A Probabilistic Analysis on a Lattice Attack against DSA
This work addresses security vulnerabilities in cryptographic systems for applications requiring robust encryption, but it is incremental as it builds on prior heuristic methods.
The paper tackles the problem of analyzing the security of DSA cryptosystems under lattice-based attacks that modify memory registers, providing a probabilistic approach to measure attack limits and validating it with computational experiments.
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 Faugère, 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.