Experiments on Distributed Parallel Processing for Speeding up Prime Factorization in the Elliptic Curve Method
نویسندگان
چکیده
منابع مشابه
Elliptic Curve Method for Integer Factorization on Parallel Architectures
The elliptic curve method (ECM) for integer factorization is an algorithm that uses the algebraic structure of the set of points of an elliptic curve for factoring integers. The running time of ECM depends on the size of the smallest prime divisor of the number to be factored. One of its main applications is the co-factorization step in the number field sieve algorithm that is used for assessin...
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The Elliptic Curve Cryptosystem shortly called as (ECC) is one of the asymmetric key cryptosystems, which provides a high security for wireless applications compared to other asymmetric key cryptosystem. The implementation of this algorithm over prime field Zp has a set of point operations, which are point addition, point subtraction, point multiplication, point division, point inversion, and p...
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Using the parametrizations of Kubert, we show how to produce in nite families of elliptic curves which have prescribed nontrivial torsion over Q and rank at least one. These curves can be used to speed up the ECM factorization algorithm of Lenstra. We also brie y discuss curves with complex multiplication in this context.
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ژورنال
عنوان ژورنال: IEEJ Transactions on Electronics, Information and Systems
سال: 2002
ISSN: 0385-4221,1348-8155
DOI: 10.1541/ieejeiss1987.122.5_885