When performing a Tate pairing (or a derivative thereof) on an ordinary pairing-friendly elliptic curve, the computation can be looked at as having two stages, the Miller loop and the so-called final exponentiation. As a result of good progress being made to reduce the Miller loop component of the algorithm (particularly with the discovery of " truncated… (More)
When using pairing-friendly ordinary elliptic curves over prime fields to implement identity-based protocols, there is often a need to hash identities to points on one or both of the two elliptic curve groups of prime order r involved in the pairing. Of these G1 is a group of points on the base field E(F p) and G 2 is instantiated as a group of points with… (More)
A ciphertext-policy attribute-based encryption protocol uses bilinear pairings to provide control access mechanisms, where the set of user's attributes is specified by means of a linear secret sharing scheme. In this paper we present the design of a software cryptographic library that achieves record timings for the computation of a 126-bit security level… (More)
In this paper we show an efficient implementation of the Tate, ate and Rate pairings in magma. This will be demonstrated by using the KSS curves with embedding degree k = 18.
Elliptic-curve cryptography is becoming the standard public-key primitive not only for mobile devices but also for high-security applications. Advantages are the higher cryptographic strength per bit in comparison with RSA and the higher speed in implementations. To improve understanding of the exact strength of the elliptic-curve discrete-logarithm… (More)