New Post-Quantum Cryptographic primitives schemes

Abstract

The sum of this computer and the Shor algorithm will compromise the security of many commonly used cryptographic algorithms based on number theory. Then, many researchers have begun to investigate to develop cryptographic algorithms that would be secure against quantum computers. In this thesis we developpe a new code-based cryptographic primitives schemes. Our contribution to code-based cryptography starts with showing that it is possible to reduce the public key length of the first provably secure group signature scheme from code-based assumptions without losing the security properties. Thereafter, we propose a new dynamic code-based group signature without trapdoor matrix. The general idea of this scheme consists in finding a collision between two ciphertexts using two different QC-MDPC matrices in McEliece cryptosystem. Our contribution continuous by using random double circulant codes to design a rank metric version of AGS identification scheme which is a five-pass protocol with a cheating probability of ½. Another way of our contribution is the presentation of the first mutual authentication protocol for RFID systems based on difficult problems from rank metric codes. We finish our contribution with a proposition of a cryptographic accumulator scheme and a fully dynamic group signature scheme. We instantiate our protocol with a double circulates code which allows us to get a small key size.