EC: Add scalar base point multiplication test case generator.

Add a new scalar base point multiplication test case generator that
where the points are *not* Montgomery-encoded. This way we don't need
to generate different test data files when the Montgomery encoding
for a curve isn't the same for 32-bit and 64-bit targets (P-521).

This version of the generator produces the test cases for all the
scalars that the current P-256 and P-384 tests generate, in the same
format; the only exception is that the point is not
Montgomery-encoded.

crypto/fipsmodule/ec/make_ec_scalar_base_mult_tests.go

@@ -12,49 +12,105 @@
  * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
  * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
 
+// go run crypto/fipsmodule/ec/make_ec_scalar_base_mult_tests.go
+
 package main
 
 import (
 	"crypto/elliptic"
 	"fmt"
+	"io"
 	"math/big"
+	"os"
+	"path/filepath"
 )
 
-const numPoints = 64
+const (
+	// The number of bits in a window for windowed point multiplication.
+	// XXX: *ring*'s tests were generated for 7 bit windows, but the code
+	// currently uses 5 bit windows.
+	windowBits = 6
 
-func printPadded(key string, n, max *big.Int) {
-	padded := make([]byte, len(max.Bytes()))
-	b := n.Bytes()
-	copy(padded[len(padded)-len(b):], b)
-	fmt.Printf("%s = %x\n", key, padded)
+	// 2 windows worth of points.
+	numPoints = 2 * (1 << windowBits)
+)
+
+func main() {
+	generateTests(elliptic.P256())
+	generateTests(elliptic.P384())
+	//generateTests(elliptic.P521())
+}
+
+func generateTests(curve elliptic.Curve) {
+	generateScalarMulBaseTests(curve)
 }
 
-func printMultiples(name string, curve elliptic.Curve) {
-	n := new(big.Int)
-	for i := -numPoints; i <= numPoints; i++ {
-		fmt.Printf("Curve = %s\n", name)
+func generateScalarMulBaseTests(curve elliptic.Curve) {
+	f, err := createFile(curve, "point_mul_base")
+	if err != nil {
+		return
+	}
+	defer f.Close()
+
+	fmt.Fprintf(f, `# This file contains multiples of the base point for various curves.
+#
+# This file is generated by make_ec_scalar_base_mult_tests.go
+
+`)
+
+	// Test low scalar values.
+	for i := 0; i <= numPoints; i++ {
+		n := new(big.Int)
+		n.SetInt64(int64(i))
+		printScalarMulBase(f, n, curve)
+	}
+	// Test each bit set at the high end.
+	for i := 1; i < numPoints; i++ {
+		n := new(big.Int)
+		n.SetInt64(int64(i))
+		n.Lsh(n, (uint)(curve.Params().N.BitLen()-windowBits-1))
+		printScalarMulBase(f, n, curve)
+	}
+	// Test highest (negative) scalar values.
+	for i := -numPoints; i <= -1; i++ {
+		n := new(big.Int)
 		n.SetInt64(int64(i))
-		if i < 0 {
+		printScalarMulBase(f, n, curve)
+	}
+}
+
+func printScalarMulBase(f io.Writer, n *big.Int, curve elliptic.Curve) {
+	if n.Sign() >= 0 && n.BitLen() <= 8 {
+		fmt.Fprintf(f, "g_scalar = %02x\n", n)
+	} else {
+		if n.Sign() < 0 {
+			neg := new(big.Int)
+			fmt.Fprintf(f, "# g_scalar = n - %d\n", neg.Neg(n))
 			n = n.Add(n, curve.Params().N)
 		}
-		fmt.Printf("# N = %d\n", i)
-		printPadded("N", n, curve.Params().N)
-		x, y := curve.ScalarBaseMult(n.Bytes())
-		printPadded("X", x, curve.Params().P)
-		printPadded("Y", y, curve.Params().P)
-		fmt.Printf("\n")
+		fmt.Fprintf(f, "g_scalar = %x\n", padded(n, curve.Params().N))
 	}
+	x, y := curve.ScalarBaseMult(n.Bytes())
+	printAffine(f, "r", x, y, curve.Params().P)
+	fmt.Fprintf(f, "\n")
 }
 
-func main() {
-	fmt.Printf(`# This file contains multiples of the base point for various curves. The point
-# at infinity is represented as X = 0, Y = 0.
-#
-# This file is generated by make_ec_scalar_base_mult_tests.go
+func printAffine(f io.Writer, key string, x, y, max *big.Int) {
+	if x.BitLen() == 0 && y.BitLen() == 0 {
+		fmt.Fprintf(f, "%s = inf\n", key)
+	} else {
+		fmt.Fprintf(f, "%s = %x, %x\n", key, padded(x, max), padded(y, max))
+	}
+}
 
-`)
-	printMultiples("P-224", elliptic.P224())
-	printMultiples("P-256", elliptic.P256())
-	printMultiples("P-384", elliptic.P384())
-	printMultiples("P-521", elliptic.P521())
+func padded(n, max *big.Int) []byte {
+	padded := make([]byte, len(max.Bytes()))
+	b := n.Bytes()
+	copy(padded[len(padded)-len(b):], b)
+	return padded
+}
+
+func createFile(curve elliptic.Curve, baseName string) (*os.File, error) {
+	outFileName := fmt.Sprintf("p%d_%s_tests.txt", curve.Params().N.BitLen(), baseName)
+	return os.Create(filepath.Join("src/ec/suite_b/ops", outFileName))
 }