Why One Should Also Secure RSA Public Key Elements

It is well known that a malicious adversary can try to retrieve secret information by inducing a fault during cryptographic operations. Following the work of Seifert on fault inductions during RSA signature verification, we consider in this paper the signature counterpart. Our article introduces the first fault attack applied on RSA in standard mode. By only corrupting one public key element, one can recover the private exponent. Indeed, similarly to Seifert’s attack, our attack is done by modifying the modulus. One of the strong points of our attack is that the assumptions on the induced faults’ effects are relaxed. In one mode, absolutely no knowledge of the fault’s behavior is needed to achieve the full recovery of the private exponent. In another mode, based on a fault model defining what is called dictionary, the attack’s efficiency is improved and the number of faults is dramatically reduced. All our attacks are very practical. Note that those attacks do work even against implementations with deterministic (e.g., RSA-FDH) or random (e.g., RSA-PFDH) paddings, except for cases where we have signatures with randomness recovery (such as RSA-PSS). The results finally presented on this paper lead us to conclude that it is also mandatory to protect RSA’s public parameters against fault attacks.