Code-Based Public-Key Cryptography

International audienceCode-based cryptography is among the most attractive post-quantum cryptographic techniques. It allows the construction of the most important cryptographic primitives (encryption, signature, zero-knowledge, hashing...) often with efficient implementations. In addition, their security is very well understood.The purpose of this course is to examine some of the main code-based cryptographic primitives, namely the McEliece and the Niederreiter public key encryption schemes, the CFS digital signature scheme, the Stern zero-knowledge identification protocol and some of their variants. For achieving this, we will first recall some fact on algebraic coding theory to introduce linear codes, binary Goppa codes, their decoding and main properties. Next we will consider the security aspects and examine the security assumptions and underlying hard problems. In particular, we will the best decoding techniques for generic linear codes. Those techniques provide the best cryptanalysis of code-based cryptosystems and their complexity analysis allows an accurate parameter selection. Finally we will present some new trends in the topic and have a look at the most important open problems