Journal of Symbolic Computation
Algorithmica
Solving sparse linear equations over finite fields
IEEE Transactions on Information Theory
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
Matrix multiplication via arithmetic progressions
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Superfast solution of real positive definite toeplitz systems
SIAM Journal on Matrix Analysis and Applications
The algebraic eigenvalue problem
The algebraic eigenvalue problem
Computation of discrete logarithms in prime fields
Designs, Codes and Cryptography
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Factoring with two large primes (extended abstract)
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Schedulers as abstract interpretations of higher-dimensional automata
PEPM '95 Proceedings of the 1995 ACM SIGPLAN symposium on Partial evaluation and semantics-based program manipulation
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
On randomized Lanczos algorithms
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Discrete Logarithms: The Past and the Future
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
Recent Progress and Prospects for Integer Factorisation Algorithms
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
Computation of Discrete Logarithms in Prime Fields (Extended Abstract)
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
Designing and Detecting Trapdoors for Discrete Log Cryptosystems
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Massively Parallel Computation of Discrete Logarithms
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
NFS with Four Large Primes: An Explosive Experiment
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Computation of Discrete Logarithms in F2607
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
The Function Field Sieve Is Quite Special
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Factoring multivariate polynomials via partial differential equations
Mathematics of Computation
Computer algebra handbook
Reliable Krylov-based algorithms for matrix null space and rank
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Perturbed quantization steganography with wet paper codes
Proceedings of the 2004 workshop on Multimedia and security
Efficient matrix rank computation with application to the study of strongly regular graphs
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
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
An algorithm for solving the discrete log problem on hyperelliptic curves
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Pivoting algorithms for maximum likelihood decoding of LDPC codes over erasure channels
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
On construction of moderate-length LDPC codes over correlated erasure channels
ICC'09 Proceedings of the 2009 IEEE international conference on Communications
A generalized method of moments for closed queueing networks
Performance Evaluation
An experiment of number field sieve over GF(p) of low hamming weight characteristic
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
Parallelization of the Lanczos algorithm on multi-core platforms
ICDCN'10 Proceedings of the 11th international conference on Distributed computing and networking
An improvement of linearization-based algebraic attacks
InfoSecHiComNet'11 Proceedings of the First international conference on Security aspects in information technology
On the discrete logarithm problem on algebraic tori
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
All in the XL family: theory and practice
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
Solving a 676-bit discrete logarithm problem in GF(36n)
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
The function field sieve in the medium prime case
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Foundations and Trends in Communications and Information Theory
Fast matrix decomposition in F2
Journal of Computational and Applied Mathematics
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Many of the fast methods for factoring integers and computing discrete logarithms require the solution of large sparse linear systems of equations over finite fields. This paper presents the results of implementations of several linear algebra algorithms. It shows that very large sparse systems can be solved efficiently by using combinations of structured Gaussian elimination and the conjugate gradient, Lanczos, and Wiedemann methods.