Solving systems of nonlinear polynomial equations faster
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Intractable problems in number theory (invited talk)
CRYPTO '88 Proceedings on Advances in cryptology
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Processor efficient parallel solution of linear systems over an abstract field
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
Dynamic threshold scheme based on the definition of cross-product in an N-dimensional linear space
CRYPTO '89 Proceedings on Advances in cryptology
On computing determinants of matrices without divisions
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Factoring high-degree polynomials by the black box Berlekamp algorithm
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Subquadratic-time factoring of polynomials over finite fields
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
On rank properties of Toeplitz matrices over finite fields
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
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
The structure of sparse resultant matrices
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Efficient parallel solution of sparse systems of linear diophantine equations
PASCO '97 Proceedings of the second international symposium on Parallel symbolic computation
Processor-efficient parallel matrix inversion over abstract fields: two extensions
PASCO '97 Proceedings of the second international symposium on Parallel symbolic computation
Certifying inconsistency of sparse linear systems
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
The complexity of the matrix eigenproblem
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Efficient computation of minimal polynomials in algebraic extensions of finite fields
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Diophantine linear system solving
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Discrete Logarithms: The Past and the Future
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Integer Smith form via the valence: experience with large sparse matrices from homology
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Black box Frobenius decompositions over small fields
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Early termination in Ben-Or/Tiwari sparse interpolation and a hybrid of Zippel's algorithm
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Black box methods for least squares problems
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Symbolic and numeric methods for exploiting structure in constructing resultant matrices
Journal of Symbolic Computation
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Certifying and repairing solutions to large LPs how good are LP-solvers?
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithms for Large Integer Matrix Problems
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Some Parallel Algorithms for Integer Factorisation
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
Recent Progress and Prospects for Integer Factorisation Algorithms
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
Solving Large Sparse Linear Systems over Finite Fields
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
A Subexponential Algorithm for Discrete Logarithms over All Finite Fields
CRYPTO '93 Proceedings of the 13th Annual International Cryptology Conference on Advances in Cryptology
On Fast and Provably Secure Message Authentication Based on Universal Hashing
CRYPTO '96 Proceedings of the 16th 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
Analysis of Bernstein's Factorization Circuit
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Factoring multivariate polynomials via partial differential equations
Mathematics of Computation
Special prime numbers and discrete logs in finite prime fields
Mathematics of Computation
An output-sensitive variant of the baby steps/giant steps determinant algorithm
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Early termination over small fields
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Computer algebra handbook
Early termination in sparse interpolation algorithms
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
The black-box Niederreiter algorithm and its implementation over the binary field
Mathematics of Computation
Computing the sign or the value of the determinant of an integer matrix, a complexity survey
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
Reliable Krylov-based algorithms for matrix null space and rank
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Elliptic and hyperelliptic curves on embedded μP
ACM Transactions on Embedded Computing Systems (TECS)
Improved algorithms for computing determinants and resultants
Journal of Complexity - Special issue: Foundations of computational mathematics 2002 workshops
IEEE Transactions on Computers
Signature of symmetric rational matrices and the unitary dual of lie groups
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
A reliable block Lanczos algorithm over small finite fields
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Preconditioners for singular black box matrices
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Journal of Algorithms
Solving sparse rational linear systems
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
A block Wiedemann rank algorithm
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Decentralized erasure codes for distributed networked storage
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
On probabilistic analysis of randomization in hybrid symbolic-numeric algorithms
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Numerical techniques for computing the inertia of products of matrices of rational numbers
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Faster inversion and other black box matrix computations using efficient block projections
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Efficient matrix rank computation with application to the study of strongly regular graphs
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Some recent progress in exact linear algebra and related questions
