Source: Wikipedia. Pages: 55. Chapters: Algebraic-group factorisation algorithm, Congruence of squares, Continued fraction factorization, Dixon's factorization method, Euler's factorization method, Factor base, Fast Library for Number Theory, Fermat's factorization method, General number field sieve, Integer factorization, Integer factorization records, Lattice sieving, Lenstra elliptic curve factorization, Pollard's p ¿ 1 algorithm, Pollard's rho algorithm, Quadratic sieve, Rational sieve, RSA Factoring Challenge, RSA numbers, Shanks' square forms factorization, Shor's algorithm, Special number field sieve, Trial division, Williams' p + 1 algorithm. Excerpt: 86 article summaries including: Integer factorization algorithms . 2 Four Integer Factorization Algorithms . 3 Some integer factorization algorithms using elliptic curves . Improvement in the filtering step of integer factorization algorithms . The Elliptic Curve Method and Other Integer Factorization Algorithms . Lattice sieving and trial division . Special number field sieve . A kilobit special number field sieve factorization . Fast library for number theory : an introduction . 11 A deterministic version of Pollard's p-1 algorithm . An Introduction to the General Number Field Sieve . Integer Factorization . 15 Semiclassical Shor's Algorithm . 16 Robustness of Shor's algorithm . 18 Shor's algorithm without partial fractions . 19 Entanglement Simulations of Shor's Algorithm . 20 A Refinement of Shor's Algorithm . Integer Factorization Methods . 23 MapReduce for Integer Factorization . 24 Faster deterministic integer factorization . 25 Shor's Algorithm for Factoring Large Integers . 27 Shor's algorithm with fewer (pure) qubits . 28 Shor's algorithm on a nearest-neighbor machine . 29 Architecture-Dependent Execution Time of Shor's Algorithm . 30 Operator Imprecision and Scaling of Shor's Algorithm . 31 Entanglement and its Role in Shor's Algorithm . 32 Implementing Shor's algorithm on Josephson Charge Qubits . 34 A Note on Integer Factorization Using Lattices . System Intergration: Cluster Network - Large Integer Factorization . A Note on Integer Factorization Using Lattices . 37 Experimental demonstration of Shor's algorithm with quantum entanglement . 38 Shor's Algorithm from the Mindset of Quantum Oracles . 39 Circuit for Shor's algorithm using 2n+3 qubits . Shor's Algorithm and Grover's Algorithm in Quantum Computing . Factoring integers with large-prime variations of the quadratic sieve . Parallel Factorization using Quadratic Sieve Algorithm on SIMD machines . Integer Factorization: Solution via Algorithm for Constrained Discrete Logarithm Problem . Review of Methods for Integer Factorization Applied to Cryptography . Factor: an integer factorization program for the IBM PC . Experimental Demonstration of a Compiled Version of Shor's Algorithm with Quantum Entanglement . 49 Quantum chaos in the spectrum of operators used in Shor's algorithm . 50 Recovering the Period in Shor's Algorithm with Gauss' Algorithm for Lattice Basis Reduction . 51 Classical simulability and the significance of modular exponentiation in Shor's algorithm . 52 Scalability of Shor's algorithm with a limited set of rotation gates . 53 Implementation of Shor's Algorithm on a Linear Nearest Neighbour Qubit Array . Survey of computatio...