diff --git a/btcec_test.go b/btcec_test.go
index 59c50697..92465f2f 100644
--- a/btcec_test.go
+++ b/btcec_test.go
@@ -18,6 +18,483 @@ import (
 	"testing"
 )
 
+// TestAddJacobian tests addition of points projected in Jacobian coordinates.
+func TestAddJacobian(t *testing.T) {
+	tests := []struct {
+		x1, y1, z1 string // Coordinates (in hex) of first point to add
+		x2, y2, z2 string // Coordinates (in hex) of second point to add
+		x3, y3, z3 string // Coordinates (in hex) of expected point
+	}{
+		// Addition with a point at infinity (left hand side).
+		// ∞ + P = P
+		{
+			"0",
+			"0",
+			"0",
+			"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
+			"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
+			"1",
+			"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
+			"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
+			"1",
+		},
+		// Addition with a point at infinity (right hand side).
+		// P + ∞ = P
+		{
+			"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
+			"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
+			"1",
+			"0",
+			"0",
+			"0",
+			"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
+			"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
+			"1",
+		},
+
+		// Addition with z1=z2=1 different x values.
+		{
+			"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
+			"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
+			"1",
+			"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
+			"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
+			"1",
+			"0cfbc7da1e569b334460788faae0286e68b3af7379d5504efc25e4dba16e46a6",
+			"e205f79361bbe0346b037b4010985dbf4f9e1e955e7d0d14aca876bfa79aad87",
+			"44a5646b446e3877a648d6d381370d9ef55a83b666ebce9df1b1d7d65b817b2f",
+		},
+		// Addition with z1=z2=1 same x opposite y.
+		// P(x, y, z) + P(x, -y, z) = infinity
+		{
+			"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
+			"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
+			"1",
+			"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
+			"f48e156428cf0276dc092da5856e182288d7569f97934a56fe44be60f0d359fd",
+			"1",
+			"0",
+			"0",
+			"0",
+		},
+		// Addition with z1=z2=1 same point.
+		// P(x, y, z) + P(x, y, z) = 2P
+		{
+			"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
+			"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
+			"1",
+			"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
+			"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
+			"1",
+			"ec9f153b13ee7bd915882859635ea9730bf0dc7611b2c7b0e37ee64f87c50c27",
+			"b082b53702c466dcf6e984a35671756c506c67c2fcb8adb408c44dd0755c8f2a",
+			"16e3d537ae61fb1247eda4b4f523cfbaee5152c0d0d96b520376833c1e594464",
+		},
+
+		// Addition with z1=z2 (!=1) different x values.
+		{
+			"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
+			"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
+			"2",
+			"5d2fe112c21891d440f65a98473cb626111f8a234d2cd82f22172e369f002147",
+			"98e3386a0a622a35c4561ffb32308d8e1c6758e10ebb1b4ebd3d04b4eb0ecbe8",
+			"2",
+			"cfbc7da1e569b334460788faae0286e68b3af7379d5504efc25e4dba16e46a60",
+			"817de4d86ef80d1ac0ded00426176fd3e787a5579f43452b2a1db021e6ac3778",
+			"129591ad11b8e1de99235b4e04dc367bd56a0ed99baf3a77c6c75f5a6e05f08d",
+		},
+		// Addition with z1=z2 (!=1) same x opposite y.
+		// P(x, y, z) + P(x, -y, z) = infinity
+		{
+			"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
+			"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
+			"2",
+			"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
+			"a470ab21467813b6e0496d2c2b70c11446bab4fcbc9a52b7f225f30e869aea9f",
+			"2",
+			"0",
+			"0",
+			"0",
+		},
+		// Addition with z1=z2 (!=1) same point.
+		// P(x, y, z) + P(x, y, z) = 2P
+		{
+			"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
+			"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
+			"2",
+			"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
+			"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
+			"2",
+			"9f153b13ee7bd915882859635ea9730bf0dc7611b2c7b0e37ee65073c50fabac",
+			"2b53702c466dcf6e984a35671756c506c67c2fcb8adb408c44dd125dc91cb988",
+			"6e3d537ae61fb1247eda4b4f523cfbaee5152c0d0d96b520376833c2e5944a11",
+		},
+
+		// Addition with z1!=z2 and z2=1 different x values.
