A timing attack on Blakley's modular multiplication algorithm, and applications to DSA

Abstract

In this paper, we introduce a timing attack scheme against a 160-bit modular multiplication with Blakley's algorithm. It is assumed that a set of public inputs are multiplied by a secret parameter and running time of each multiplication is given, but the multiplication result is not known and a machine similar to victim machine isn't available. The proposed attack extracts all 160 bits of the secret parameter. Running time of Blakley's algorithm is analyzed and it is shown that running time of each step is dependent on the running time of other steps. The dependencies make the parameters of the attack be dependent on the secret key, while it makes the attack rather complicated. A heuristic algorithm is used to find the parameters of the attack. As a real scenario, the attack is applied against on-line implementation of Digital Signature Algorithm, which employs Blakley's modular multiplication. Practical results show that secret key of DSA will be found using 1,000,000 timing samples. © Springer-Verlag Berlin Heidelberg 2007.