Add to ORKGThe purpose of this paper is to generate cryptographically strong elliptic curves over prime fields Fp, where p is a Mersenne prime, one of the special primes or a random prime. We search for elliptic curves which orders are also prime numbers. The cryptographically strong elliptic curves are those for which the discrete logarithm problem is computationally hard. The required mathematical conditions are formulated in terms of parameters characterizing the elliptic curves.We present an algorithm to generate such curves. Examples of elliptic curves of prime order are generated with Magma
AbstractIn this paper, we give a family of elliptic curves E in the form y2=x3−c over the prime fiel...
This paper proposes a method for generating a certain composite order ordinary pairing–friendly elli...
We study and improve the CM-method for the creation of elliptic curves with specified group order ov...
The purpose of this paper is to generate cryptographically strong elliptic curves over prime fields ...
This paper proposes an algorithm for generating prime order elliptic curves over extension field who...
Nowadays the generation of cryptosystems requires two main aspects. First the security, and then the...
Cryptography is a constantly evolving field – elliptic curve groups have been a major part of this f...
With the dramatically increasing volume of sensitive information being transmitted wirelessly via th...
This article explores the use of elliptic curves with order 2r = 2 mod 4, which we call double-odd e...
We present a variation on the CM method that produces elliptic curves over prime fields with nearly ...
The subject of the thesis at hand is the description of an efficient algorithm for finding an ellipt...
Elliptic curves have found widespread use in number theory and applications thereof, such as cryptog...
The goal of this thesis is to study cryptographic applications of elliptic curves over the ring Fp["...
In the recent years, the need of information security has rapidly increased due to an enormous growt...
In the paper presents the mathematics of elliptic curves. As well as the derivation of addition form...
AbstractIn this paper, we give a family of elliptic curves E in the form y2=x3−c over the prime fiel...
This paper proposes a method for generating a certain composite order ordinary pairing–friendly elli...
We study and improve the CM-method for the creation of elliptic curves with specified group order ov...
The purpose of this paper is to generate cryptographically strong elliptic curves over prime fields ...
This paper proposes an algorithm for generating prime order elliptic curves over extension field who...
Nowadays the generation of cryptosystems requires two main aspects. First the security, and then the...
Cryptography is a constantly evolving field – elliptic curve groups have been a major part of this f...
With the dramatically increasing volume of sensitive information being transmitted wirelessly via th...
This article explores the use of elliptic curves with order 2r = 2 mod 4, which we call double-odd e...
We present a variation on the CM method that produces elliptic curves over prime fields with nearly ...
The subject of the thesis at hand is the description of an efficient algorithm for finding an ellipt...
Elliptic curves have found widespread use in number theory and applications thereof, such as cryptog...
The goal of this thesis is to study cryptographic applications of elliptic curves over the ring Fp["...
In the recent years, the need of information security has rapidly increased due to an enormous growt...
In the paper presents the mathematics of elliptic curves. As well as the derivation of addition form...
AbstractIn this paper, we give a family of elliptic curves E in the form y2=x3−c over the prime fiel...
This paper proposes a method for generating a certain composite order ordinary pairing–friendly elli...
We study and improve the CM-method for the creation of elliptic curves with specified group order ov...