Fault Attacks on a Cloud-Assisted ECDSA White-Box Based on the Residue Number System

Ahstract-White-box cryptography aims at protecting software implementations of cryptographic algorithms when the attacker has complete control over the execution environment. Since the early 2000's, white-box implementations of block ciphers have received great interest from the community. Nevertheless and despite the needs of the industry, asymmetric cryptography has not really been studied in this context for many years. Indeed, it was only in 2020 that Zhou et al. published the very first asymmetric white-box design which aims at protecting ECDSA implementations. Their publication was a great step forward for the community which could finally tackle the subject of asymmetric white-box. In this paper, we study the security of this scheme and we exhibit efficient ways to recover the private key by using fault analysis. Indeed, we detail two different attacks which require two fault injections only to obtain the corresponding ECDSA private key. Finally, we also suggest a countermeasure that prevents both our attacks without impacting the size of the white-box or the performances of the scheme.