Advances in Applied Mathematics
Solving sparse linear equations over finite fields
IEEE Transactions on Information Theory
A public key cryptosystem and a signature scheme based on discrete logarithms
Proceedings of CRYPTO 84 on Advances in cryptology
The quadratic sieve factoring algorithm
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
Discrete logarithms in finite fields and their cryptographic significance
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
A pipeline architecture for factoring large integers with the quadratic sieve algorithm
SIAM Journal on Computing - Special issue on cryptography
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Parallel algorithms for integer factorisation
Number theory and cryptography
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
An FFT extension of the elliptic curve method of factorization
An FFT extension of the elliptic curve method of factorization
Discrete weighted transforms and large-integer arithmetic
Mathematics of Computation
Prime numbers and computer methods for factorization (2nd ed.)
Prime numbers and computer methods for factorization (2nd ed.)
Parallel collision search with application to hash functions and discrete logarithms
CCS '94 Proceedings of the 2nd ACM Conference on Computer and communications security
Factoring with two large primes
Mathematics of Computation
A course in computational algebraic number theory
A course in computational algebraic number theory
Randomized algorithms
Introduction to Special Section on Quantum Computation
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
A Fortran Multiple-Precision Arithmetic Package
ACM Transactions on Mathematical Software (TOMS)
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Cryptography: Theory and Practice
Cryptography: Theory and Practice
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
NFS with Four Large Primes: An Explosive Experiment
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
The Magic Words are Squeamish Ossifrage
ASIACRYPT '94 Proceedings of the 4th International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
A World Wide Number Field Sieve Factoring Record: On to 512 Bits
ASIACRYPT '96 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Computing Discrete Logarithms with the General Number Field Sieve
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
A Multiple Polynominal General Number Field Sieve
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
Modelling the Yield of Number Field Sieve Polynominals
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Massively parallel elliptic curve factoring
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
A block Lanczos algorithm for finding dependencies over GF(2)
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
Discrete Logarithms: The Past and the Future
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Recent Progress and Prospects for Integer Factorisation Algorithms
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
Factorization of a 512-bit RSA modulus
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Parallelization of Pollard's Rho Integer factorization algorithm
Proceedings of the Second International Conference on Computational Science, Engineering and Information Technology
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Algorithms for finding the prime factors of large composite numbers are of practical importance because of the widespread use of public key cryptosystems whose security depends on the presumed difficulty of the factorisation problem. In recent years the limits of the best integer factorisation algorithms have been extended greatly, due in part to Moore's law and in part to algorithmic improvements. It is now routine to factor 100-decimal digit numbers, and feasible to factor numbers of 155 decimal digits (512 bits). We describe several integer factorisation algorithms, consider their suitability for implementation on parallel machines, and give examples of their current capabilities.