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The number field sieve is an algorithm for finding the prime factors of large integers. It depends on algebraic number theory. Proposed by John Pollard in 1988, the method was used in 1990 to factor the ninth Fermat number, a 155-digit integer. The algorithm is most suited to numbers of a special form, but there is a promising variant that applies in general. This volume contains six research papers that describe the operation of the number field sieve, from both theoretical and practical perspectives. Pollard's original manuscript is included. In addition, there is an annotated bibliography of directly related literature.
Number theory --- Cribles (Mathématiques) --- Number sieves --- Sieves (Mathematics) --- Zeven (Wiskunde) --- 51 --- Mathematics --- Sieves (Mathematics). --- 51 Mathematics --- Nombres, Théorie des --- Informatique --- Data processing --- Informatique. --- Data processing. --- Theorie des nombres --- Theorie multiplicative
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Mathematical statistics --- Getaltheorie --- Nombres [Theorie des ] --- Number theory --- Economics --- Index numbers (Economics) --- Economie politique --- Nombres-indices --- Statistical methods --- Méthodes statistiques --- -Index numbers (Economics) --- AA / International- internationaal --- 304.1 --- Numbers, Index --- Prices --- Economic indicators --- Indexation (Economics) --- Economic theory --- Political economy --- Social sciences --- Economic man --- Theorie van de indexcijfers. --- Statistical methods. --- Index numbers (Economics). --- Méthodes statistiques --- Theorie van de indexcijfers --- Economics - Statistical methods
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Mathematical analysis --- Getaltheorie --- Mathematical sequences --- Nombres [Theorie des ] --- Number theory --- Numerical sequences --- Numerieke reeksen --- Reeksen (Wiskunde) --- Sequences (Mathematics) --- Spectra (Wiskunde) --- Spectral theory (Mathematics) --- Spectre (Mathematiques) --- Suites (Mathématiques) --- Suites numériques --- Wiskundige reeksen --- Number theory. --- 51 --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Algebra --- Mathematics --- Number study --- Numbers, Theory of --- 51 Mathematics
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Chiffrement --- Codes secrets --- Correspondance secrète --- Cryptage --- Cryptanalyse --- Cryptanalysis --- Cryptografie --- Cryptographie --- Cryptography --- Cryptologie --- Cryptology --- Déchiffrement --- Décodage --- Décryptage --- Décryptement --- Fractales --- Fractals --- Geometry [Non-Euclidean ] --- Getaltheorie --- Géometrie non-euclidienne --- Lettres secrètes --- Meetkunde [Niet-euclidische ] --- Messages cryptographiques --- Nombres [Theorie des ] --- Number theory --- Secret codes --- Secret writing --- Steganography --- Stéganographie --- Écriture cryptographique --- Écriture secrète --- Geometry, Non-Euclidean --- Géométrie non-euclidienne --- Théorie des nombres --- Geometry, Non-Euclidean. --- Number theory. --- Fractals. --- Cryptography. --- Géométrie non-euclidienne --- Théorie des nombres --- Number study --- Numbers, Theory of --- Algebra --- Non-Euclidean geometry --- Geometry --- Parallels (Geometry) --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Signs and symbols --- Symbolism --- Writing --- Ciphers --- Data encryption (Computer science) --- Foundations --- Geometry, Non-Euclidian. --- Number Theory --- Mathematiques --- Geometrie classique --- Arithmetique --- Vulgarisation
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