+		{
+			"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
+			"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
+			"2",
+			"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
+			"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
+			"1",
+			"3ef1f68795a6ccd1181e23eab80a1b9a2cebdcde755413bf097936eb5b91b4f3",
+			"0bef26c377c068d606f6802130bb7e9f3c3d2abcfa1a295950ed81133561cb04",
+			"252b235a2371c3bd3246b69c09b86cf7aad41db3375e74ef8d8ebeb4dc0be11a",
+		},
+		// Addition with z1!=z2 and z2=1 same x opposite y.
+		// P(x, y, z) + P(x, -y, z) = infinity
+		{
+			"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
+			"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
+			"2",
+			"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
+			"f48e156428cf0276dc092da5856e182288d7569f97934a56fe44be60f0d359fd",
+			"1",
+			"0",
+			"0",
+			"0",
+		},
+		// Addition with z1!=z2 and z2=1 same point.
+		// P(x, y, z) + P(x, y, z) = 2P
+		{
+			"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
+			"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
+			"2",
+			"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
+			"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
+			"1",
+			"9f153b13ee7bd915882859635ea9730bf0dc7611b2c7b0e37ee65073c50fabac",
+			"2b53702c466dcf6e984a35671756c506c67c2fcb8adb408c44dd125dc91cb988",
+			"6e3d537ae61fb1247eda4b4f523cfbaee5152c0d0d96b520376833c2e5944a11",
+		},
+
+		// Addition with z1!=z2 and z2!=1 different x values.
+		// P(x, y, z) + P(x, y, z) = 2P
+		{
+			"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
+			"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
+			"2",
+			"91abba6a34b7481d922a4bd6a04899d5a686f6cf6da4e66a0cb427fb25c04bd4",
+			"03fede65e30b4e7576a2abefc963ddbf9fdccbf791b77c29beadefe49951f7d1",
+			"3",
+			"3f07081927fd3f6dadd4476614c89a09eba7f57c1c6c3b01fa2d64eac1eef31e",
+			"949166e04ebc7fd95a9d77e5dfd88d1492ecffd189792e3944eb2b765e09e031",
+			"eb8cba81bcffa4f44d75427506737e1f045f21e6d6f65543ee0e1d163540c931",
+		}, // Addition with z1!=z2 and z2!=1 same x opposite y.
+		// P(x, y, z) + P(x, -y, z) = infinity
+		{
+			"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
+			"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
+			"2",
+			"dcc3768780c74a0325e2851edad0dc8a566fa61a9e7fc4a34d13dcb509f99bc7",
+			"cafc41904dd5428934f7d075129c8ba46eb622d4fc88d72cd1401452664add18",
+			"3",
+			"0",
+			"0",
+			"0",
+		},
+		// Addition with z1!=z2 and z2!=1 same point.
+		// P(x, y, z) + P(x, y, z) = 2P
+		{
+			"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
+			"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
+			"2",
+			"dcc3768780c74a0325e2851edad0dc8a566fa61a9e7fc4a34d13dcb509f99bc7",
+			"3503be6fb22abd76cb082f8aed63745b9149dd2b037728d32ebfebac99b51f17",
+			"3",
+			"9f153b13ee7bd915882859635ea9730bf0dc7611b2c7b0e37ee65073c50fabac",
+			"2b53702c466dcf6e984a35671756c506c67c2fcb8adb408c44dd125dc91cb988",
+			"6e3d537ae61fb1247eda4b4f523cfbaee5152c0d0d96b520376833c2e5944a11",
+		},
+	}
+
+	t.Logf("Running %d tests", len(tests))
+	for i, test := range tests {
+		// Convert hex to field values.
+		x1 := btcec.NewFieldVal().SetHex(test.x1)
+		y1 := btcec.NewFieldVal().SetHex(test.y1)
+		z1 := btcec.NewFieldVal().SetHex(test.z1)
+		x2 := btcec.NewFieldVal().SetHex(test.x2)
+		y2 := btcec.NewFieldVal().SetHex(test.y2)
+		z2 := btcec.NewFieldVal().SetHex(test.z2)
+		x3 := btcec.NewFieldVal().SetHex(test.x3)
+		y3 := btcec.NewFieldVal().SetHex(test.y3)
+		z3 := btcec.NewFieldVal().SetHex(test.z3)
+
+		// Ensure the test data is using points that are actually on
+		// the curve (or the point at infinity).
