Zero-knowledge proofs and isogeny-based cryptosystems

In this thesis, we present some public-key cryptographic schemes. This work is divided in two halves. The rst half deals with zero-knowledge proofs in the classical setting and under falsi able assumptions. In particular, we improve upon the e ciency of an argument for linear equations, and we prese...

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Bibliographic Details
Author: Silva Velón, Javier
Format: doctoral thesis
Status:Published version
Publication Date:2021
Country:España
Institution:CBUC, CESCA
Repository:TDR. Tesis Doctorales en Red
OAI Identifier:oai:www.tdx.cat:10803/671222
Online Access:http://hdl.handle.net/10803/671222
Access Level:Open access
Keyword:Proof systems
Zero-knowledge proofs
Falsi able assumptions
Isogenies
Public-key cryptography
Sistemes de prova
Proves de coneixement nul
Hipòtesis falsificables
Isogènies
Criptografia de clau pública
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Summary:In this thesis, we present some public-key cryptographic schemes. This work is divided in two halves. The rst half deals with zero-knowledge proofs in the classical setting and under falsi able assumptions. In particular, we improve upon the e ciency of an argument for linear equations, and we present a proof of correct computation of a circuit that is of size logarithmic in the depth of the circuit. In the second half, we introduce a signature scheme, an encryption scheme and a trapdoor DDH scheme based on isogenies of supersingular elliptic curves. The signature and encryption schemes are secure against quantum adversaries.