Titlebook: Elliptic Curve Public Key Cryptosystems; Alfred Menezes Book 1993 Springer Science+Business Media New York 1993 Potential.algorithms.crypt

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Implementation of elliptic Curve cryptosystems,te fields. For a secure system, it is evident from the results of Chapter 5 that the curve and underlying field should be judiciously chosen. However we should point out that for a given underlying field there are a large number of suitable elliptic curve to choose from. If the logarithm problem in

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Counting Points on Elliptic Curves Over F2m,field . The algorithm has a running time of 0(log. . bit operations, and is rather cumbersome in practice. Buchmann and Muller [20] combined Schoof’s algorithm with Shanks’ baby-step giant-step algorithm, and were able to compute orders of curves over F., where . is a 27-decimal digit prime. The alg

enormous

Book 1993hms for factoring integers and primalityproving, and in the construction of public key cryptosystems...Elliptic Curve Public Key Cryptosystems. provides an up-to-dateand self-contained treatment of elliptic curve-based public keycryptology. Elliptic curve cryptosystems potentially provideequivalent

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0893-3405 nt algorithms for factoring integers and primalityproving, and in the construction of public key cryptosystems...Elliptic Curve Public Key Cryptosystems. provides an up-to-dateand self-contained treatment of elliptic curve-based public keycryptology. Elliptic curve cryptosystems potentially providee

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Balázs Király,Margit Pap,Ákos Pilgermajer [68]. Unless otherwise stated, proofs of these results can be found in the book by J. Silverman [140]. For an elementary introduction to elliptic curves, we recommend the notes by Charlap and Robbins [26], and also to the recent book by Silverman and Tate [141].

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https://doi.org/10.1007/b137592sed. In Section 4.1 we briefly survey the algorithms known for this problem. In Section 4.2, we demonstrate efficient reductions of the logarithm problems in singular elliptic curves and some other groups to the logarithm problem in a finite field.

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FAWN

Introduction to Elliptic Curves, [68]. Unless otherwise stated, proofs of these results can be found in the book by J. Silverman [140]. For an elementary introduction to elliptic curves, we recommend the notes by Charlap and Robbins [26], and also to the recent book by Silverman and Tate [141].

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