+		if !z1.IsZero() && !btcec.S256().TstIsJacobianOnCurve(x1, y1, z1) {
+			t.Errorf("#%d first point is not on the curve -- "+
+				"invalid test data", i)
+			continue
+		}
+		if !z2.IsZero() && !btcec.S256().TstIsJacobianOnCurve(x2, y2, z2) {
+			t.Errorf("#%d second point is not on the curve -- "+
+				"invalid test data", i)
+			continue
+		}
+		if !z3.IsZero() && !btcec.S256().TstIsJacobianOnCurve(x3, y3, z3) {
+			t.Errorf("#%d expected point is not on the curve -- "+
+				"invalid test data", i)
+			continue
+		}
+
+		// Add the two points.
+		rx, ry, rz := btcec.NewFieldVal(), btcec.NewFieldVal(), btcec.NewFieldVal()
+		btcec.S256().TstAddJacobian(x1, y1, z1, x2, y2, z2, rx, ry, rz)
+
+		// Ensure result matches expected.
+		if !rx.Equals(x3) || !ry.Equals(y3) || !rz.Equals(z3) {
+			t.Errorf("#%d wrong result\ngot: (%v, %v, %v)\n"+
+				"want: (%v, %v, %v)", i, rx, ry, rz, x3, y3, z3)
+			continue
+		}
+	}
+}
+
+// TestAddAffine tests addition of points in affine coordinates.
+func TestAddAffine(t *testing.T) {
+	tests := []struct {
+		x1, y1 string // Coordinates (in hex) of first point to add
+		x2, y2 string // Coordinates (in hex) of second point to add
+		x3, y3 string // Coordinates (in hex) of expected point
+	}{
+		// Addition with a point at infinity (left hand side).
+		// ∞ + P = P
+		{
+			"0",
+			"0",
+			"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
+			"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
+			"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
+			"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
+		},
+		// Addition with a point at infinity (right hand side).
+		// P + ∞ = P
+		{
+			"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
+			"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
+			"0",
+			"0",
+			"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
+			"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
+		},
+
+		// Addition with different x values.
+		{
+			"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
+			"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
+			"d74bf844b0862475103d96a611cf2d898447e288d34b360bc885cb8ce7c00575",
+			"131c670d414c4546b88ac3ff664611b1c38ceb1c21d76369d7a7a0969d61d97d",
+			"fd5b88c21d3143518d522cd2796f3d726793c88b3e05636bc829448e053fed69",
+			"21cf4f6a5be5ff6380234c50424a970b1f7e718f5eb58f68198c108d642a137f",
+		},
+		// Addition with same x opposite y.
+		// P(x, y) + P(x, -y) = infinity
+		{
+			"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
+			"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
+			"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
+			"f48e156428cf0276dc092da5856e182288d7569f97934a56fe44be60f0d359fd",
+			"0",
+			"0",
+		},
+		// Addition with same point.
+		// P(x, y) + P(x, y) = 2P
+		{
+			"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
+			"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
+			"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
+			"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
+			"59477d88ae64a104dbb8d31ec4ce2d91b2fe50fa628fb6a064e22582196b365b",
+			"938dc8c0f13d1e75c987cb1a220501bd614b0d3dd9eb5c639847e1240216e3b6",
+		},
+	}
+
+	t.Logf("Running %d tests", len(tests))
+	for i, test := range tests {
+		// Convert hex to field values.
+		x1, y1 := fromHex(test.x1), fromHex(test.y1)
+		x2, y2 := fromHex(test.x2), fromHex(test.y2)
+		x3, y3 := fromHex(test.x3), fromHex(test.y3)
+
+		// Ensure the test data is using points that are actually on
+		// the curve (or the point at infinity).
