In practice, this algorithm produces an elliptic curve of order 2 times a prime number. Therefore, these elliptic curves are appropriate for practical uses.
Jul 6, 2021 · In this paper, we propose an efficient technique to generate an elliptic curve of nearly prime order. Precisely, this algorithm produces an ...
Constructing an elliptic curve of prime order has a significant role in elliptic curve cryptography. In this paper, we propose an efficient technique to ...
Mar 3, 2017 · The elliptic curves we use for cryptography have large prime order subgroups (to make the discrete log program hard), perhaps you can use the ...
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Abstract. A variation of the Complex Multiplication (CM) method for generating elliptic curves of known order over finite fields is proposed.
Dec 15, 2008 · We prove in this paper that, under the GRH, there are at least 2.778 C_E^{\rm twin} x / (\log{x})^2 primes p such that |E(\F_p)| has at most 8 prime factors,
Pairing-friendly curves of prime or near-prime order are absolutely essential in certain pairing-based schemes like short signatures with longer useful life.
More precisely, they carried out an elliptic curve version of the classical result that there are infinitely many primes p such that p+2 has at most 4 distinct ...
We give a conjectural formula for the probability that the order of the quotient group E(\funnyFqp)/E(\funnyFq) E ( \funnyF q p ) / E ( \funnyF q ) is prime, ...
In mathematics, elliptic curve primality testing techniques, or elliptic curve primality proving (ECPP), are among the quickest and most widely used methods ...