What basic knowledge is required to understand SIKE?

Cryptography Asked by Vivekanand V on December 19, 2021

I’m interested in learning about Supersingular Isogeny based Key Encapsulation mechanism.
Currently, I only know all the basic knowledge about how standard Elliptic Curve Cryptography, works, using Weierstrass equations. This includes the the mathematical group structure on how the Elliptic curve points are defined, and operations like point doubling and addition. I also learned how to implement it in C , with parameters of cryptographic size.

Since, SIKE is dependent on Elliptic curves, and mapping between curves, I’m guessing that my basic knowledge of how Classical Elliptic Curve Crypto works, would provide me (a beginner) some vantage point to begin understand how SIKE takes off from the ground up.

I realise, that the security of SIKE is not dependent on the classical Discrete Logarithm problem.

I cannot find online material, that presents SIKE and the mathematical basis required for it for a beginner.
Even, if that’s not the case, I’m willing to learn the math required from the ground up.

Every, help will be greatly appreciated!
Thankyou, everyone in advance!

One Answer

Craig Costello has tried writing precisely what you're interested in, see SIKE for Beginners. It refers to numerous other surveys for isogeny-based crypto which may be useful (lecture notes by De Feo, and surveys by Galbraith-Vercauteren and Smith).

Galbraith also has a book on the math behind crypto. Chapter 25 deals with isogenies, so may be useful for mathematical background (but does not discuss SIKE).

Answered by Mark on December 19, 2021

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