Improving the arithmetic of elliptic curves in the Jacobi model
The use of elliptic curve cryptosystems on embedded systems has been becoming widespread for some years. Therefore the resistance of such cryptosystems to side-channel attacks is becoming crucial. Several techniques have recently been developed. One of these consists in finding a representation of the elliptic curve such that formulae for doubling and addition are the same. Until now, one of the best results has been obtained by using the Jacobi model. In this Letter, we improve the arithmetic of elliptic curves in the Jacobi model and we relax some conditions required to work efficiently on this model. We thus obtained the fastest unified addition formulae for elliptic curve cryptography (assuming that the curve has a 2-torsion point). (c) 2007 Elsevier B.V. All rights reserved.
elliptic curves side-channel attacks unified addition formulae cryptography