# Combined Attack on CRT-RSA. Why Public Verification Must Not Be Public?

3 PolSys - Polynomial Systems
LIP6 - Laboratoire d'Informatique de Paris 6, Inria Paris-Rocquencourt
Abstract : This article introduces a new Combined Attack on a CRT-RSA implementation resistant against Side-Channel Analysis and Fault Injection attacks. Such implementations prevent the attacker from obtaining the signature when a fault has been induced during the computation. Indeed, such a value would allow the attacker to recover the RSA private key by computing the $gcd$ of the public modulus and the faulty signature. The principle of our attack is to inject a fault during the signature computation and to perform a Side-Channel Analysis targeting a sensitive value processed during the Fault Injection countermeasure execution. The resulting information is then used to factorize the public modulus, leading to the disclosure of the whole RSA private key. After presenting a detailed account of our attack, we explain how its complexity can be significantly reduced by using lattice reduction techniques. We also provide simulations that confirm the efficiency of our attack as well as two different countermeasures having a very small impact on the performance of the algorithm. As it performs a Side-Channel Analysis during a Fault Injection countermeasure to retrieve the secret value, this article recalls the need for Fault Injection and Side-Channel Analysis countermeasures as monolithic implementations.
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Conference papers

Cited literature [40 references]

https://hal.inria.fr/hal-00777788
Contributor : Guénaël Renault <>
Submitted on : Thursday, December 12, 2013 - 12:20:02 PM
Last modification on : Thursday, March 21, 2019 - 12:59:38 PM
Document(s) archivé(s) le : Friday, March 14, 2014 - 9:22:06 AM

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CA-CRT-RSA.pdf
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### Citation

Guillaume Barbu, Alberto Battistelllo, Guillaume Dabosville, Christophe Giraud, Guénaël Renault, et al.. Combined Attack on CRT-RSA. Why Public Verification Must Not Be Public?. PKC 2013 - Public-Key Cryptography, Feb 2013, Nara, Japan. pp.198-215, ⟨10.1007/978-3-642-36362-7_13⟩. ⟨hal-00777788⟩

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