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
Next sessions
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Verification of Rust Cryptographic Implementations with Aeneas
Speaker : Aymeric Fromherz - Inria
From secure communications to online banking, cryptography is the cornerstone of most modern secure applications. Unfortunately, cryptographic design and implementation is notoriously error-prone, with a long history of design flaws, implementation bugs, and high-profile attacks. To address this issue, several projects proposed the use of formal verification techniques to statically ensure the[…] -
On the average hardness of SIVP for module lattices of fixed rank
Speaker : Radu Toma - Sorbonne Université
In joint work with Koen de Boer, Aurel Page, and Benjamin Wesolowski, we study the hardness of the approximate Shortest Independent Vectors Problem (SIVP) for random module lattices. We use here a natural notion of randomness as defined originally by Siegel through Haar measures. By proving a reduction, we show it is essentially as hard as the problem for arbitrary instances. While this was[…] -
Endomorphisms via Splittings
Speaker : Min-Yi Shen - No Affiliation
One of the fundamental hardness assumptions underlying isogeny-based cryptography is the problem of finding a non-trivial endomorphism of a given supersingular elliptic curve. In this talk, we show that the problem is related to the problem of finding a splitting of a principally polarised superspecial abelian surface. In particular, we provide formal security reductions and a proof-of-concept[…]-
Cryptography
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