Description
In this thesis, we study two differentprimitives. Lossy trapdoor functions and zero-knwoledge proof systems.The lossy trapdoor functions (LTFs) arefunction families in which injective functionsand lossy ones are computationally indistin-guishable. Since their introduction, they havebeen found useful in constructing various cryp-tographic primitives. We give in this thesisefficient constructions of two different vari-ants of LTF: Lossy Algebraic Filter andR-LTF. With these two different variants, wecan improve the efficiency of the KDM-CCA(Key-Depended-Message Chosen-Ciphertext-Attack) encryption schemes, fuzzy extractoresand deterministic encryption.In the second part of this thesis, we in-vestigated on constructions of zero-knowledgeproof systems. We give the first logarithmic-size ring-signature with tight security usinga variant of Groth-KolhweizΣ-protocol in therandom oracle model. We also proposed onenew construction of lattice-based Designated-Verifier Non-Interactive Zero-Knowledge argu-ments (DVNIZK). Using this new construction, we build a lattice-based voting scheme in the standard model. lien: rien