منابع مشابه
Twists of Elliptic Curves
If E is an elliptic curve over Q, then let E(D) denote the D−quadratic twist of E. It is conjectured that there are infinitely many primes p for which E(p) has rank 0, and that there are infinitely many primes ` for which E(`) has positive rank. For some special curves E we show that there is a set S of primes p with density 1 3 for which if D = Q pj is a squarefree integer where pj ∈ S, then E...
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In this paper we prove a relation between the period of an elliptic curve and the period of its real and imaginary quadratic twists. This relation is often misstated in the literature.
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Previously known techniques to construct pairing-friendly curves of prime or near-prime order are restricted to embedding degree k 6 6. More general methods produce curves over Fp where the bit length of p is often twice as large as that of the order r of the subgroup with embedding degree k; the best published results achieve ρ ≡ log(p)/ log(r) ∼ 5/4. In this paper we make the first step towar...
متن کاملConstructing elliptic curves of prime order
We present a very efficient algorithm to construct an elliptic curve E and a finite field F such that the order of the point group E(F) is a given prime number N . Heuristically, this algorithm only takes polynomial time e O((logN)), and it is so fast that it may profitably be used to tackle the related problem of finding elliptic curves with point groups of prime order of prescribed size. We a...
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A variation of the Complex Multiplication (CM) method for generating elliptic curves of known order over finite fields is proposed. We give heuristics and timing statistics in the mildly restricted setting of prime curve order. These may be seen to corroborate earlier work of Koblitz in the class number one setting. Our heuristics are based upon a recent conjecture by R. Gross and J. Smith on n...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2019
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2019.v26.n4.a10