CryptoBook
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    • Introduction to Isogeny Cryptography
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  1. Isogeny Based Cryptography

Introduction to Isogeny Cryptography

PreviousThe Birthday paradox / attackNextIsogenies

Last updated 4 years ago

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Making this section as a motivation to make sure this is part of the book. Something to work towards.

Page Plan

  • Describe that there is a drive towards post-quantum algorithms

  • The incredible fact that paths within isogeny graphs commute (with the help of torsion points)

  • Supersingular ℓ\ellℓ isogeny graphs are (ℓ+1)(\ell + 1)(ℓ+1)regular Ramanujan graphs

  • Using paths through these graphs has spawned a whole bunch of protocols

    • SIKE / BIKE / ...

    • Hashes

    • ...

  • First we will look at the fundementals that allow these protocols to be expected as good candidates for post-quantum

  • Then we look at these protocols in more detail. Hopefully with SageMath implementations for each

References I plan to use

  • Introduction by Craig Costello

  • Mathematics of Isogeny Based Cryptography by Luca De Feo

    • -

  • The Arithmetic of Elliptic Curves by Joseph H. Silverman

https://eprint.iacr.org/2019/1321.pdf
https://arxiv.org/pdf/1711.04062.pdf
https://www.springer.com/gp/book/9780387094939