+		if !(x1.Sign() == 0 && y1.Sign() == 0) && !btcec.S256().IsOnCurve(x1, y1) {
+			t.Errorf("#%d first point is not on the curve -- "+
+				"invalid test data", i)
+			continue
+		}
+		if !(x2.Sign() == 0 && y2.Sign() == 0) && !btcec.S256().IsOnCurve(x2, y2) {
+			t.Errorf("#%d second point is not on the curve -- "+
+				"invalid test data", i)
+			continue
+		}
+		if !(x3.Sign() == 0 && y3.Sign() == 0) && !btcec.S256().IsOnCurve(x3, y3) {
+			t.Errorf("#%d expected point is not on the curve -- "+
+				"invalid test data", i)
+			continue
+		}
+
+		// Add the two points.
+		rx, ry := btcec.S256().Add(x1, y1, x2, y2)
+
+		// Ensure result matches expected.
+		if rx.Cmp(x3) != 00 || ry.Cmp(y3) != 0 {
+			t.Errorf("#%d wrong result\ngot: (%x, %x)\n"+
+				"want: (%x, %x)", i, rx, ry, x3, y3)
+			continue
+		}
+	}
+}
+
+// TestDoubleJacobian tests doubling of points projected in Jacobian
+// coordinates.
+func TestDoubleJacobian(t *testing.T) {
+	tests := []struct {
+		x1, y1, z1 string // Coordinates (in hex) of point to double
+		x3, y3, z3 string // Coordinates (in hex) of expected point
+	}{
+		// Doubling a point at infinity is still infinity.
+		{
+			"0",
+			"0",
+			"0",
+			"0",
+			"0",
+			"0",
+		},
+		// Doubling with z1=1.
+		{
+			"34f9460f0e4f08393d192b3c5133a6ba099aa0ad9fd54ebccfacdfa239ff49c6",
+			"0b71ea9bd730fd8923f6d25a7a91e7dd7728a960686cb5a901bb419e0f2ca232",
+			"1",
+			"ec9f153b13ee7bd915882859635ea9730bf0dc7611b2c7b0e37ee64f87c50c27",
+			"b082b53702c466dcf6e984a35671756c506c67c2fcb8adb408c44dd0755c8f2a",
+			"16e3d537ae61fb1247eda4b4f523cfbaee5152c0d0d96b520376833c1e594464",
+		},
+		// Doubling with z1!=1.
+		{
+			"d3e5183c393c20e4f464acf144ce9ae8266a82b67f553af33eb37e88e7fd2718",
+			"5b8f54deb987ec491fb692d3d48f3eebb9454b034365ad480dda0cf079651190",
+			"2",
+			"9f153b13ee7bd915882859635ea9730bf0dc7611b2c7b0e37ee65073c50fabac",
+			"2b53702c466dcf6e984a35671756c506c67c2fcb8adb408c44dd125dc91cb988",
+			"6e3d537ae61fb1247eda4b4f523cfbaee5152c0d0d96b520376833c2e5944a11",
+		},
+	}
+
+	t.Logf("Running %d tests", len(tests))
+	for i, test := range tests {
+		// Convert hex to field values.
+		x1 := btcec.NewFieldVal().SetHex(test.x1)
+		y1 := btcec.NewFieldVal().SetHex(test.y1)
+		z1 := btcec.NewFieldVal().SetHex(test.z1)
+		x3 := btcec.NewFieldVal().SetHex(test.x3)
+		y3 := btcec.NewFieldVal().SetHex(test.y3)
+		z3 := btcec.NewFieldVal().SetHex(test.z3)
+
+		// Ensure the test data is using points that are actually on
+		// the curve (or the point at infinity).
+		if !z1.IsZero() && !btcec.S256().TstIsJacobianOnCurve(x1, y1, z1) {
+			t.Errorf("#%d first point is not on the curve -- "+
+				"invalid test data", i)
+			continue
+		}
+		if !z3.IsZero() && !btcec.S256().TstIsJacobianOnCurve(x3, y3, z3) {
+			t.Errorf("#%d expected point is not on the curve -- "+
+				"invalid test data", i)
+			continue
+		}
+
+		// Double the point.
