Integer Factorization Number Theory (16 results)

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In computational number theory, Williams' p + 1 algorithm is an integer factorization algorithm, one of the family of algebraic-group factorisation algorithms. It was invented by H. C. Williams in 1982. So, for different values of M we calculate gcd(N,VM 2), and when the result is not equal to 1 or to N, we have found a non-trivial factor of N. The values of M used are successive factorials, and VM is the M-th value of the sequence characterized by VM 1.…

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, algebraic number theory is a major branch of number theory which studies algebraic structures related to algebraic integers. This is generally accomplished by considering a ring of algebraic integers O in an algebraic number field K/Q, and studying their algebraic properties such as factorization, the behaviour of ideals, and field extensions. In this setting, the familiar features of the integers such as unique factorization need not hold. The virtue of the primary machinery employed Galois theory, group cohomology, group representations, and L-functions is that it allows one to deal with new phenomena and yet partially recover the behaviour of the usual integers.…

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In mathematics, the RSA numbers are a set of large semiprimes (numbers with exactly two prime factors) that are part of the RSA Factoring Challenge. The challenge was to find the prime factors but it was declared inactive in 2007. It was created by RSA Laboratories in 1991 to encourage research into computational number theory and the practical difficulty of factoring large integers. RSA Laboratories published a number of semiprimes with 100 to 617 decimal digits. Cash prizes of varying size were offered for factorization of some of them. The smallest RSA number was factored in a few days. Most of the numbers have still not been factored and many of them are expected to remain unfactored for quite some time. As of March 2008[update], 12 of the 54 listed numbers have been factored: The 9 smallest from RSA-100 to RSA-160, plus RSA-576, RSA-640 and RSA-200.…

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In number theory, a smooth number is an integer which factors completely into small prime numbers; the term seems coined by Leonard Adleman. Smooth numbers are especially important in cryptography relying on factorization.A positive integer is called B-smooth if none of its prime factors are greater than B. For example, 1,620 has prime factorization 22 × 34 × 5; therefore 1,620 is 5-smooth because none of its prime factors are greater than 5. 5-smooth numbers are also called regular numbers or Hamming numbers; 7-smooth numbers are sometimes called highly composite, although this conflicts with another meaning of that term.…

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In cryptography and number theory, TWIRL (The Relation Locator) is a hypothetical hardware device designed to speed up the sieving step of the general number field sieve integer factorization algorithm. During the sieving step, the algorithm searches for numbers with a certain mathematical relationship. In distributed factoring projects, this is the step that is parallelized to a large number of processors. TWIRL is still a hypothetical device - it has not yet been built. However, its designers, Adi Shamir and Eran Tromer, estimate that if TWIRL were built, it would be able to factor 1024-bit numbers in one year at the cost of 'a few dozen million '. TWIRL could therefore have enormous repercussions in cryptography and computer security - many high-security systems still use 1024-bit RSA keys, which TWIRL would be able to break in a reasonable amount of time and for reasonable costs.…

Taschenbuch. Condition: Neu. Twirl | Twirl, Cryptography, Number Theory, Integer Factorization | Cornelia Cecilia Eglantine | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786139337118 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand. …

Taschenbuch. Condition: Neu. Williams' p + 1 Algorithm | Computational Number Theory, Integer Factorization | Lambert M. Surhone (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786131187780 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand.…

Taschenbuch. Condition: Neu. Prime Place | Mathematics, Number Theory, Algebraic Structure, Algebraic Integer, Algebraic Number Field, Unique Factorization | Lambert M. Surhone (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786130515355 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand.…

Taschenbuch. Condition: Neu. Smooth Number | Number Theory, Integer, Integer Factorization, Prime Number, Leonard Adleman, Cryptography, Negative and Positive Numbers | Lambert M. Surhone (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786131243578 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand. …

Taschenbuch. Condition: Neu. RSA numbers | Mathematics, Semiprime, Prime Factor, RSA Factoring Challenge, RSA Security, Computational Number Theory, Integer Factorization, Integer, Decimal, Binary Numeral System | Lambert M. Surhone (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786130352578 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand.…

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Please note that the content of this book primarily consists of articlesavailable from Wikipedia or other free sources online. In number theoryinteger factorization or prime factorization is the breaking down of acomposite number into smaller non-trivial divisors, which whenmultiplied together equal the original integer. When the numbers arevery large, no efficient integer factorization algorithm is publiclyknown; an effort concluded in 2009 by several researchers factored a232-digit number (RSA-768) utilizing hundreds of machines over a span of2 years. The presumed difficulty of this problem is at the heart ofcertain algorithms in cryptography such as RSA.…

Taschenbuch. Condition: Neu. Prime Factor | Number Theory, Integer, Prime Number, Integer Factorization, Additive Function | Lambert M. Surhone (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786133309395 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand. …

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Please note that the content of this book primarily consists of articlesavailable from Wikipedia or other free sources online. In number theorythe prime factors of a positive integer are the prime numbers thatdivide that integer exactly, without leaving a remainder. The process offinding these numbers is called integer factorization, or primefactorization. A prime factor can be visualized by understandingEuclid's geometric position. He saw a whole number as a line segmentwhich has a smallest line segment greater than 1 that can divide equallyinto it. For a prime factor p of n, the multiplicity of p is the largestexponent a for which pa divides n. The prime factorization of a positiveinteger is a list of the integer's prime factors, together with theirmultiplicity. The fundamental theorem of arithmetic says that everypositive integer has a unique prime factorization.…

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Please note that the content of this book primarily consists of articlesavailable from Wikipedia or other free sources online. Paul Leyland is aBritish number theorist who has studied integer factorization andprimality testing.He has contributed to the factorization of RSA-129RSA-140, and RSA-155, as well as potential factorial primes as large as400! + 1. He has also studied Cunningham numbers, Cullen numbersWoodall numbers, etc., and numbers of the form xy + yx, which are nowcalled Leyland numbers. He has been involved with the NFSNet project.In2002 he co-authored a paper with Samuel S. Wagstaff Jr. entitled 'MPQSwith three large primes' in the Proceedings of the Algorithmic NumberTheory Symposium 2002. Since Wagstaff co-authored a paper with PaulErd¿s, this means Leyland has an Erd¿s number of 2.…

Taschenbuch. Condition: Neu. Paul Leyland | Number Theory, Integer Factorization, Primality Test | Lambert M. Surhone (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786134818698 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand. …

Taschenbuch. Condition: Neu. Special Number Field Sieve | Number Theory, Mathematics, Integer Factorization, General Number Field Sieve, Mersenne Number | Lambert M. Surhone (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786131201653 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand. …