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
Solving homogeneous linear equations over GF(2) via block Wiedemann algorithm
Mathematics of Computation
A Uniform Approach for the Fast Computation of Matrix-Type Pade Approximants
SIAM Journal on Matrix Analysis and Applications
Mathematics of Computation
Matrix-free linear system solving and applications to symbolic computation
Matrix-free linear system solving and applications to symbolic computation
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Modern computer algebra
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Solving Large Sparse Linear Systems over Finite Fields
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
The Solution of McCurley's Discrete Log Challenge
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Strategies in Filtering in the Number Field Sieve
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
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
Factorization of a 512-bit RSA modulus
EUROCRYPT'00 Proceedings of the 19th 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
On the complexity of polynomial matrix computations
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Polynomial evaluation and interpolation on special sets of points
Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage
Parallel computation of the rank of large sparse matrices from algebraic K-theory
Proceedings of the 2007 international workshop on Parallel symbolic computation
Polynomial evaluation and interpolation on special sets of points
Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage
A kilobit special number field sieve factorization
ASIACRYPT'07 Proceedings of the Advances in Crypotology 13th international conference on Theory and application of cryptology and information security
Faster multiplication in GF(2)[x]
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
Factorization of a 768-bit RSA modulus
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
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
Solving quadratic equations with XL on parallel architectures
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
On the matrix berlekamp-massey algorithm
ACM Transactions on Algorithms (TALG)
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This paper describes a new algorithm for computing linear generators (vector generating polynomials) for matrix sequences, running in subquadratic time. This algorithm applies in particular to the sequential stage of Coppersmith's block Wiedemann algorithm. Experiments showed that our method can be substituted in place of the quadratic one proposed by Coppersmith, yielding important speedups even for realistic matrix sizes. The base fields we were interested in were finite fields of large characteristic. As an example, we have been able to compute a linear generator for a sequence of 4 × 4 matrices of length 242 304 defined over F2607-1 in less than 2 days on one 667 MHz alpha ev67 CPU.