+		rx, ry, rz := btcec.NewFieldVal(), btcec.NewFieldVal(), btcec.NewFieldVal()
+		btcec.S256().TstDoubleJacobian(x1, y1, z1, rx, ry, rz)
+
+		// Ensure result matches expected.
+		if !rx.Equals(x3) || !ry.Equals(y3) || !rz.Equals(z3) {
+			t.Errorf("#%d wrong result\ngot: (%v, %v, %v)\n"+
+				"want: (%v, %v, %v)", i, rx, ry, rz, x3, y3, z3)
+			continue
+		}
+	}
+}
+
+// TestDoubleAffine tests doubling of points in affine coordinates.
+func TestDoubleAffine(t *testing.T) {
+	tests := []struct {
+		x1, y1 string // Coordinates (in hex) of point to double
+		x3, y3 string // Coordinates (in hex) of expected point
+	}{
+		// Doubling a point at infinity is still infinity.
+		// 2*∞ = ∞ (point at infinity)
+
+		{
+			"0",
+			"0",
+			"0",
+			"0",
+		},
+
+		// Random points.
+		{
+			"e41387ffd8baaeeb43c2faa44e141b19790e8ac1f7ff43d480dc132230536f86",
+			"1b88191d430f559896149c86cbcb703193105e3cf3213c0c3556399836a2b899",
+			"88da47a089d333371bd798c548ef7caae76e737c1980b452d367b3cfe3082c19",
+			"3b6f659b09a362821dfcfefdbfbc2e59b935ba081b6c249eb147b3c2100b1bc1",
+		},
+		{
+			"b3589b5d984f03ef7c80aeae444f919374799edf18d375cab10489a3009cff0c",
+			"c26cf343875b3630e15bccc61202815b5d8f1fd11308934a584a5babe69db36a",
+			"e193860172998751e527bb12563855602a227fc1f612523394da53b746bb2fb1",
+			"2bfcf13d2f5ab8bb5c611fab5ebbed3dc2f057062b39a335224c22f090c04789",
+		},
+		{
+			"2b31a40fbebe3440d43ac28dba23eee71c62762c3fe3dbd88b4ab82dc6a82340",
+			"9ba7deb02f5c010e217607fd49d58db78ec273371ea828b49891ce2fd74959a1",
+			"2c8d5ef0d343b1a1a48aa336078eadda8481cb048d9305dc4fdf7ee5f65973a2",
+			"bb4914ac729e26d3cd8f8dc8f702f3f4bb7e0e9c5ae43335f6e94c2de6c3dc95",
+		},
+		{
+			"61c64b760b51981fab54716d5078ab7dffc93730b1d1823477e27c51f6904c7a",
+			"ef6eb16ea1a36af69d7f66524c75a3a5e84c13be8fbc2e811e0563c5405e49bd",
+			"5f0dcdd2595f5ad83318a0f9da481039e36f135005420393e72dfca985b482f4",
+			"a01c849b0837065c1cb481b0932c441f49d1cab1b4b9f355c35173d93f110ae0",
+		},
+	}
+
+	t.Logf("Running %d tests", len(tests))
+	for i, test := range tests {
+		// Convert hex to field values.
+		x1, y1 := fromHex(test.x1), fromHex(test.y1)
+		x3, y3 := fromHex(test.x3), fromHex(test.y3)
+
+		// Ensure the test data is using points that are actually on
+		// the curve (or the point at infinity).
+		if !(x1.Sign() == 0 && y1.Sign() == 0) && !btcec.S256().IsOnCurve(x1, y1) {
+			t.Errorf("#%d first point is not on the curve -- "+
+				"invalid test data", i)
+			continue
+		}
+		if !(x3.Sign() == 0 && y3.Sign() == 0) && !btcec.S256().IsOnCurve(x3, y3) {
+			t.Errorf("#%d expected point is not on the curve -- "+
+				"invalid test data", i)
+			continue
+		}
+
+		// Double the point.
+		rx, ry := btcec.S256().Double(x1, y1)
+
+		// Ensure result matches expected.
