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Learn about the group of integers coprime to n under multiplication modulo n, denoted by or . Find out its order, structure, generators, and applications in number theory and cryptography.
Montgomery modular multiplication is a fast method for performing modular arithmetic operations using a special representation called Montgomery form. It is widely used in cryptography and requires division by a constant R, which is usually a power of two.
A comprehensive table of the time complexity of various algorithms for common mathematical operations on integers, polynomials, special functions, number theory, matrix algebra, and more. See big O notation, elementary functions, and quantum algorithms.
Learn about different methods to multiply two numbers, from long multiplication to fast algorithms with lower time complexity. Compare examples, pseudocode, and usage in computers.
Restoring division is a slow division method that operates on fixed-point fractional numbers and depends on the assumption that the divisor is not zero. It produces the quotient and remainder of Euclidean division using a recurrence equation and a partial remainder.
Learn how to find the greatest common divisor (GCD) of two or more integers, also known as greatest common factor (GCF), using different methods such as prime factorization and Euclid's algorithm. See examples, applications, and geometric views of GCD.