Synthesis of Fault Attacks on Cryptographic Implementations

International audienceFault attacks are attacks in which an adversary with physical access to a cryptographic device, say a smartcard, tampers with the execution of an algorithm to retrieve secret mate-rial. Since the seminal Bellcore attack on modular exponen-tiation, there has been extensive work to discover new fault attacks against cryptographic schemes and develop counter-measures against such attacks. Originally focused on high-level algorithmic descriptions, these efforts increasingly fo-cus on concrete implementations. While lowering the ab-straction level leads to new fault attacks, it also makes their discovery significantly more challenging. In order to face this trend, it is therefore desirable to develop principled, tool-supported approaches that allow a systematic analy-sis of the security of cryptographic implementations against fault attacks. We propose, implement, and evaluate a new approach for finding fault attacks against cryptographic implementa-tions. Our approach is based on identifying implementation-independent mathematical properties, or fault conditions. We choose fault conditions so that it is possible to recover secret data purely by computing on sufficiently many data points that satisfy them. Fault conditions capture the essence of a large number of attacks from the literature, including lattice-based attacks on RSA. Moreover, they provide a ba-sis for discovering automatically new attacks: using fault conditions, we specify the problem of finding faulted imple-mentations as a program synthesis problem. Using a special-ized form of program synthesis, we discover multiple faulted attacks on RSA and ECDSA. Several of the attacks found by our tool are new, and of independent interest