptic curves;
• algorithms for computation of discrete logarithms;
• algorithms for solving linear equations over finite fields;
• algorithms for performing arithmetic operations on large integers.

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