Using Modular Extension to Provably Protect Edwards Curves Against Fault Attacks

Margaux Dugardin; Sylvain Guilley; Martin Moreau; Zakaria Najm; Pablo Rauzy

Using Modular Extension to Provably Protect Edwards Curves Against Fault Attacks

Margaux Dugardin ^{1, 2} Sylvain Guilley ^{2, 3} Martin Moreau ³ Zakaria Najm ⁴ Pablo Rauzy ^{5, 6}

1 THALES COMMUNICATIONS & SECURITY

2 Télécom ParisTech

3 Secure-IC S.A.S

4 ST-ROUSSET - STMicroelectronics [Rousset]

5 CITI - CITI Centre of Innovation in Telecommunications and Integration of services

6 LIASD - Laboratoire d'Informatique Avancée de Saint-Denis

Abstract : Fault injection attacks are a real-world threat to cryptosystems, in particular asymmetric cryptography. In this paper, we focus on countermeasures which guarantee the integrity of the computation result, hence covering most existing and future fault attacks. Namely, we study the modular extension protection scheme in previously existing and newly contributed variants of the countermeasure on elliptic curve scalar multiplication (ECSM) algorithms. We find that an existing countermeasure is incorrect and we propose new " test-free " variant of the modular extension scheme that fixes it. We then formally prove the correctness and security of modular extension: specifically, the fault non-detection probability is inversely proportional to the security parameter. Finally, we implement an ECSM protected with test-free modular extension during the elliptic curve operation to evaluate the efficient of this method on Edwards and twisted Edwards curves.

Keywords : fault injection attack modular extension asymmetric cryptography elliptic curve cryptography Edwards curves

Document type :

Conference papers

Domain :

Computer Science [cs] / Cryptography and Security [cs.CR]

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