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Parallel computation of the rank of large sparse matrices from algebraic K-theory
Proceedings of the 2007 international workshop on Parallel symbolic computation
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Efficient Secure Linear Algebra in the Presence of Covert or Computationally Unbounded Adversaries
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
The design of e-traveler's check with efficiency and mutual authentication
Proceedings of the 3rd International Conference on Ubiquitous Information Management and Communication
On finding multiplicities of characteristic polynomial factors of black-box matrices
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Nearly optimal symbolic-numerical algorithms for structured integer matrices and polynomials
Proceedings of the 2009 conference on Symbolic numeric computation
Measuring and computing natural generators for homology groups
Computational Geometry: Theory and Applications
An Optimal Bloom Filter Replacement Based on Matrix Solving
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
Oracle-Assisted Static Diffie-Hellman Is Easier Than Discrete Logarithms
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
LT codes decoding: design and analysis
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Journal of Algorithms
An algorithm to solve integer linear systems exactly using numerical methods
Journal of Symbolic Computation
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
Secure linear algebra using linearly recurrent sequences
TCC'07 Proceedings of the 4th conference on Theory of cryptography
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Exact sparse matrix-vector multiplication on GPU's and multicore architectures
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
transalpyne: a language for automatic transposition
ACM Communications in Computer Algebra
An intelligent numerical algorithm for solving system of linear algebraic equations
Proceedings of the 1st Amrita ACM-W Celebration on Women in Computing in India
Journal of Symbolic Computation
Generating a d-dimensional linear subspace efficiently
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Algebraic and numerical algorithms
Algorithms and theory of computation handbook
Solving Very Sparse Rational Systems of Equations
ACM Transactions on Mathematical Software (TOMS)
A generalized method of moments for closed queueing networks
Performance Evaluation
Exact solutions to linear systems of equations using output sensitive lifting
ACM Communications in Computer Algebra
Algebraic cryptanalysis of curry and flurry using correlated messages
Inscrypt'09 Proceedings of the 5th international conference on Information security and cryptology
Kaltofen's division-free determinant algorithm differentiated for matrix adjoint computation
Journal of Symbolic Computation
Proceedings of the 36th international symposium on Symbolic and algebraic computation
An output-sensitive algorithm for persistent homology
Proceedings of the twenty-seventh annual symposium on Computational geometry
Parallelization of the Lanczos algorithm on multi-core platforms
ICDCN'10 Proceedings of the 11th international conference on Distributed computing and networking
Using wiedemann's algorithm to compute the immunity against algebraic and fast algebraic attacks
INDOCRYPT'06 Proceedings of the 7th international conference on Cryptology in India
Experiment of multithreading symbolic and algebraic computations with OpenMP
ICMS'06 Proceedings of the Second international conference on Mathematical Software
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
An algorithm to solve the discrete logarithm problem with the number field sieve
PKC'06 Proceedings of the 9th international conference on Theory and Practice of 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
Algebraic attacks on clock-controlled stream ciphers
ACISP'06 Proceedings of the 11th Australasian conference on Information Security and Privacy
Fast matrix rank algorithms and applications
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Exact solutions to linear programming problems
Operations Research Letters
Finite Fields and Their Applications
A note on the factorization method of Niederreiter
Finite Fields and Their Applications
New Techniques for the Computation of Linear Recurrence Coefficients
Finite Fields and Their Applications
On the Density of Normal Bases in Finite Fields
Finite Fields and Their Applications
Improving the berlekamp algorithm for binomials xn-a
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
On the complexity of solving quadratic Boolean systems
Journal of Complexity
Solving quadratic equations with XL on parallel architectures
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
An output-sensitive algorithm for persistent homology
Computational Geometry: Theory and Applications
Implicitization of curves and (hyper)surfaces using predicted support
Theoretical Computer Science
On the matrix berlekamp-massey algorithm
ACM Transactions on Algorithms (TALG)
Matrix sparsification and nested dissection over arbitrary fields
Journal of the ACM (JACM)
Fast matrix rank algorithms and applications
Journal of the ACM (JACM)
Fast matrix decomposition in F2
Journal of Computational and Applied Mathematics
Block Wiedemann algorithm on multicore architectures
ACM Communications in Computer Algebra
Probabilistic analysis of Wiedemann's algorithm for minimal polynomial computation
ACM Communications in Computer Algebra
| Hi-index | 754.84 |
A "coordinate recurrence" method for solving sparse systems of linear equations over finite fields is described. The algorithms discussed all requireO(n_{1}(omega + n_{1})log^{k}n_{1})field operations, wheren_{1}is the maximum dimension of the coefficient matrix,omegais approximately the number of field operations required to apply the matrix to a test vector, and the value ofkdepends on the algorithm. A probabilistic algorithm is shown to exist for finding the determinant of a square matrix. Also, probabilistic algorithms are shown to exist for finding the minimum polynomial and rank with some arbitrarily small possibility of error.