Public Key Perturbation of Randomized RSA Implementations

Among all countermeasures that have been proposed to thwart side-channel attacks against RSA implementations, the exponent randomization method - also known as exponent blinding - has been very early suggested by P. Kocher in 1996, and formalized by J.-S. Coron at CHES 1999. Although it has been used for a long time, some authors pointed out the fact that it does not intrinsically remove all sources of leakage. At CHES 2003, P.-A. Fouque and F. Valette devised the so-called "Doubling Attack" that can recover the blinded secret exponent from an SPA analysis. In this paper, we consider the case of fault injections. Although it was conjectured by A. Berzati et al. at CT-RSA 2009 that exponent randomization avoids fault attacks, we describe here how to recover the RSA private key under a practical fault model. Our attack belongs to the family of public key perturbations and is the first fault attack against RSA implementations with the exponent randomization countermeasure. In practice, for a 1024-bit RSA signature algorithms, the attack succeeds from about 1000 faulty signatures.