crypto/secp256k1: fix undefined behavior in BitCurve.Add (#22621)

This commit changes the behavior of BitCurve.Add to be more inline
with btcd. It fixes two different bugs:

1) When adding a point at infinity to another point, the other point
   should be returned. While this is undefined behavior, it is better
   to be more inline with the go standard library.
   Thus (0,0) + (a, b) = (a,b)

2) Adding the same point to itself produced the point at infinity.
   This is incorrect, now doubleJacobian is used to correctly calculate it.
   Thus (a,b) + (a,b) == 2* (a,b) and not (0,0) anymore.

The change also adds a differential fuzzer for Add, testing it against btcd.

Co-authored-by: Felix Lange <fjl@twurst.com>

crypto/secp256k1/curve.go

@@ -35,15 +35,8 @@ package secp256k1
 import (
 	"crypto/elliptic"
 	"math/big"
-	"unsafe"
 )
 
-/*
-#include "libsecp256k1/include/secp256k1.h"
-extern int secp256k1_ext_scalar_mul(const secp256k1_context* ctx, const unsigned char *point, const unsigned char *scalar);
-*/
-import "C"
-
 const (
 	// number of bits in a big.Word
 	wordBits = 32 << (uint64(^big.Word(0)) >> 63)
@@ -133,7 +126,18 @@ func (BitCurve *BitCurve) affineFromJacobian(x, y, z *big.Int) (xOut, yOut *big.
 
 // Add returns the sum of (x1,y1) and (x2,y2)
 func (BitCurve *BitCurve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) {
+	// If one point is at infinity, return the other point.
+	// Adding the point at infinity to any point will preserve the other point.
+	if x1.Sign() == 0 && y1.Sign() == 0 {
+		return x2, y2
+	}
+	if x2.Sign() == 0 && y2.Sign() == 0 {
+		return x1, y1
+	}
 	z := new(big.Int).SetInt64(1)
+	if x1.Cmp(x2) == 0 && y1.Cmp(y2) == 0 {
+		return BitCurve.affineFromJacobian(BitCurve.doubleJacobian(x1, y1, z))
+	}
 	return BitCurve.affineFromJacobian(BitCurve.addJacobian(x1, y1, z, x2, y2, z))
 }
 
@@ -242,41 +246,6 @@ func (BitCurve *BitCurve) doubleJacobian(x, y, z *big.Int) (*big.Int, *big.Int,
 	return x3, y3, z3
 }
 
-func (BitCurve *BitCurve) ScalarMult(Bx, By *big.Int, scalar []byte) (*big.Int, *big.Int) {
-	// Ensure scalar is exactly 32 bytes. We pad always, even if
-	// scalar is 32 bytes long, to avoid a timing side channel.
-	if len(scalar) > 32 {
-		panic("can't handle scalars > 256 bits")
-	}
-	// NOTE: potential timing issue
-	padded := make([]byte, 32)
-	copy(padded[32-len(scalar):], scalar)
-	scalar = padded
-
-	// Do the multiplication in C, updating point.
-	point := make([]byte, 64)
-	readBits(Bx, point[:32])
-	readBits(By, point[32:])
-
-	pointPtr := (*C.uchar)(unsafe.Pointer(&point[0]))
-	scalarPtr := (*C.uchar)(unsafe.Pointer(&scalar[0]))
-	res := C.secp256k1_ext_scalar_mul(context, pointPtr, scalarPtr)
-
-	// Unpack the result and clear temporaries.
-	x := new(big.Int).SetBytes(point[:32])
-	y := new(big.Int).SetBytes(point[32:])
-	for i := range point {
-		point[i] = 0
-	}
-	for i := range padded {
-		scalar[i] = 0
-	}
-	if res != 1 {
-		return nil, nil
-	}
-	return x, y
-}
-
 // ScalarBaseMult returns k*G, where G is the base point of the group and k is
 // an integer in big-endian form.
 func (BitCurve *BitCurve) ScalarBaseMult(k []byte) (*big.Int, *big.Int) {

crypto/secp256k1/panic_cb.go

@@ -2,6 +2,8 @@
 // Use of this source code is governed by a BSD-style license that can be found in
 // the LICENSE file.
 
+// +build !gofuzz cgo
+
 package secp256k1
 
 import "C"

crypto/secp256k1/scalar_mult_cgo.go

@@ -0,0 +1,56 @@
+// Copyright 2015 Jeffrey Wilcke, Felix Lange, Gustav Simonsson. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be found in
+// the LICENSE file.
+
+// +build !gofuzz cgo
+
+package secp256k1
+
+import (
+	"math/big"
+	"unsafe"
+)
+
+/*
+
+#include "libsecp256k1/include/secp256k1.h"
+
+extern int secp256k1_ext_scalar_mul(const secp256k1_context* ctx, const unsigned char *point, const unsigned char *scalar);
+
+*/
+import "C"
+
+func (BitCurve *BitCurve) ScalarMult(Bx, By *big.Int, scalar []byte) (*big.Int, *big.Int) {
+	// Ensure scalar is exactly 32 bytes. We pad always, even if
+	// scalar is 32 bytes long, to avoid a timing side channel.
+	if len(scalar) > 32 {
+		panic("can't handle scalars > 256 bits")
+	}
+	// NOTE: potential timing issue
+	padded := make([]byte, 32)
+	copy(padded[32-len(scalar):], scalar)
+	scalar = padded
+
+	// Do the multiplication in C, updating point.
+	point := make([]byte, 64)
+	readBits(Bx, point[:32])
+	readBits(By, point[32:])
+
+	pointPtr := (*C.uchar)(unsafe.Pointer(&point[0]))
+	scalarPtr := (*C.uchar)(unsafe.Pointer(&scalar[0]))
+	res := C.secp256k1_ext_scalar_mul(context, pointPtr, scalarPtr)
+
+	// Unpack the result and clear temporaries.
+	x := new(big.Int).SetBytes(point[:32])
+	y := new(big.Int).SetBytes(point[32:])
+	for i := range point {
+		point[i] = 0
+	}
+	for i := range padded {
+		scalar[i] = 0
+	}
+	if res != 1 {
+		return nil, nil
+	}
+	return x, y
+}

crypto/secp256k1/scalar_mult_nocgo.go

@@ -0,0 +1,13 @@
+// Copyright 2015 Jeffrey Wilcke, Felix Lange, Gustav Simonsson. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be found in
+// the LICENSE file.
+
+// +build gofuzz !cgo
+
+package secp256k1
+
+import "math/big"
+
+func (BitCurve *BitCurve) ScalarMult(Bx, By *big.Int, scalar []byte) (*big.Int, *big.Int) {
+	panic("ScalarMult is not available when secp256k1 is built without cgo")
+}

crypto/secp256k1/secp256.go

@@ -2,6 +2,8 @@
 // Use of this source code is governed by a BSD-style license that can be found in
 // the LICENSE file.
 
+// +build !gofuzz cgo
+
 // Package secp256k1 wraps the bitcoin secp256k1 C library.
 package secp256k1