2018-07-30 02:07:02 +00:00
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# Fiat
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Some of the code in this directory is generated by
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[Fiat](https://github.com/mit-plv/fiat-crypto) and thus these files are
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licensed under the MIT license. (See LICENSE file.)
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## Curve25519
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To generate the field arithmetic procedures in `curve25519.c` from a fiat-crypto
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2019-12-31 13:08:08 +00:00
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checkout (as of `7892c66d5e0e5770c79463ce551193ceef870641`), run
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2018-07-30 02:07:02 +00:00
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`make src/Specific/solinas32_2e255m19_10limbs/femul.c` (replacing `femul` with
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the desired field operation). The "source" file specifying the finite field and
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referencing the desired implementation strategy is
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`src/Specific/solinas32_2e255m19_10limbs/CurveParameters.v`, specifying roughly
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"unsaturated arithmetic modulo 2^255-19 using 10 limbs of radix 2^25.5 in 32-bit
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unsigned integers with a single carry chain and two wraparound carries" where
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only the prime is considered normative and everything else is treated as
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"compiler hints".
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2019-12-31 13:08:08 +00:00
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The 64-bit implementation uses 5 limbs of radix 2^51 with instruction scheduling
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taken from curve25519-donna-c64. It is found in
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`src/Specific/solinas64_2e255m19_5limbs_donna`.
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2018-07-30 02:07:02 +00:00
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## P256
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To generate the field arithmetic procedures in `p256.c` from a fiat-crypto
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checkout, run
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`make src/Specific/montgomery64_2e256m2e224p2e192p2e96m1_4limbs/femul.c`.
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The corresponding "source" file is
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`src/Specific/montgomery64_2e256m2e224p2e192p2e96m1_4limbs/CurveParameters.v`,
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specifying roughly "64-bit saturated word-by-word Montgomery reduction modulo
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2^256 - 2^224 + 2^192 + 2^96 - 1". Again, everything except for the prime is
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untrusted. There is currently a known issue where `fesub.c` for p256 does not
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manage to complete the build (specialization) within a week on Coq 8.7.0.
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<https://github.com/JasonGross/fiat-crypto/tree/3e6851ddecaac70d0feb484a75360d57f6e41244/src/Specific/montgomery64_2e256m2e224p2e192p2e96m1_4limbs>
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does manage to build that file, but the work on that branch was never finished
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(the correctness proofs of implementation templates still apply, but the
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now abandoned prototype specialization facilities there are unverified).
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## Working With Fiat Crypto Field Arithmetic
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The fiat-crypto readme <https://github.com/mit-plv/fiat-crypto#arithmetic-core>
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contains an overview of the implementation templates followed by a tour of the
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specialization machinery. It may be helpful to first read about the less messy
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parts of the system from chapter 3 of <http://adam.chlipala.net/theses/andreser.pdf>.
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There is work ongoing to replace the entire specialization mechanism with
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something much more principled <https://github.com/mit-plv/fiat-crypto/projects/4>.
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