Cryptology ePrint Archive: Report 2020/1368

On the Worst-Case Side-Channel Security of ECC Point Randomization in Embedded Devices

Melissa Azouaoui and François Durvaux and Romain Poussier and François-Xavier Standaert and Kostas Papagiannopoulos and Vincent Verneuil

Abstract: Point randomization is an important countermeasure to protect Elliptic Curve Cryptography (ECC) implementations against side-channel attacks. In this paper, we revisit its worst-case security in front of advanced side-channel adversaries taking advantage of analytical techniques in order to exploit all the leakage samples of an implementation. Our main contributions in this respect are the following: first, we show that due to the nature of the attacks against the point randomization (which can be viewed as Simple Power Analyses), the gain of using analytical techniques over simpler divide-and-conquer attacks is limited. Second, we take advantage of this observation to evaluate the theoretical noise levels necessary for the point randomization to provide strong security guarantees and compare different elliptic curve coordinates systems. Then, we turn this simulated analysis into actual experiments and show that reasonable security levels can be achieved by implementations even on low-cost (e.g. 8-bit) embedded devices. Finally, we are able to bound the security on 32-bit devices against worst-case adversaries.

Category / Keywords: implementation / Side-Channel Analysis, Elliptic Curve Cryptography, Point Randomization, Belief Propagation, Single-Trace Attacks

Original Publication (with minor differences): INDOCRYPT 2020

Date: received 30 Oct 2020

Contact author: melissa azouaoui at nxp com

Available format(s): PDF | BibTeX Citation

Version: 20201102:104155 (All versions of this report)

Short URL:

[ Cryptology ePrint archive ]