Code-based Cryptography: Lecture Notes

TL;DR

This paper provides an introductory overview of code-based cryptography, emphasizing the decoding problem's role in post-quantum security, with focus on McEliece and Alekhnovich schemes.

Contribution

It offers a comprehensive foundation on code-based cryptography, highlighting its security against quantum attacks and explaining key cryptographic schemes.

Findings

Decoding problem is central to code-based cryptography security.

McEliece and Alekhnovich schemes are prominent post-quantum cryptographic methods.

Code-based cryptography remains secure against quantum adversaries.

Abstract

These lecture notes have been written for courses given at \'Ecole normale sup\'erieure de Lyon and summer school 2022 in post-quantum cryptography that took place in the university of Budapest. Our objective is to give a general introduction to the foundations of code-based cryptography which is currently known to be secure even against quantum adversaries. In particular we focus our attention to the decoding problem whose hardness is at the ground of the security of many cryptographic primitives, the most prominent being McEliece and Alekhnovich' encryption schemes.