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5. Isogeny-based cryptosystems


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      Problem 5.1.

      [Kirsten Eisentraeger] Can quantum algorithms be used to attack SIDH by using the extra points? Are there SIDH attacks better than claw-finding?


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          Problem 5.2.

          [Lorenz Panny] Are there CSIDH attacks better than hidden shift? What is the cost of the hidden shift attack?


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              Problem 5.3.

              [Dan Boneh] Solve Decisional Diffie-Hellman (DDH) in the context of CSIDH: Let $E_0$ be a supersingular elliptic curve defined over $\mathbb F_p$ with endomorphism ring $\mathbb Z[\pi]$. Distinguish between triples $(\mathfrak a * E_0, \mathfrak b* E_0,\mathfrak c* E_0)$ and triples $(\mathfrak a * E_0, \mathfrak b* E_0,\mathfrak a\mathfrak b * E_0)$ where $\mathfrak a, \mathfrak b, \mathfrak c$ are ideals in $\mathbb Z[\pi]$ of odd norm.

                  Cite this as: AimPL: Quantum algorithms for analysis of public-key crypto, available at http://aimpl.org/quantumalg.