A Differential Fault Attack on the Grain Family of Stream Ciphers

In this paper we study a differential fault attack against the Grain family of stream ciphers. The attack works due to certain properties of the Boolean functions and corresponding choices of the taps from the LFSR. The existing works, by Berzati et al. (2009) and Karmakar et al. (2011), are applicable only on Grain-128 exploiting certain properties of the combining Boolean function h. That idea could not easily be extended to the corresponding Boolean function used in Grain v1. Here we show that the differential fault attack can indeed be efficiently mounted for the Boolean function used in Grain v1. In this case we exploit the idea that there exists certain suitable α such that $h(\mathbf{x}) + h({\mathbf x} + \mathbf{\alpha})$ is linear. In our technique, we present methods to identify the fault locations and then construct set of linear equations to obtain the contents of the LFSR and the NFSR. As a countermeasure to such fault attack, we provide exact design criteria for Boolean functions to be used in Grain like structure.