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Efficient lattice-based zero-knowledge proofs and applications

Abstract : Lattice based cryptography has developed greatly in the last two decades, both with new and stimulating results such as fully-homomorphic encryption, and with great progress in the efficiency of existing cryptographic primitives like encryption and signatures which are becoming competitive with their number theoretic counterparts. On the other hand, even though they are a crucial part of many privacy-based protocols, zero-knowledge proofs of knowledge are still lagging behind in expressiveness and efficiency. The first goal of this thesis is to improve the quality of lattice-based proofs of knowledge. We construct new zero-knowledge proofs of knowledge such as a subset membership proof with size independent of the subset. We also work towards making zero-knowledge proofs more practical, by introducing a new amortized proof of knowledge that subsumes all previous results. Our second objective will be to use the proofs of knowledge we designed to construct novel and efficient cryptographic primitives. We build a group signature whose size does not depend on the size of the group, as well as a practical and highly scalable lattice-based e-voting scheme.
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Rafaël Del Pino. Efficient lattice-based zero-knowledge proofs and applications. Cryptography and Security [cs.CR]. Université Paris sciences et lettres, 2018. English. ⟨NNT : 2018PSLEE055⟩. ⟨tel-02445482⟩

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