Common Points on Elliptic Curves: The Achilles’ Heel of Fault Attack Countermeasures
Elliptic curve cryptosystems offer many advantages over RSA-like cryptography, such as speed and memory saving. Nonetheless the advent of side-channel and fault-injection attacks mined the security of such implementations. Several countermeasures have been devised to thwart these threats, so that simple attacks on state-of-the-art secured implementations seem unlikely. We took up the challenge and show that a simple fault attack using a very relaxed fault model can defeat well known countermeasures. After introducing the notion of common points, we exhibit a new fault-injection attack that breaks state-of-the-art secured implementations. Our new attack is particularly dangerous since no control on the injected error is required and only one fault is sufficient to retrieve the secret.
KeywordsElliptic curves Fault attack Common points
I am grateful to Christophe Giraud for the many fruitful discussions and the time he spent to help me writing this paper. I would also like to thank Guillaume Barbu, Laurie Genelle, Emmanuelle Dottax, Franck Rondepierre and the anonymous reviewers of COSADE 2014 for their helpful comments.
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