The Side-Channel Resistance of Error Correcting Codes for Post Quantum Cryptography

This thesis examines: how can we secure error correcting codes against side-channel attacks so that they can be securely used in cryptography?, as well as how can they be used to improve certain lattice-based cryptosystems? The thesis discusses how error correcting codes can be used to reduce the size of ciphertexts produced by LWE based schemes. Examining the use of Gray codes to reduce the number of bit errors when multi-bit encryption techniques are used, the full analysis of how various techniques could be applied to current KEMs (rather than to just a general scheme) with scripts to enable researchers to find improved parameter sets from a given starting point, and to provide specific parameter sets for these KEMs. We move on to show how various linear algebra algorithms, including LUP Decomposition, can be made to be secure against side-channel attacks. We prove the security of these algorithms in the probing mode as well as giving experimental proofs. We then show how these algorithms can be used to create a secure version of the BCH code decoding algorithm. We also prove the security of these algorithms in the probing mode as well as giving experimental proofs. Having shown how to secure the BCH code decoding algorithm, we finally show how to secure the decoding algorithm for Polar codes. As with the BCH code decoding algorithm, we also prove the security of these algorithms in the probing mode as well as giving experimental proofs.