Post-Quantum Cryptography: SIDH
Background: Many common cryptographic techniques can be easily broken by quantum computers. Currently, it is still unclear when quantum computers become useable for practical applications. Nevertheless, it is important to research cryptographic algorithms that are resistant to quantum computer computation.
This assignment will address the possible quantum resistance and implementations of SIKE/CSIDH. This starts with explorations into the isogeny-based key exchange and its underpinnings. The topic will demand mathematical maturity, preferably with some background in algebraic geometry.
Implementation-wise, one should start with setups from SIKE/CSIDH and try to find the strongest attacks, both classical and quantum, and then consider drawbacks that one might hope to solve. Are there curves and parameters that may be used to alleviate the SIKE protocol in time/space efficiency?