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serai/crypto/embedwards25519/README.md

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One Round DKG (#589) * Upstream GBP, divisor, circuit abstraction, and EC gadgets from FCMP++ * Initial eVRF implementation Not quite done yet. It needs to communicate the resulting points and proofs to extract them from the Pedersen Commitments in order to return those, and then be tested. * Add the openings of the PCs to the eVRF as necessary * Add implementation of secq256k1 * Make DKG Encryption a bit more flexible No longer requires the use of an EncryptionKeyMessage, and allows pre-defined keys for encryption. * Make NUM_BITS an argument for the field macro * Have the eVRF take a Zeroizing private key * Initial eVRF-based DKG * Add embedwards25519 curve * Inline the eVRF into the DKG library Due to how we're handling share encryption, we'd either need two circuits or to dedicate this circuit to the DKG. The latter makes sense at this time. * Add documentation to the eVRF-based DKG * Add paragraph claiming robustness * Update to the new eVRF proof * Finish routing the eVRF functionality Still needs errors and serialization, along with a few other TODOs. * Add initial eVRF DKG test * Improve eVRF DKG Updates how we calculcate verification shares, improves performance when extracting multiple sets of keys, and adds more to the test for it. * Start using a proper error for the eVRF DKG * Resolve various TODOs Supports recovering multiple key shares from the eVRF DKG. Inlines two loops to save 2**16 iterations. Adds support for creating a constant time representation of scalars < NUM_BITS. * Ban zero ECDH keys, document non-zero requirements * Implement eVRF traits, all the way up to the DKG, for secp256k1/ed25519 * Add Ristretto eVRF trait impls * Support participating multiple times in the eVRF DKG * Only participate once per key, not once per key share * Rewrite processor key-gen around the eVRF DKG Still a WIP. * Finish routing the new key gen in the processor Doesn't touch the tests, coordinator, nor Substrate yet. `cargo +nightly fmt && cargo +nightly-2024-07-01 clippy --all-features -p serai-processor` does pass. * Deduplicate and better document in processor key_gen * Update serai-processor tests to the new key gen * Correct amount of yx coefficients, get processor key gen test to pass * Add embedded elliptic curve keys to Substrate * Update processor key gen tests to the eVRF DKG * Have set_keys take signature_participants, not removed_participants Now no one is removed from the DKG. Only `t` people publish the key however. Uses a BitVec for an efficient encoding of the participants. * Update the coordinator binary for the new DKG This does not yet update any tests. * Add sensible Debug to key_gen::[Processor, Coordinator]Message * Have the DKG explicitly declare how to interpolate its shares Removes the hack for MuSig where we multiply keys by the inverse of their lagrange interpolation factor. * Replace Interpolation::None with Interpolation::Constant Allows the MuSig DKG to keep the secret share as the original private key, enabling deriving FROST nonces consistently regardless of the MuSig context. * Get coordinator tests to pass * Update spec to the new DKG * Get clippy to pass across the repo * cargo machete * Add an extra sleep to ensure expected ordering of `Participation`s * Update orchestration * Remove bad panic in coordinator It expected ConfirmationShare to be n-of-n, not t-of-n. * Improve documentation on functions * Update TX size limit We now no longer have to support the ridiculous case of having 49 DKG participations within a 101-of-150 DKG. It does remain quite high due to needing to _sign_ so many times. It'd may be optimal for parties with multiple key shares to independently send their preprocesses/shares (despite the overhead that'll cause with signatures and the transaction structure). * Correct error in the Processor spec document * Update a few comments in the validator-sets pallet * Send/Recv Participation one at a time Sending all, then attempting to receive all in an expected order, wasn't working even with notable delays between sending messages. This points to the mempool not working as expected... * Correct ThresholdKeys serialization in modular-frost test * Updating existing TX size limit test for the new DKG parameters * Increase time allowed for the DKG on the GH CI * Correct construction of signature_participants in serai-client tests Fault identified by akil. * Further contextualize DkgConfirmer by ValidatorSet Caught by a safety check we wouldn't reuse preprocesses across messages. That raises the question of we were prior reusing preprocesses (reusing keys)? Except that'd have caused a variety of signing failures (suggesting we had some staggered timing avoiding it in practice but yes, this was possible in theory). * Add necessary calls to set_embedded_elliptic_curve_key in coordinator set rotation tests * Correct shimmed setting of a secq256k1 key * cargo fmt * Don't use `[0; 32]` for the embedded keys in the coordinator rotation test The key_gen function expects the random values already decided. * Big-endian secq256k1 scalars Also restores the prior, safer, Encryption::register function.
2024-08-16 11:26:07 -07:00
# embedwards25519
A curve defined over the Ed25519 scalar field.
This curve was found via
[tevador's script](https://gist.github.com/tevador/4524c2092178df08996487d4e272b096)
for finding curves (specifically, curve cycles), modified to search for curves
whose field is the Ed25519 scalar field (not the Ed25519 field).
