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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| 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 62 |
| 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. |
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