Add inverse Elligator2 mapping to Curve25519. #357
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The result of the sqrt(2u(u+A)) test can be used directly to compute the final field element. This optimization was adapted from Loup Vaillant's Monocypher library.
SnowyCoder
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Jun 21, 2023
Code stolen from @lealanko dalek-cryptography#357 This commit only modifies the API to be more "standard" conforming (as described in https://www.elligator.org/), having a tweak and "dirty" key generation. Also various tests were added to ensure that it conforms to already-developed implementations. The original pull-request differed from standard implementations when checking for element positivity since FieldElement::is_positive performs an entirely different check than what the standard describes. Since this commit includes standard-conformity, the original maps downloaded from https://www.elligator.org/ are included in the vendor folder.
koba-e964
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| @@ -193,6 +193,81 @@ pub(crate) fn elligator_encode(r_0: &FieldElement) -> MontgomeryPoint { | |||
| MontgomeryPoint(u.to_bytes()) | |||
| } | |||
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| /// Perform the inverse Elligator2 mapping from a Montgomery point to | |||
| /// field element. This algorithm is based on [Elligator: | |||
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nit: the indefinite article
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| /// field element. This algorithm is based on [Elligator: | |
| /// a field element. This algorithm is based on [Elligator: |
| // Both r and -r are valid results. Pick the nonnegative one. | ||
| let result = FieldElement::conditional_select(&r, &-&r, r.is_negative()); | ||
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| return Some(result); |
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You may omit return here in the last line of a function, as in other functions in this file.
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| return Some(result); | |
| Some(result) |
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This PR adds
montgomery_elligator_decode, an inverse tomontgomery_elligator_encode. This is my first contribution, so I'm very interested in advice on how to best accommodate Dalek's conventions.Some points of note:
encodefunction is clearly named from the perspective of hash-to-curve operations, where pre-existing uniform data is "encoded" into a curve point. However, the inverse mapping can be used to map an existing curve point invertibly into uniform-looking data. Calling this operation "decode" is confusing. I would suggest more neutral naming likemap_to_fieldandmap_from_field.OsRngsince that means that test runs are unpredictable..montgomery_elligator_encodedoes compute the sign of the v-coordinate (aseps_is_sq) but it does not return it. This is an unfortunate asymmetry with the inverse function (whose output depends on the sign), and it may be critical for applications that require a full curve point, not just a u-coordinate.I can try to address some of these issues already within this PR if that's a reasonable thing to do.