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We give a systematic overview of techniques to compute efficient arithmetic modulo 2xpy±12xpy±1. This is useful for computations in the supersingular isogeny Diffie-Hellman (SIDH) key-exchange protoco...
A New Model of Binary Elliptic Curves with Fast Arithmetic
Elliptic curve binary field scalar multiplication unified addition law differential addition cryptography
2010/11/30
This paper presents a new model of ordinary elliptic curves with fast arithmetic over field of characteristic two. In addition, we propose two isomorphism maps between new curves and Weierstrass curve...
Fast Arithmetic on ATmega128 for Elliptic Curve Cryptography
Optimal Extension Field Binary Fields Embedded Security
2009/6/9
Authentication protocols are indispensable in wireless sensor
networks. Commonly they are based on asymmetric cryptographic algorithms.
In this paper we investigate all categories of finite fields s...
FAST ARITHMETIC ON JACOBIANS OF PICARD CURVES
Jacobians Picard curves algebraic curves cryptography
2009/4/8
In this paper we present a fast addition algorithm in the Jacobian of a Picard curve over a finite field Fq of characteristic different from 3. This algorithm has a nice geometric interpretation, comp...