Two Approaches for Achieving Efficient Code-Based Cryptosystems

Code-based cryptography (CBC) is one of the most prominent post-quantum alternatives to conventional cryptography. Although quantumresistant and several times faster than its conventional counterparts, CBC is not widely deployed in practice. This is mostly due to its huge public-key sizes of several kilobytes. In this thesis, two different approaches to overcome this problem are introduced. One based on algebraic codes and another on graph-based codes. Effectively, in both cases, the public-key size is reduced to only a few kilobits, thus suppressing the main hindrance for the use of CBC in real-world applications. Moreover, under a quite reasonable assumption, we show that the security of the graph-based approach relies on a single well-studied problem. This is an important advantage in comparison with all CBC schemes and variants, including the classical McEliece scheme based on binary Goppa codes.