For AES 128 security level there are several natural choices for pairing-friendly elliptic curves. In particular, as we will explain, one might choose curves with k = 9 or curves w...
Abstract. We provide the first construction of a hash function into ordinary elliptic curves that is indifferentiable from a random oracle, based on Icart's deterministic enco...
In this paper, a thorough bottom-up optimization process (field, point and scalar arithmetic) is used to speed up the computation of elliptic curve point multiplication and report ...
Pairing based cryptography is a new public key cryptographic scheme. An elliptic curve suitable for pairing based cryptography is called a “pairing-friendly” elliptic curve. Af...
The security of most elliptic curve cryptosystems is based on the intractability of the Elliptic Curve Discrete Logarithm Problem (ECDLP). Such a problem turns out to be computati...
Josep M. Miret, D. Sadornil, J. Tena, R. Tomas, Ma...
Abstract. 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 formula...
Daniel J. Bernstein, Tanja Lange, Reza Rezaeian Fa...
The theory of 4-descent on elliptic curves has been developed in the PhD theses of Siksek [18], Womack [21] and Stamminger [20]. Prompted by our use of 4-descent in the search for ...
Abstract. This paper revisits a model for elliptic curves over Q introduced by Huff in 1948 to study a diophantine problem. Huff's model readily extends over fields of odd cha...
Our purpose is to describe elliptic curves with complex multiplication which in characteristic 2 have the following useful properties for constructing Diffie-HeUman type cryptosys...
In this paper, we present two efficient algorithms computing scalar multiplications of a point in an elliptic curve defined over a small finite field, the Frobenius map of which ha...
Jung Hee Cheon, Sung-Mo Park, Sangwoo Park, Daeho ...