Algorithmica
Advances in Applied Mathematics
Solving sparse linear equations over finite fields
IEEE Transactions on Information Theory
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
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
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.)
Factoring with two large primes
Mathematics of Computation
A course in computational algebraic number theory
A course in computational algebraic number theory
Moore's law: past, present, and future
IEEE Spectrum
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 method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Some Parallel Algorithms for Integer Factorisation
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
Solving Large Sparse Linear Systems over Finite Fields
CRYPTO '90 Proceedings of the 10th 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
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
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
Cryptanalysis of RSA Using the Ratio of the Primes
AFRICACRYPT '09 Proceedings of the 2nd International Conference on Cryptology in Africa: Progress in Cryptology
Computational Complexity in Non-Turing Models of Computation
Electronic Notes in Theoretical Computer Science (ENTCS)
A tutorial on high performance computing applied to cryptanalysis
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Fast matrix decomposition in F2
Journal of Computational and Applied Mathematics
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The integer factorisation and discrete logarithm problems are of practical importance because of the widespread use of public key cryptosystems whose security depends on the presumed diffculty of solving these problems. This paper considers primarily the integer 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 outline several integer factorisation algorithms, consider their suitability for implementation on parallel machines, and give examples of their current capabilities. In particular, we consider the problem of parallel solution of the large, sparse linear systems which arise with the MPQS and NFS methods.