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authorJ08nY2024-08-23 18:56:17 +0200
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+Go
+==
+
+| Version: ``go1.21.4``
+| Repository: https://github.com/golang/go
+| Docs:
+
+Primitives
+----------
+
+ECDH, ECDSA over P-224, P-256, P-384 and P-521.
+Ed25519, X25519
+
+ECDH
+^^^^
+
+KeyGen:
+ - Short-Weierstrass
+ - `Fixed window (w=4) <https://github.com/golang/go/blob/go1.21.4/src/crypto/internal/nistec/p224.go#L412>`__ (link points to P-224, but others are the same) via ``privateKeyToPublicKey -> ScalarBaseMult``
+ - Projective
+ - `add-2015-rcb <https://github.com/golang/go/blob/go1.21.4/src/crypto/internal/nistec/p224.go#L215>`__, `dbl-2015-rcb <https://github.com/golang/go/blob/go1.21.4/src/crypto/internal/nistec/p224.go#L270>`__
+
+Derive:
+ - Short-Weierstrass
+ - `Fixed window (w=4) <https://github.com/golang/go/blob/go1.21.4/src/crypto/internal/nistec/p224.go#L342>`__ via ``ecdh -> ScalarMult``.
+ - Same formulas as in Keygen.
+
+Also supports constant-time, 64-bit assembly implementation of P256 described in https://eprint.iacr.org/2013/816.pdf
+
+ECDSA
+^^^^^
+
+KeyGen:
+ - Same as ECDH KeyGen via ``ecdsa.go:GenerateKey -> generateNISTEC -> randomPoint -> ScalarBaseMult``.
+
+Sign:
+ - Same as KeyGen via ``ecdsa.go:SignASN1 -> signNISTEC -> randomPoint -> ScalarBaseMult``.
+
+Verify:
+ - Two separate scalar multiplications ``ScalarBaseMult`` (same as KeyGen) and ``ScalarMult`` (same as ECDH Derive) via ``ecdsa.go:VerifyASN1 -> verifyNISTEC``.
+
+X25519
+^^^^^^
+
+KeyGen:
+ - Montgomery
+ - `Ladder <https://github.com/golang/go/blob/go1.21.4/src/crypto/ecdh/x25519.go#L54>`__ via ``privateKeyToPublicKey -> x25519ScalarMult``.
+ - xz
+ - Unknown formula: `ladd-go-1214 <https://github.com/J08nY/pyecsca/blob/master/test/data/formulas/ladd-go-1214.op3>`__
+
+Derive:
+ - Same as KeyGen via ``x25519.go:ecdh -> x25519ScalarMult``.
+
+Ed25519
+^^^^^^^
+
+KeyGen:
+ - Twisted-Edwards
+ - Pippenger's signed 4-bit method with precomputation via ``ed25519.go:GenerateKey -> NewKeyFromSeed -> newKeyFromSeed -> ScalarBaseMult``.
+ - `Extended coordinates <https://github.com/golang/go/blob/go1.21.4/src/crypto/internal/edwards25519/edwards25519.go#L28>`__ mixed with `y-x,y+x,2dxy <https://github.com/golang/go/blob/go1.21.4/src/crypto/internal/edwards25519/edwards25519.go#L52>`__ coordinates
+ - `AddAffine <https://github.com/golang/go/blob/go1.21.4/src/crypto/internal/edwards25519/edwards25519.go#L312>`__ (and similar SubAffine)::
+
+ YplusX.Add(&p.y, &p.x)
+ YminusX.Subtract(&p.y, &p.x)
+
+ PP.Multiply(&YplusX, &q.YplusX)
+ MM.Multiply(&YminusX, &q.YminusX)
+ TT2d.Multiply(&p.t, &q.T2d)
+
+ Z2.Add(&p.z, &p.z)
+
+ v.X.Subtract(&PP, &MM)
+ v.Y.Add(&PP, &MM)
+ v.Z.Add(&Z2, &TT2d)
+ v.T.Subtract(&Z2, &TT2d)
+
+Sign:
+ - Same as Keygen via ``ed25519.go: Sign -> sign -> ScalarBaseMult``.
+
+Verify:
+ - Bos-Coster method via ``ed25519.go: Verify -> verify -> VarTimeDoubleScalarBaseMult``.
+ - Same coordinates and formulas as in Keygen.