Dynamic countermeasure against the Zero Power Analysis

Elliptic Curve Cryptography can be vulnerable to Side-Channel Attacks, such as the Zero Power Analysis (ZPA). This attack takes advantage of the occurrence of special points that bring a zero-value when computing a doubling or an addition of points. This paper consists in analysing this attack. Some properties of the said special points are explicited. A novel dynamic countermeasure is described. The elliptic curve formulæ are updated depending on the elliptic curve and the provided base point.

[1]  L. Washington.  Elliptic Curves: Number Theory and Cryptography, Second Edition , 2008 .

[2]  David Naccache,et al.  Low-Cost Countermeasure against RPA , 2012, CARDIS.

[3]  Elena Trichina,et al.  Implementation of Elliptic Curve Cryptography with Built-In Counter Measures against Side Channel Attacks , 2002, CHES.

[4]  Jean-Sébastien Coron,et al.  Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems , 1999, CHES.

[5]  Atsuko Miyaji,et al.  Efficient Elliptic Curve Exponentiation Using Mixed Coordinates , 1998, ASIACRYPT.

[6]  Louis Goubin,et al.  A Refined Power-Analysis Attack on Elliptic Curve Cryptosystems , 2003, Public Key Cryptography.

[7]  Tsuyoshi Takagi,et al.  Zero-Value Point Attacks on Elliptic Curve Cryptosystem , 2003, ISC.

[8]  Tsuyoshi Takagi,et al.  On the Optimal Parameter Choice for Elliptic Curve Cryptosystems Using Isogeny , 2004, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[9]  Nigel P. Smart,et al.  An Analysis of Goubin's Refined Power Analysis Attack , 2003, CHES.

[10]  Christophe Clavier,et al.  Universal Exponentiation Algorithm , 2001, CHES.

[11]  Marc Joye,et al.  Protections against Differential Analysis for Elliptic Curve Cryptography , 2001, CHES.

[12]  Marc Joye,et al.  Co-Z Addition Formulæ and Binary Ladders on Elliptic Curves - (Extended Abstract) , 2010, CHES.

[13]  Vincent Verneuil,et al.  Atomicity Improvement for Elliptic Curve Scalar Multiplication , 2010, CARDIS.

[14]  Kouichi Itoh,et al.  Efficient Countermeasures against Power Analysis for Elliptic Curve Cryptosystems , 2004, CARDIS.

[15]  Nicolas Meloni,et al.  New Point Addition Formulae for ECC Applications , 2007, WAIFI.

[16]  Marc Joye,et al.  (Virtually) Free Randomization Techniques for Elliptic Curve Cryptography , 2003, ICICS.