We present a general framework for constructing families of elliptic curves of prime order with prescribed embedding degree. We demonstrate this method by constructing curves with ...
We present an algorithm for generating elliptic curves of prime order over Optimal Extension Fields suitable for use in cryptography. The algorithm is based on the theory of Comple...
We develop an abstract framework that encompasses the key properties of bilinear groups of composite order that are required to construct secure pairing-based cryptosystems, and we...
Abstract. We further analyze the solutions to the Diophantine equations from which prime-order elliptic curves of embedding degrees k = 3, 4 or 6 (MNT curves) may be obtained. We g...
In their seminal paper, Miyaji, Nakabayashi and Takano [12] describe a simple method for the creation of elliptic curves of prime order with embedding degree 3, 4, or 6. Such curve...