Efficient FPGA Implementations of High-Dimensional Cube Testers on the Stream Cipher Grain-128

Cube testers are a generic class of methods for building distinguishers, based on cube attacks and on algebraic property-testers. In this paper, we report on an efficient FPGA implementation of cube testers on the stream cipher Grain-128. Our best result (a distinguisher on Grain-128 reduced to 237 rounds, out of 256) was achieved after a computation involving 2 clockings of Grain-128, with a 256×32 parallelization. An extrapolation of our results with standard methods suggests the possibility of a distinguishing attack on the full Grain-128 in time 2, which is well below the 2 complexity of exhaustive search. We also describe the method used for finding good cubes (a simple evolutionary algorithm), and report preliminary results on Grain-v1 obtained with a bitsliced C implementation. For instance, running a 30-dimensional cube tester on Grain-128 takes 10 seconds with our FPGA machine, against about 45 minutes with our bitsliced C implementation, and more than a day with a straightforward C implementation.