Correct decoding identity for embedwards25519/secq256k1
2025-01-29 23:01:45 -05:00
```ignore
One Round DKG (#589) * Upstream GBP, divisor, circuit abstraction, and EC gadgets from FCMP++ * Initial eVRF implementation Not quite done yet. It needs to communicate the resulting points and proofs to extract them from the Pedersen Commitments in order to return those, and then be tested. * Add the openings of the PCs to the eVRF as necessary * Add implementation of secq256k1 * Make DKG Encryption a bit more flexible No longer requires the use of an EncryptionKeyMessage, and allows pre-defined keys for encryption. * Make NUM_BITS an argument for the field macro * Have the eVRF take a Zeroizing private key * Initial eVRF-based DKG * Add embedwards25519 curve * Inline the eVRF into the DKG library Due to how we're handling share encryption, we'd either need two circuits or to dedicate this circuit to the DKG. The latter makes sense at this time. * Add documentation to the eVRF-based DKG * Add paragraph claiming robustness * Update to the new eVRF proof * Finish routing the eVRF functionality Still needs errors and serialization, along with a few other TODOs. * Add initial eVRF DKG test * Improve eVRF DKG Updates how we calculcate verification shares, improves performance when extracting multiple sets of keys, and adds more to the test for it. * Start using a proper error for the eVRF DKG * Resolve various TODOs Supports recovering multiple key shares from the eVRF DKG. Inlines two loops to save 2**16 iterations. Adds support for creating a constant time representation of scalars < NUM_BITS. * Ban zero ECDH keys, document non-zero requirements * Implement eVRF traits, all the way up to the DKG, for secp256k1/ed25519 * Add Ristretto eVRF trait impls * Support participating multiple times in the eVRF DKG * Only participate once per key, not once per key share * Rewrite processor key-gen around the eVRF DKG Still a WIP. * Finish routing the new key gen in the processor Doesn't touch the tests, coordinator, nor Substrate yet. `cargo +nightly fmt && cargo +nightly-2024-07-01 clippy --all-features -p serai-processor` does pass. * Deduplicate and better document in processor key_gen * Update serai-processor tests to the new key gen * Correct amount of yx coefficients, get processor key gen test to pass * Add embedded elliptic curve keys to Substrate * Update processor key gen tests to the eVRF DKG * Have set_keys take signature_participants, not removed_participants Now no one is removed from the DKG. Only `t` people publish the key however. Uses a BitVec for an efficient encoding of the participants. * Update the coordinator binary for the new DKG This does not yet update any tests. * Add sensible Debug to key_gen::[Processor, Coordinator]Message * Have the DKG explicitly declare how to interpolate its shares Removes the hack for MuSig where we multiply keys by the inverse of their lagrange interpolation factor. * Replace Interpolation::None with Interpolation::Constant Allows the MuSig DKG to keep the secret share as the original private key, enabling deriving FROST nonces consistently regardless of the MuSig context. * Get coordinator tests to pass * Update spec to the new DKG * Get clippy to pass across the repo * cargo machete * Add an extra sleep to ensure expected ordering of `Participation`s * Update orchestration * Remove bad panic in coordinator It expected ConfirmationShare to be n-of-n, not t-of-n. * Improve documentation on functions * Update TX size limit We now no longer have to support the ridiculous case of having 49 DKG participations within a 101-of-150 DKG. It does remain quite high due to needing to _sign_ so many times. It'd may be optimal for parties with multiple key shares to independently send their preprocesses/shares (despite the overhead that'll cause with signatures and the transaction structure). * Correct error in the Processor spec document * Update a few comments in the validator-sets pallet * Send/Recv Participation one at a time Sending all, then attempting to receive all in an expected order, wasn't working even with notable delays between sending messages. This points to the mempool not working as expected... * Correct ThresholdKeys serialization in modular-frost test * Updating existing TX size limit test for the new DKG parameters * Increase time allowed for the DKG on the GH CI * Correct construction of signature_participants in serai-client tests Fault identified by akil. * Further contextualize DkgConfirmer by ValidatorSet Caught by a safety check we wouldn't reuse preprocesses across messages. That raises the question of we were prior reusing preprocesses (reusing keys)? Except that'd have caused a variety of signing failures (suggesting we had some staggered timing avoiding it in practice but yes, this was possible in theory). * Add necessary calls to set_embedded_elliptic_curve_key in coordinator set rotation tests * Correct shimmed setting of a secq256k1 key * cargo fmt * Don't use `[0; 32]` for the embedded keys in the coordinator rotation test The key_gen function expects the random values already decided. * Big-endian secq256k1 scalars Also restores the prior, safer, Encryption::register function.
2024-08-16 11:26:07 -07:00
p = 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed
q = 0x0fffffffffffffffffffffffffffffffe53f4debb78ff96877063f0306eef96b
D = -420435
y^2 = x^3 - 3*x + 4188043517836764736459661287169077812555441231147410753119540549773825148767
```
The embedding degree is `(q-1)/2`.
This curve should not be used with single-coordinate ladders, and points should
always be represented in a compressed form (preventing receiving off-curve
points).
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