Analysis of the Xedni calculus attack

Analysis of the Xedni calculus attack (2000)

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by Michael J. Jacobson , Neal Koblitz , Joseph H. Silverman , Andreas Stein , Edlyn Teske

Venue:	Design, Codes and Cryptography
Citations:	12 - 2 self

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@ARTICLE{Jacobson00analysisof,
    author = {Michael J. Jacobson and Neal Koblitz and Joseph H. Silverman and Andreas Stein and Edlyn Teske},
    title = {Analysis of the Xedni calculus attack},
    journal = {Design, Codes and Cryptography},
    year = {2000},
    volume = {20},
    pages = {41--64}
}

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Abstract

Abstract. The xedni calculus attack on the elliptic curve discrete logarithm problem (ECDLP) involves lifting points from the finite field Fp to the rational numbers Q and then constructing an elliptic curve over Q that passes through them. If the lifted points are linearly dependent, then the ECDLP is solved. Our purpose is to analyze the practicality of this algorithm. We find that asymptotically the algorithm is virtually certain to fail, because of an absolute bound on the size of the coefficients of a relation satisfied by the lifted points. Moreover, even for smaller values of p experiments show that the odds against finding a suitable lifting are prohibitively high.

Citations

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