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Article

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.
J. Low Power Electron. Appl. 2017, 7(1), 3; https://0-doi-org.brum.beds.ac.uk/10.3390/jlpea7010003
Received: 30 October 2016 / Accepted: 22 January 2017 / Published: 1 February 2017
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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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. https://0-doi-org.brum.beds.ac.uk/10.3390/jlpea7010003

AMA Style

Chmielewski Ł, Massolino PMC, Vliegen J, Batina L, Mentens N. Completing the Complete ECC Formulae with Countermeasures. Journal of Low Power Electronics and Applications. 2017; 7(1):3. https://0-doi-org.brum.beds.ac.uk/10.3390/jlpea7010003

Chicago/Turabian Style

Chmielewski, Łukasz, Pedro M.C. Massolino, Jo Vliegen, Lejla Batina, and Nele Mentens. 2017. "Completing the Complete ECC Formulae with Countermeasures" Journal of Low Power Electronics and Applications 7, no. 1: 3. https://0-doi-org.brum.beds.ac.uk/10.3390/jlpea7010003

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