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A solution to the extended GCD problem with applications

1997
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Proceedings of the 1997 international symposium on Symbolic and algebraic computation - ISSAC '97
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This paper considers a variation of the extended gcd problem: the "modulo N extended gcd problem", Given an integer row vector [a, ]~=1. the modulo N extended gcd problem asks for an integer vector [c,]~=l such that n gcd(~c, a" N) = gcd(al, a~, . . .,a~, N) ,:1 A deterministic algorithm is presented which returns an exceptionally small solution for a given instance of the problem: both ma.x~=~Ic, I and the number of nonzero c,'s will he boundedbyO(logN). The gcd algorithm presented here has

doi:10.1145/258726.258762
fatcat:i5qyi3wkurc4hbwqc6qjw4bley