Fault Attack on SQIsign

Abstract

In this paper, we introduce the first fault attack on SQIsign. By injecting a fault into the ideal generator during the commitment phase, we demonstrate a meaningful probability of inducing the generation of order O-0. The probability is bounded by one parameter, the degree of commitment isogeny. We also show that the probability can be reasonably estimated by assuming uniform randomness of a random variable, and provide empirical evidence supporting the validity of this approximation. In addition, we identify a loop-abort vulnerability due to the iterative structure of the isogeny operation. Exploiting these vulnerabilities, we present key recovery fault attack scenarios for two versions of SQIsign-one deterministic and the other randomized. We then analyze the time complexity and the number of queries required for each attack. Finally, we discuss straightforward countermeasures that can be implemented against the attack.