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J. Low Power Electron. Appl. 2017, 7(1), 3; doi:10.3390/jlpea7010003

Completing the Complete ECC Formulae with Countermeasures

1
Riscure BV, 2628 XJ Delft, The Netherlands
2
Institute for Computing and Information Sciences (ICIS), Radboud University, 6525 HP Nijmegen, The Netherlands
3
KU Leuven-imec-COSIC, KU Leuven, 3000 Leuven, Belgium
*
Author to whom correspondence should be addressed.
Received: 30 October 2016 / Accepted: 22 January 2017 / Published: 1 February 2017
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Abstract

This work implements and evaluates the recent complete addition formulae for the prime order elliptic curves of Renes, Costello and Batina on an FPGA platform. We implement three different versions:(1) an unprotected architecture; (2) an architecture protected through coordinate randomization; and (3) an architecture with both coordinate randomization and scalar splitting in place. The evaluation is done through timing analysis and test vector leakage assessment (TVLA). The results show that applying an increasing level of countermeasures leads to an increasing resistance against side-channel attacks. This is the first work looking into side-channel security issues of hardware implementations of the complete formulae. View Full-Text
Keywords: elliptic curve cryptography; FPGA; Weierstrass curves; complete formulas; side-channel attacks and countermeasures elliptic curve cryptography; FPGA; Weierstrass curves; complete formulas; side-channel attacks and countermeasures
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Chmielewski, Ł.; Massolino, P.M.C.; Vliegen, J.; Batina, L.; Mentens, N. Completing the Complete ECC Formulae with Countermeasures. J. Low Power Electron. Appl. 2017, 7, 3.

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J. Low Power Electron. Appl. EISSN 2079-9268 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
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