Post-Quantum Cryptography in the Hamming Metric, the Rank Metric, and the Sum-Rank Metric

This thesis studies code-based cryptography from three different perspectives. First, three problems related to code-based cryptography are investigated and algorithms to solve them are presented. Then, attacks on the Twisted Reed-Solomon based McEliece scheme and on an implementation of the Hamming Quasi-Cyclic are developed. Last, the new scheme, LIGA, is proposed. It is based on the hardness of list decoding and interleaved decoding of Gabidulin codes; it features short ciphertext and key sizes, and no decryption failures.