Public Key Perturbation of Randomized RSA Implementations

Abstract

Abstract. 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 socalled "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.

Making RSA–PSS Provably Secure against Non-random Faults

“…This assumption can be justified by the fact that RSA-CRT computations are usually the privileged target of fault attacks since the secret exponent as well as the secret primes are involved. Sometimes, faults can be injected on public parameters [10,6], however such faults modify computation with secret values, σ p and σ q during CRT recombinaison and so this is treated in our model. In this model, we do not consider safe errors which consider specific implementations.…”

The Fault Attack Jungle - A Classification Model to Guide You

“…For example, a parity check of an addition or a multiplication. [27], [4], [3], [44], [11] [12], [21], [36], [39], [8], [23], [41], [42], [48], [28], [5], [24], [7], [17], [38], [43] [41], [42], [38], [43] Fault Model Bit Wise Word Wise Variable Wise [39], [9], [2], [5], [36], [12], [21], [8], [23] [4], [3], [47] [51], [25], [27], [44], [11], [48], [28], [24], [49], [7], [17] Abstraction Level…”

“…Cryptographic Primitive Level Protocol Level [3], [42], [28], [5], [24], [49], [7], [17], [38], [43] [36], [39], [4], [8], [23], [44], [11], [41], [48], [21] [12], [25], [27] At this point, it is important to emphasize that the security pyramid which depicts a design flow of a cryptographic engine does not consider validity of input parameters or the integrity of a program code intended to run on a platform. Since an attacker can exploit the faulty input parameters or a malicious program flow to leak a secret from a device, countermeasures that thwart such kinds of attacks are considered here too.…”

Modulus fault attacks against RSA–CRT signatures

“…The initial attack [27] only allowed to bypass RSA verification, but key-recovery attacks were later discovered by Brier et al [9], and improved or extended in [19,6,4,5]. These key-recovery attacks only apply to RSA without CRT, and they require significantly more faults than Boneh et al 's attack, at least on the order of 1000 faulty signatures.…”

“…The previously mentioned fault attacks [9,19,6,4,5] on RSA using faulty moduli only apply to standard RSA without CRT, and they use non-lattice techniques. Our attack seems to be the first attack on RSA-CRT with faulted moduli.…”