SpringerLink - Book Chapter

Protections against Differential Analysis for Elliptic Curve Cryptography — An Algebraic Approach —

Book Series

Lecture Notes in Computer Science

Publisher

Springer Berlin / Heidelberg

ISSN

0302-9743 (Print) 1611-3349 (Online)

Volume

Volume 2162/2001

Book

Cryptographic Hardware and Embedded Systems — CHES 2001

DOI

10.1007/3-540-44709-1

2001

ISBN

978-3-540-42521-2

DOI

10.1007/3-540-44709-1_31

Pages

377-390

Subject Collection

Computer Science

SpringerLink Date

Monday, January 01, 2001

Protections against Differential Analysis for Elliptic Curve Cryptography — An Algebraic Approach —

Marc Joye⁷ and Christophe Tymen⁸

(7)	Card Security Group, Gemplus Card International, Parc d’Activités de Gémenos, B.P. 100, 13881 Gémenos, France

(8)	Ecole Normale Supérieure, 45 rue d’Ulm, 75230 Paris, France

Abstract

We propose several new methods to protect the scalar multiplication on an elliptic curve against Differential Analysis. The basic idea consists in transforming the curve through various random morphisms to provide a non-deterministic execution of the algorithm.

The solutions we suggest complement and improve the state-of-the-art, but also provide a practical toolbox of efficient countermeasures. These should suit most of the needs for protecting implementations of crypto-algorithms based on elliptic curves.

Keywords Public-key cryptography - Side-channel attacks - Differential power analysis (DPA) - Timing attacks - Elliptic curves - Smart-cards

Marc Joye
Email: marc.joye@gemplus.com
URL: http://www.geocities.com/marcjoye/

Christophe Tymen
Email: christophe.tymen@gemplus.com

Protections against Differential Analysis for Elliptic Curve Cryptography — An Algebraic Approach —

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