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- Hüseyin Hisil, Kenneth Koon-Ho Wong, Gary Carter, Ed Dawson
- ASIACRYPT
- 2008

This paper introduces fast algorithms for performing group operations on twisted Edwards curves, pushing the recent speed limits of Elliptic Curve Cryptography (ECC) forward in a wide range of… (More)

- Joppe W. Bos, Craig Costello, Hüseyin Hisil, Kristin E. Lauter
- Journal of Cryptology
- 2013

In this paper, we highlight the benefits of using genus 2 curves in public-key cryptography. Compared to the standardized genus 1 curves, or elliptic curves, arithmetic on genus 2 curves is typically… (More)

- Hüseyin Hisil, Kenneth Koon-Ho Wong, Gary Carter, Ed Dawson
- ACISP
- 2009

This paper provides new results about efficient arithmetic on (extended) Jacobi<lb>quartic form elliptic curves y = dx + 2ax + 1. Recent works have shown that<lb>arithmetic on an elliptic curve in… (More)

- Joppe W. Bos, Craig Costello, Hüseyin Hisil, Kristin E. Lauter
- CHES
- 2013

This paper explores the potential for using genus 2 curves over quadratic extension fields in cryptography, motivated by the fact that they allow for an 8-dimensional scalar decomposition when using… (More)

- Hüseyin Hisil, Gary Carter, Ed Dawson
- INDOCRYPT
- 2007

This paper is on efficient implementation techniques of Elliptic Curve Cryptography. In particular, we improve timings for Jacobiquartic (3M+4S) and Hessian (7M+1S or 3M+6S) doubling operations. We… (More)

- Hüseyin Hisil, Craig Costello
- Journal of Cryptology
- 2014

This paper presents a new projective coordinate system and new explicit algorithms which together boost the speed of arithmetic in the divisor class group of genus 2 curves. The proposed formulas… (More)

- Hüseyin Hisil, Kenneth Koon-Ho Wong, Gary Carter, Ed Dawson
- AISC
- 2007

This paper improves implementation techniques of Elliptic Curve Cryptography. We introduce new formulae and algorithms for the group law on Jacobi quartic, Jacobi intersection, Edwards, and Hessian… (More)

- Craig Costello, Hüseyin Hisil, Benjamin E Smith
- EUROCRYPT
- 2013

We describe an implementation of fast elliptic curve scalar multiplication, optimized for Diffie–Hellman Key Exchange at the 128-bit security level. The algorithms are compact (using only… (More)

This paper presents efficient formulas for computing cryptographic pairings on the curve y = cx + 1 over fields of large characteristic. We provide examples of pairing-friendly elliptic curves of… (More)

- Craig Costello, Hüseyin Hisil
- ASIACRYPT
- 2017

We derive a new formula for computing arbitrary odd-degree isogenies between elliptic curves in Montgomery form. The formula lends itself to a simple and compact algorithm that can efficiently… (More)