+		if rx.Cmp(x3) != 00 || ry.Cmp(y3) != 0 {
+			t.Errorf("#%d wrong result\ngot: (%x, %x)\n"+
+				"want: (%x, %x)", i, rx, ry, x3, y3)
+			continue
+		}
+	}
+}
+
 func TestOnCurve(t *testing.T) {
 	s256 := btcec.S256()
 	if !s256.IsOnCurve(s256.Params().Gx, s256.Params().Gy) {
diff --git a/field_test.go b/field_test.go
new file mode 100644
index 00000000..7c381175
--- /dev/null
+++ b/field_test.go
@@ -0,0 +1,743 @@
+// Copyright (c) 2013 Conformal Systems LLC.
+// Copyright (c) 2013 Dave Collins
+// Use of this source code is governed by an ISC
+// license that can be found in the LICENSE file.
+
+package btcec_test
+
+import (
+	"github.com/conformal/btcec"
+	"reflect"
+	"testing"
+)
+
+// TestSetInt ensures that setting a field value to various native integers
+// works as expected.
+func TestSetInt(t *testing.T) {
+	tests := []struct {
+		in  uint
+		raw [10]uint32
+	}{
+		{5, [10]uint32{5, 0, 0, 0, 0, 0, 0, 0, 0, 0}},
+		// 2^26
+		{67108864, [10]uint32{67108864, 0, 0, 0, 0, 0, 0, 0, 0, 0}},
+		// 2^26 + 1
+		{67108865, [10]uint32{67108865, 0, 0, 0, 0, 0, 0, 0, 0, 0}},
+		// 2^32 - 1
+		{4294967295, [10]uint32{4294967295, 0, 0, 0, 0, 0, 0, 0, 0, 0}},
+	}
+
+	t.Logf("Running %d tests", len(tests))
+	for i, test := range tests {
+		f := btcec.NewFieldVal().SetInt(test.in)
+		result := f.TstRawInts()
+		if !reflect.DeepEqual(result, test.raw) {
+			t.Errorf("fieldVal.Set #%d wrong result\ngot: %v\n"+
+				"want: %v", i, result, test.raw)
+			continue
+		}
+	}
+}
+
+// TestZero ensures that zeroing a field value zero works as expected.
+func TestZero(t *testing.T) {
+	f := btcec.NewFieldVal().SetInt(2)
+	f.Zero()
+	for idx, rawInt := range f.TstRawInts() {
+		if rawInt != 0 {
+			t.Errorf("internal field integer at index #%d is not "+
+				"zero - got %d", idx, rawInt)
+		}
+	}
+}
+
+// TestIsZero ensures that checking if a field IsZero works as expected.
+func TestIsZero(t *testing.T) {
+	f := btcec.NewFieldVal()
+	if !f.IsZero() {
+		t.Errorf("new field value is not zero - got %v (rawints %x)", f,
+			f.TstRawInts())
+	}
+
+	f.SetInt(1)
+	if f.IsZero() {
+		t.Errorf("field claims it's zero when it's not - got %v "+
+			"(raw rawints %x)", f, f.TstRawInts())
+	}
+
+	f.Zero()
+	if !f.IsZero() {
+		t.Errorf("field claims it's not zero when it is - got %v "+
+			"(raw rawints %x)", f, f.TstRawInts())
+	}
+}
+
+// TestStringer ensures the stringer returns the appropriate hex string.
