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Bit-slicing is a software implementation technique that treats an N-bitprocessor datapath as N parallel single-bit datapaths. The natural spatialredundancy of bit-sliced software can be used to build countermeasures againstimplementation attacks. While the merits of bit-slicing for side-channelcountermeasures have been studied before, their application for protection ofpost-quantum algorithms against fault injection is still unexplored. We presentan end-to-end analysis of the efficacy of bit-slicing to detect and thwartelectromagnetic fault injection (EMFI) attacks on post-quantum cryptography(PQC). We study Dilithium, a digital signature finalist of the NIST PQCcompetition. We present a bit-slice-redundant design for the Number-TheoreticTransform (NTT), the most complex and compute-intensive component in Dilithium.We show a data-redundant countermeasure for NTT which offers two concurrentbits for every single bit in the original implementation. We then implement afull Dilithium signature sequence on a 667 MHz ARM Cortex-A9 processorintegrated in a Xilinx Zynq SoC. We perform a detailed EM fault-injectionparameter search to optimize the location, intensity and timing of injected EMpulses. We demonstrate that, under optimized fault injection parameters, about10% of the injected faults become potentially exploitable. However, thebit-sliced NTT design is able to catch the majority of these potentiallyexploitable faults, even when the remainder of the Dilithium algorithm as wellas the control flow is left unprotected. To our knowledge, this is the firstdemonstration of a bitslice-redundant design of Dilithium that offersdistributed fault detection throughout the execution of the algorithm.

An End-to-End Analysis of EMFI on Bit-sliced Post-Quantum Implementations