Improvements to Yggdrasil demo (#1114)

* Improvements to Yggdrasil demo

* Fix missing copyright

* Fix tie-break

cmd/dendrite-demo-yggdrasil/convert/25519.go

@@ -0,0 +1,53 @@
+// Copyright 2019 Google LLC
+//
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file or at
+// https://developers.google.com/open-source/licenses/bsd
+//
+// Original code from https://github.com/FiloSottile/age/blob/bbab440e198a4d67ba78591176c7853e62d29e04/internal/age/ssh.go
+
+package convert
+
+import (
+	"crypto/ed25519"
+	"crypto/sha512"
+	"math/big"
+
+	"golang.org/x/crypto/curve25519"
+)
+
+var curve25519P, _ = new(big.Int).SetString("57896044618658097711785492504343953926634992332820282019728792003956564819949", 10)
+
+func Ed25519PrivateKeyToCurve25519(pk ed25519.PrivateKey) []byte {
+	h := sha512.New()
+	_, _ = h.Write(pk.Seed())
+	out := h.Sum(nil)
+	return out[:curve25519.ScalarSize]
+}
+
+func Ed25519PublicKeyToCurve25519(pk ed25519.PublicKey) []byte {
+	// ed25519.PublicKey is a little endian representation of the y-coordinate,
+	// with the most significant bit set based on the sign of the x-coordinate.
+	bigEndianY := make([]byte, ed25519.PublicKeySize)
+	for i, b := range pk {
+		bigEndianY[ed25519.PublicKeySize-i-1] = b
+	}
+	bigEndianY[0] &= 0b0111_1111
+
+	// The Montgomery u-coordinate is derived through the bilinear map
+	//     u = (1 + y) / (1 - y)
+	// See https://blog.filippo.io/using-ed25519-keys-for-encryption.
+	y := new(big.Int).SetBytes(bigEndianY)
+	denom := big.NewInt(1)
+	denom.ModInverse(denom.Sub(denom, y), curve25519P) // 1 / (1 - y)
+	u := y.Mul(y.Add(y, big.NewInt(1)), denom)
+	u.Mod(u, curve25519P)
+
+	out := make([]byte, curve25519.PointSize)
+	uBytes := u.Bytes()
+	for i, b := range uBytes {
+		out[len(uBytes)-i-1] = b
+	}
+
+	return out
+}