• cryptography
• CSIDH
• explicit isogeny
• isogeny
• oblivious transfer
• supersingular elliptic curves

This thesis studies isogeny-based cryptography and its applications to oblivious transfer protocols.

Isogeny crypto is based on difficult problems on the graph of isogenies between supersingular elliptic curves. Is one of the candidates in the NIST competition for post-quantum cryptography, and in particular for key exchanges with the SIKE protocol. Since quantum computers break all current public key cryptography, it is essential to find post-quantum alternatives.

We study how to apply isogeny-based constructions to the oblivious transfer protocol, which is a fundamental building block for multi-party computation, the field of cryptography that deals with secure function evaluation with many parties.

The security of MPC and in particular OT procols is usually defined using the Universal Composability framework, which gives simulation-based definitions. Many protocols need additional technicalities for working in the UC framework, which decrease efficiency. Inspired by the algebraic group model, we will define a new "explicit isogeny" model of computation, that seems to help in proving UC security of more efficient OT protocols.