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README: update for checksumsets etc. 

Signed-off-by: Daira Hopwood <daira@jacaranda.org>
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Daira Hopwood 2020-11-23 01:24:03 +00:00
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@ -35,7 +35,7 @@ use `--sequential`.)
Prerequisites:
* apt-get install sagemath
* pip install sortedcontainers
* pip3 install sortedcontainers
Run ``sage verify.sage Ep`` and ``sage verify.sage Eq``; or ``./run.sh`` to run both
and also print out the results.
@ -43,3 +43,14 @@ and also print out the results.
The output of ``amicable.sage`` with the above options includes isogenies of degree 3,
suitable for use with the "simplified SWU" method for hashing to an elliptic curve.
This is based on code from Appendix A of [Wahby and Boneh 2019](https://eprint.iacr.org/2019/403.pdf).
To check the correctness of the endomorphism optimization described in the Halo paper, run
``python3 injectivitylemma.py`` and ``python3 checksumsets.py``. To also generate animations
showing the minimum distances between multiples of ζ used in the proof, run ``./animation.sh``.
``animation.sh`` has the following prerequisites:
* apt-get install ffmpeg ffcvt
* pip3 install bintrees Pillow
``checksumsets.py`` on its own only requires the ``bintrees`` Python package.