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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Solving homogeneous linear equations over $ {\rm GF}(2)$ via block Wiedemann algorithm

Author: Don Coppersmith
Journal: Math. Comp. 62 (1994), 333-350
MSC: Primary 11Y16; Secondary 11-04, 15A06, 15A33
MathSciNet review: 1192970
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Abstract: We propose a method of solving large sparse systems of homogeneous linear equations over $ GF(2)$, the field with two elements. We modify an algorithm due to Wiedemann. A block version of the algorithm allows us to perform 32 matrix-vector operations for the cost of one. The resulting algorithm is competitive with structured Gaussian elimination in terms of time and has much lower space requirements. It may be useful in the last stage of integer factorization.

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Article copyright: © Copyright 1994 American Mathematical Society

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