Number Theory for Computing
Springer Science & Business Media, 9 de març 2013 - 381 pàgines
Mathematicians do not study objects, but relations among objectsj they are indifferent to the replacement of objects by others as long as relations do not change. Matter is not important, only form interests them. HENRI POINCARE (1854-1912) Computer scientists working on algorithms for factorization would be well advised to brush up on their number theory. IAN STEWART  The theory of numbers, in mathematics, is primarily the theory of the prop erties of integers (i.e., the whole numbers), particularly the positive integers. For example, Euclid proved 2000 years aga in his Elements that there exist infinitely many prime numbers. The subject has long been considered as the purest branch of mathematics, with very few applications to other areas. How ever, recent years have seen considerable increase in interest in several central topics of number theory, precisely because of their importance and applica tions in other areas, particularly in computing and information technology.
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algebraic Alice amicable pairs arithmetic binary bit operations called CFRAC Chinese Remainder Theorem ciphertext complexity Computer Science congruence conjecture decryption defined Definition denoted deterministic Diophantine equation discrete logarithm problem divisor element elliptic curve encryption Euclid's algorithm Euler's example exponential Fermat numbers Field Sieve finite Gauss gcd(a gcd(a,n hence infinitely input integer factorization introduce Jacobi symbol known Legendre symbol Lucas mathematician mathematics Mersenne primes method mod NB mod q multiplicative Note number theory O(log odd number odd perfect number odd prime Photo by courtesy plaintext polynomial positive integer primality testing prime factors Prime Number Theorem primitive root probabilistic probable prime proof public-key cryptography public-key cryptosystems quadratic residue quantum computer random number Re(s relatively prime residue classes residues modulo Riemann Hypothesis secret key secure sequence simple continued fraction solve subsection Suppose Table twin primes Z/nZ zeros