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A probabilistic analysis on a lattice attack against DSA

Abstract : Analyzing the security of cryptosystems under attacks based on the malicious modification of memory registers is a research topic of high importance. This type of attack may affect the randomness of the secret parameters by forcing a limited number of bits to a certain value which can be unknown to the attacker. In this context, we revisit the attack on DSA presented by Faugère, Goyet and Renault during the conference SAC 2012: we modify their method and provide a probabilistic approach in opposition to the heuristic proposed therein to measure the limits of the attack. More precisely, the main problem is formulated as a closest vector problem in a lattice, then we study the distribution of vectors with bounded norm in the lattices involved and apply the result to predict the attack behavior. The benefits of this approach are several: The probability of success of this attack can be lower bounded under some conjecture, which is validated by computational experiments. Also, it finds applications to the FLUSH+RELOAD side-channel attack, studied by van de Pol, Smart and Yarom. At the end of the article, there is a summary of findings.
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Contributor : Guénaël Renault Connect in order to contact the contributor
Submitted on : Sunday, December 13, 2020 - 3:44:19 PM
Last modification on : Wednesday, September 1, 2021 - 3:28:42 AM



Ana Gomez, Domingo Gomez-Perez, Guénaël Renault. A probabilistic analysis on a lattice attack against DSA. Designs, Codes and Cryptography, Springer Verlag, 2019, 87 (11), pp.2469-2488. ⟨10.1007/s10623-019-00633-w⟩. ⟨hal-03059975⟩



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