btcec: Add regression tests for field.go.

This adds new tests to the TestNormalize, TestMul, TestAdd2 functions
which trigger an issue with modular reduction that was fixed in the
prevous commit to prevent regressions.

btcec/field_test.go

@@ -233,6 +233,18 @@ func TestNormalize(t *testing.T) {
 			[10]uint32{0xfffffc2f, 0xffffff80, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0x3fffc0},
 			[10]uint32{0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x000000},
 		},
+		// Prime larger than P where both first and second words are larger
+		// than P's first and second words
+		{
+			[10]uint32{0xfffffc30, 0xffffff86, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0x3fffc0},
+			[10]uint32{0x00000001, 0x00000006, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x000000},
+		},
+		// Prime larger than P where only the second word is larger
+		// than P's second words.
+		{
+			[10]uint32{0xfffffc2a, 0xffffff87, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0x3fffc0},
+			[10]uint32{0x03fffffb, 0x00000006, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x000000},
+		},
 		// 2^256 - 1
 		{
 			[10]uint32{0xffffffff, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0x3fffc0},
@@ -481,6 +493,8 @@ func TestAdd2(t *testing.T) {
 		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e", "1", "0"},
 		// secp256k1 prime + 1
 		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", "1", "1"},
+		// close but over the secp256k1 prime
+		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffff000000000", "f1ffff000", "1ffff3d1"},
 		// Random samples.
 		{
 			"ad82b8d1cc136e23e9fd77fe2c7db1fe5a2ecbfcbde59ab3529758334f862d28",
@@ -593,6 +607,12 @@ func TestMul(t *testing.T) {
 		{"1", "0", "0"},
 		{"0", "1", "0"},
 		{"1", "1", "1"},
+		// slightly over prime
+		{
+			"ffffffffffffffffffffffffffffffffffffffffffffffffffffffff1ffff",
+			"1000",
+			"1ffff3d1",
+		},
 		// secp256k1 prime-1 * 2
 		{
 			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",