Timing Attacks on Error Correcting Codes in Post-Quantum Schemes

While error correcting codes (ECC) have the potential to significantly reduce the failure probability of post-quantum schemes, they add an extra ECC decoding step to the algorithm. Even though this additional step does not compute directly on the secret key, it is susceptible to side-channel attacks. We show that if no precaution is taken, it is possible to use timing information to distinguish between ciphertexts that result in an error before decoding and ciphertexts that do not contain errors, due to the variable execution time of the ECC decoding algorithm. We demonstrate that this information can be used to break the IND-CCA security of post-quantum secure schemes by presenting an attack on two round 1 candidates to the NIST Post-Quantum Standardization Process: the Ring-LWE scheme LAC and the Mersenne prime scheme Ramstake. This attack recovers the full secret key using a limited number of timed decryption queries and is implemented on the reference and the optimized implementations of both submissions. It is able to retrieve LAC's secret key for all security levels in under 2 minutes using less than $2^16 $ decryption queries and Ramstake's secret key in under 2 minutes using approximately $2400$ decryption queries. The attack generalizes to other lattice-based schemes with ECC in which any side-channel information about the presence of errors is leaked during decoding.