A series of recent algorithmic advances has delivered highly effective methods for pairing evaluation and parameter generation. However, the resulting multitude of options means m...
We derive a new algorithm for computing the Tate pairing on an elliptic curve over a finite field. The algorithm uses a generalisation of elliptic divisibility sequences known as...
A proxy re-encryption system allows the proxy to transform ciphertexts encrypted under Alice’s public key into the different ciphertexts that can be decrypted by Bob’s secret ...
— In EUROCRYPT 2006, Cheon proposed breakthrough algorithms for pairing-related problems such as the q-weak/strong Diffie-Hellman problem. Using that the exponents of an element ...
Let C be a curve of genus g, defined over a finite field Fq, where q = pm for a prime p. Let N be a large integer coprime to p, dividing the order of the Jacobian variety associ...
We assemble and reorganize the recent work in the area of hyperelliptic pairings: We survey the research on constructing hyperelliptic curves suitable for pairing-based cryptograph...
Steven D. Galbraith, Florian Hess, Frederik Vercau...
We provide the first explicit construction of genus 2 curves over finite fields whose Jacobians are ordinary, have large prime-order subgroups, and have small embedding degree. ...