From 8b985dba31c07a4962c0953d812144f59785bf99 Mon Sep 17 00:00:00 2001
From: arnaucube <root@arnaucube.com>
Date: Sat, 13 Mar 2021 09:09:05 +0100
Subject: [PATCH] Add Point Compression & Decompression methods

---
 blindsecp256k1.go      | 74 ++++++++++++++++++++++++++++++++++++++++--
 blindsecp256k1_test.go | 46 ++++++++++++++++++++++++++
 2 files changed, 118 insertions(+), 2 deletions(-)

diff --git a/blindsecp256k1.go b/blindsecp256k1.go
index 053b3da..05c6342 100644
--- a/blindsecp256k1.go
+++ b/blindsecp256k1.go
@@ -27,6 +27,18 @@ import (
 // )
 
 var (
+	zero *big.Int = big.NewInt(0)
+
+	// B (from y^2 = x^3 + B)
+	B *big.Int = btcec.S256().B
+
+	// P represents the secp256k1 finite field
+	P *big.Int = btcec.S256().P
+
+	// Q = (P+1)/4
+	Q = new(big.Int).Div(new(big.Int).Add(P,
+		big.NewInt(1)), big.NewInt(4)) // nolint:gomnd
+
 	// G represents the base point of secp256k1
 	G *Point = &Point{
 		X: btcec.S256().Gx,
@@ -35,8 +47,6 @@ var (
 
 	// N represents the order of G of secp256k1
 	N *big.Int = btcec.S256().N
-
-	zero *big.Int = big.NewInt(0)
 )
 
 // Point represents a point on the secp256k1 curve
@@ -76,6 +86,66 @@ func (p *Point) isValid() error {
 	return nil
 }
 
+// Compress packs a Point to a byte array of 33 bytes
+func (p *Point) Compress() [33]byte {
+	xBytes := p.X.Bytes()
+	odd := byte(0)
+	if isOdd(p.Y) {
+		odd = byte(1)
+	}
+	var b [33]byte
+	copy(b[32-len(xBytes):32], xBytes)
+	b[32] = odd
+	return b
+}
+
+func isOdd(b *big.Int) bool {
+	return b.Bit(0) != 0
+}
+
+// DecompressPoint unpacks a Point from the given byte array of 33 bytes
+// https://bitcointalk.org/index.php?topic=162805.msg1712294#msg1712294
+func DecompressPoint(b [33]byte) (*Point, error) {
+	x := new(big.Int).SetBytes(b[:32])
+	var odd bool
+	if b[32] == byte(1) {
+		odd = true
+	}
+
+	// secp256k1: y2 = x3+ ax2 + b (where A==0, B==7)
+
+	// compute x^3 + B mod p
+	x3 := new(big.Int).Mul(x, x)
+	x3 = new(big.Int).Mul(x3, x)
+	// x3 := new(big.Int).Exp(x, big.NewInt(3), nil)
+	x3 = new(big.Int).Add(x3, B)
+	x3 = new(big.Int).Mod(x3, P)
+
+	// sqrt mod p of x^3 + B
+	y := new(big.Int).ModSqrt(x3, P)
+	if y == nil {
+		return nil, fmt.Errorf("not sqrt mod of x^3")
+	}
+	if odd != isOdd(y) {
+		y = new(big.Int).Sub(P, y)
+		// TODO if needed Mod
+	}
+
+	// check that y is a square root of x^3 + B
+	y2 := new(big.Int).Mul(y, y)
+	y2 = new(big.Int).Mod(y2, P)
+	if !bytes.Equal(y2.Bytes(), x3.Bytes()) {
+		return nil, fmt.Errorf("invalid square root")
+	}
+
+	if odd != isOdd(y) {
+		return nil, fmt.Errorf("odd does not match oddness")
+	}
+
+	p := &Point{X: x, Y: y}
+	return p, nil
+}
+
 // WIP
 func newRand() *big.Int {
 	var b [32]byte
diff --git a/blindsecp256k1_test.go b/blindsecp256k1_test.go
index a6ff47f..44cba52 100644
--- a/blindsecp256k1_test.go
+++ b/blindsecp256k1_test.go
@@ -1,6 +1,7 @@
 package blindsecp256k1
 
 import (
+	"encoding/hex"
 	"math/big"
 	"testing"
 
@@ -84,3 +85,48 @@ func TestHashMOddBytes(t *testing.T) {
 //         _, err = sk.BlindSign(mBlinded, k)
 //         assert.Equal(t, "mBlinded too small", err.Error())
 // }
+
+func TestPointCompressDecompress(t *testing.T) {
+	p := G
+	b := p.Compress()
+	assert.Equal(t,
+		"79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f8179800",
+		hex.EncodeToString(b[:]))
+	p2, err := DecompressPoint(b)
+	require.Nil(t, err)
+	assert.Equal(t, p, p2)
+
+	for i := 2; i < 1000; i++ {
+		p := G.Mul(big.NewInt(int64(i)))
+		b := p.Compress()
+		assert.Equal(t, 33, len(b))
+
+		p2, err := DecompressPoint(b)
+		require.Nil(t, err)
+		assert.Equal(t, p, p2)
+	}
+}
+
+func BenchmarkCompressDecompress(b *testing.B) {
+	const n = 256
+	var points [n]*Point
+	var compPoints [n][33]byte
+
+	for i := 0; i < n; i++ {
+		points[i] = G.Mul(big.NewInt(int64(i)))
+	}
+	for i := 0; i < n; i++ {
+		compPoints[i] = points[i].Compress()
+	}
+
+	b.Run("Compress", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			_ = points[i%n].Compress()
+		}
+	})
+	b.Run("DecompressPoint", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			_, _ = DecompressPoint(compPoints[i%n])
+		}
+	})
+}