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An OutputSensitive Variant of the Baby Steps/Giant Steps Determinant Algorithm
, 2001
"... This paper provides an adaptive version of the unblocked baby steps/giant steps algorithm [20, Section 2]. The result is most easily stated when b # where # is the determinant to be computed and # with 1 is not known. Note that by Hadamard's bound # # n(b + log 2 (n)/2), so # = 0 co ..."
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This paper provides an adaptive version of the unblocked baby steps/giant steps algorithm [20, Section 2]. The result is most easily stated when b # where # is the determinant to be computed and # with 1 is not known. Note that by Hadamard's bound # # n(b + log 2 (n)/2), so # = 0 covers the worst case. We describe a Monte Carlo algorithm that produces # in (n bit operations, again with standard matrix arithmetic. The corresponding bit complexity of the early termination Gaussian elimination method is 4# , which is always more, and that of the algorithm by [10] is (n 1+1/2
On the complexity of computing determinants (Extended Abstract)
 ASCM 2001
"... The computation of the determinant of an n × n matrix A of numbers or polynomials is a challenge for both numerical and symbolic methods. Numerical methods, such as Clarkson’s algorithm [10, 7] for the sign of the determinant must deal with conditionedness that determines the number of mantissa bits ..."
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Cited by 2 (0 self)
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The computation of the determinant of an n × n matrix A of numbers or polynomials is a challenge for both numerical and symbolic methods. Numerical methods, such as Clarkson’s algorithm [10, 7] for the sign of the determinant must deal with conditionedness that determines the number of mantissa bits
Computation of discrete logarithms in F2607
 In Advances in Cryptology (AsiaCrypt 2001), Springer LNCS 2248
"... Abstract. We describe in this article how we have been able to extend the record for computationsof discrete logarithmsin characteristic 2 from the previousrecord over F 2 503 to a newer mark of F 2 607, using Coppersmith’s algorithm. This has been made possible by several practical improvementsto t ..."
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Cited by 1 (0 self)
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Abstract. We describe in this article how we have been able to extend the record for computationsof discrete logarithmsin characteristic 2 from the previousrecord over F 2 503 to a newer mark of F 2 607, using Coppersmith’s algorithm. This has been made possible by several practical improvementsto the algorithm. Although the computationshave been carried out on fairly standard hardware, our opinion is that we are nearing the current limitsof the manageable sizesfor thisalgorithm, and that going substantially further will require deeper improvements to the method. 1
Evaluation Report on the Discrete Logarithm Problem over finite fields
"... This document is an evaluation of the discrete logarithm problem over finite fields (DLP), as a basis for designing cryptographic schemes. It relies on the analysis of numerous research papers on the subject. The present report is organized as follows: firstly, we review the DLP and several ..."
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This document is an evaluation of the discrete logarithm problem over finite fields (DLP), as a basis for designing cryptographic schemes. It relies on the analysis of numerous research papers on the subject. The present report is organized as follows: firstly, we review the DLP and several