Finding suitable curves for the elliptic curve method of factorization

Finding Suitable Curves for the Elliptic Curve Method of Factorization

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.

Fpga Implementation of Elliptic Curve Method for Factorization

The security of the most popular asymmetric cryptographic scheme RSA depends on the hardness of factoring large numbers. The best known method for factorization large integers is the General Number Field Sieve (GNFS). One important step within the GNFS is the factorization of midsize numbers for smoothness testing, an efficient algorithm for which is the Elliptic Curve Method (ECM). We present ...

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...

Elliptic Curve Factorization Method: Towards Better Exploitation of Reconfigurable Hardware

Currently, the best known algorithm for factorizing modulus of the RSA public key cryptosystem is the Number Field Sieve. One of its important phases usually combines a sieving technique and a method for checking smoothness of mid-size numbers. For this factorization, the Elliptic Curve Method (ECM) is an attractive solution. As ECM is highly regular and many parallel computations are required,...

Elliptic Curves Suitable for Pairing Based Cryptography