caa a22 4500 475807308 CHVBK 20180406123750.0 cr unu---uuuuu 170329e20000401xx s 000 0 eng 10.1023/A:1008312401197 doi (NATIONALLICENCE)springer-10.1023/A:1008312401197 Analysis of the Xedni Calculus Attack [Elektronische Daten] [Michael Jacobson, Neal Koblitz, Joseph Silverman, Andreas Stein, Edlyn Teske] The xedni calculus attack on the elliptic curve discrete logarithm problem (ECDLP) involves lifting points from the finite field $${\mathbb{F}}_p$$ to the rational numbers $${\mathbb{Q}}$$ and then constructing an elliptic curve over $${\mathbb{Q}}$$ 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. Kluwer Academic Publishers, 2000 elliptic curve nationallicence discrete logarithm nationallicence Xedni calculus nationallicence Jacobson Michael aut Koblitz Neal aut Silverman Joseph aut Stein Andreas aut Teske Edlyn Centre for Applied Cryptographic Research, University of Waterloo, Waterloo, N2L 3G1, Ontario, Canada aut Designs, Codes and Cryptography Kluwer Academic Publishers 20/1(2000-04-01), 41-64 0925-1022 20:1<41 2000 20 10623 https://doi.org/10.1023/A:1008312401197 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1008312401197 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jacobson Michael aut NATIONALLICENCE 700 1- Koblitz Neal aut NATIONALLICENCE 700 1- Silverman Joseph aut NATIONALLICENCE 700 1- Stein Andreas aut NATIONALLICENCE 700 1- Teske Edlyn Centre for Applied Cryptographic Research, University of Waterloo, Waterloo, N2L 3G1, Ontario, Canada aut NATIONALLICENCE 773 0- Designs, Codes and Cryptography Kluwer Academic Publishers 20/1(2000-04-01), 41-64 0925-1022 20:1<41 2000 20 10623 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer