A Probabilistic Analysis on a Lattice Attack against DSA

TL;DR

This paper provides a probabilistic analysis of a lattice-based attack on DSA, simplifying previous methods and predicting attack success using lattice vector distributions validated through experiments.

Contribution

It introduces a probabilistic framework for analyzing the lattice attack on DSA, improving upon previous heuristic approaches.

Findings

The probabilistic model accurately predicts attack success rates.

Simplified the original lattice attack method.

Validated predictions with computational experiments.

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 attacks 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 Faug\`ere, Goyet and Renault during the conference SAC 2012: we simplify their method and we provide a probabilistic approach in opposition to the heuristic proposed in the former to measure the limits of the attack. More precisely, the main problem is formulated as the search for a closest vector to a lattice, then we study the distribution of the vectors with bounded norms in a this family of lattices and we apply the result to predict the behavior of the attack. We validated this approach by computational experiments.