Profiling Attack against RSA Key Generation Based on a Euclidean Algorithm

Abstract

A profiling attack is a powerful variant among the noninvasive side channel attacks. In this work, we target RSA key generation relying on the binary version of the extended Euclidean algorithm for modular inverse and GCD computations. To date, this algorithm has only been exploited by simple power analysis; therefore, the countermeasures described in the literature are focused on mitigating only this kind of attack. We demonstrate that one of those countermeasures is not effective in preventing profiling attacks. The feasibility of our approach relies on the extraction of several leakage vectors from a single power trace. Moreover, because there are known relationships between the secrets and the public modulo in RSA, the uncertainty in some of the guessed secrets can be reduced by simple tests. This increases the effectiveness of the proposed attack.

Compact and Efficient Constant-Time GCD and Modular Inversion with Short-Iteration

“…p − 1 and q − 1; 2) 4|(p − 1)(q − 1), 2|(p − 1) and 2|(q − 1), the partial operational flow at the beginning of BEA (or BEEA) can be predicted in advance. Using all these characteristics, SPA, cache-timing attack (CTA), and machine learningbased profiling attack (MLPA) threaten the security of RSA key generation [4]- [6].…”

Parallel implementation of Wiener's attack on RSA: Algorithm design and performance evaluation

“…Since the publishment of the RSA cryptosystem, the system has been analyzed by numerous researchers to find its vulnerability [2]. Past studies have shown that if the private keys or public keys of the RSA system are not chosen carefully, the cryptosystem is feasible to be broken by a third party in a reasonable amount of time [2][3][4]. However, once the flaw of the cryptosystem is known, improvement can be made and thus the system is more robust.…”