منابع مشابه
ECM using Edwards curves
This paper introduces EECM-MPFQ, a fast implementation of the elliptic-curve method of factoring integers. EECM-MPFQ uses fewer modular multiplications than the well-known GMP-ECM software, takes less time than GMP-ECM, and finds more primes than GMP-ECM. The main improvements above the modular-arithmetic level are as follows: (1) use Edwards curves instead of Montgomery curves; (2) use extende...
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We present JKL-ECM, an implementation of the elliptic curve method of integer factorization which uses certain twisted Hessian curves in a family studied by Jeon, Kim and Lee. This implementation takes advantage of torsion subgroup injection for families of elliptic curves over a quartic number field, in addition to the ‘small parameter’ speedup. We produced thousands of curves with torsion Z/6...
متن کاملEdwards curves and CM curves
Edwards curves are a particular form of elliptic curves that admit a fast, unified and complete addition law. Relations between Edwards curves and Montgomery curves have already been described. Our work takes the view of parameterizing elliptic curves given by their j-invariant, a problematic that arises from using curves with complex multiplication, for instance. We add to the catalogue the li...
متن کاملBinary Edwards Curves
This paper presents a new shape for ordinary elliptic curves over fields of characteristic 2. Using the new shape, this paper presents the first complete addition formulas for binary elliptic curves, i.e., addition formulas that work for all pairs of input points, with no exceptional cases. If n ≥ 3 then the complete curves cover all isomorphism classes of ordinary elliptic curves over F2n . Th...
متن کاملTwisted Edwards Curves Revisited
This paper introduces fast algorithms for performing group operations on twisted Edwards curves, pushing the recent speed limits of Elliptic Curve Cryptography (ECC) forward in a wide range of applications. Notably, the new addition algorithm uses 8M for suitably selected curve constants. In comparison, the fastest point addition algorithms for (twisted) Edwards curves stated in the literature ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2012
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2012-02633-0