+func TestStringer(t *testing.T) {
+	tests := []struct {
+		in       string
+		expected string
+	}{
+		{"0", "0000000000000000000000000000000000000000000000000000000000000000"},
+		{"1", "0000000000000000000000000000000000000000000000000000000000000001"},
+		{"a", "000000000000000000000000000000000000000000000000000000000000000a"},
+		{"b", "000000000000000000000000000000000000000000000000000000000000000b"},
+		{"c", "000000000000000000000000000000000000000000000000000000000000000c"},
+		{"d", "000000000000000000000000000000000000000000000000000000000000000d"},
+		{"e", "000000000000000000000000000000000000000000000000000000000000000e"},
+		{"f", "000000000000000000000000000000000000000000000000000000000000000f"},
+		{"f0", "00000000000000000000000000000000000000000000000000000000000000f0"},
+		// 2^26-1
+		{
+			"3ffffff",
+			"0000000000000000000000000000000000000000000000000000000003ffffff",
+		},
+		// 2^32-1
+		{
+			"ffffffff",
+			"00000000000000000000000000000000000000000000000000000000ffffffff",
+		},
+		// 2^64-1
+		{
+			"ffffffffffffffff",
+			"000000000000000000000000000000000000000000000000ffffffffffffffff",
+		},
+		// 2^96-1
+		{
+			"ffffffffffffffffffffffff",
+			"0000000000000000000000000000000000000000ffffffffffffffffffffffff",
+		},
+		// 2^128-1
+		{
+			"ffffffffffffffffffffffffffffffff",
+			"00000000000000000000000000000000ffffffffffffffffffffffffffffffff",
+		},
+		// 2^160-1
+		{
+			"ffffffffffffffffffffffffffffffffffffffff",
+			"000000000000000000000000ffffffffffffffffffffffffffffffffffffffff",
+		},
+		// 2^192-1
+		{
+			"ffffffffffffffffffffffffffffffffffffffffffffffff",
+			"0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffff",
+		},
+		// 2^224-1
+		{
+			"ffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
+			"00000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
+		},
+		// 2^256-4294968273 (the btcec prime, so should result in 0)
+		{
+			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
+			"0000000000000000000000000000000000000000000000000000000000000000",
+		},
+		// 2^256-4294968274 (the secp256k1 prime+1, so should result in 1)
+		{
+			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc30",
+			"0000000000000000000000000000000000000000000000000000000000000001",
+		},
+
+		// Invalid hex
+		{"g", "0000000000000000000000000000000000000000000000000000000000000000"},
+		{"1h", "0000000000000000000000000000000000000000000000000000000000000000"},
+		{"i1", "0000000000000000000000000000000000000000000000000000000000000000"},
+	}
+
+	t.Logf("Running %d tests", len(tests))
+	for i, test := range tests {
+		f := btcec.NewFieldVal().SetHex(test.in)
+		result := f.String()
+		if result != test.expected {
+			t.Errorf("fieldVal.String #%d wrong result\ngot: %v\n"+
+				"want: %v", i, result, test.expected)
+			continue
+		}
+	}
+}
+
+// TestNormalize ensures that normalizing the internal field words works as
+// expected.
+func TestNormalize(t *testing.T) {
+	tests := []struct {
+		raw        [10]uint32 // Intentionally denormalized value
+		normalized [10]uint32 // Normalized form of the raw value
+	}{
+		{
+			[10]uint32{0x00000005, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+			[10]uint32{0x00000005, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+		},
+		// 2^26
+		{
+			[10]uint32{0x04000000, 0x0, 0, 0, 0, 0, 0, 0, 0, 0},
+			[10]uint32{0x00000000, 0x1, 0, 0, 0, 0, 0, 0, 0, 0},
+		},
+		// 2^26 + 1
+		{
+			[10]uint32{0x04000001, 0x0, 0, 0, 0, 0, 0, 0, 0, 0},
+			[10]uint32{0x00000001, 0x1, 0, 0, 0, 0, 0, 0, 0, 0},
+		},
+		// 2^32 - 1
+		{
+			[10]uint32{0xffffffff, 0x00, 0, 0, 0, 0, 0, 0, 0, 0},
+			[10]uint32{0x03ffffff, 0x3f, 0, 0, 0, 0, 0, 0, 0, 0},
+		},
+		// 2^32
+		{
+			[10]uint32{0x04000000, 0x3f, 0, 0, 0, 0, 0, 0, 0, 0},
+			[10]uint32{0x00000000, 0x40, 0, 0, 0, 0, 0, 0, 0, 0},
+		},
+		// 2^32 + 1
+		{
+			[10]uint32{0x04000001, 0x3f, 0, 0, 0, 0, 0, 0, 0, 0},
+			[10]uint32{0x00000001, 0x40, 0, 0, 0, 0, 0, 0, 0, 0},
+		},
+		// 2^64 - 1
+		{
+			[10]uint32{0xffffffff, 0xffffffc0, 0xfc0, 0, 0, 0, 0, 0, 0, 0},
+			[10]uint32{0x03ffffff, 0x03ffffff, 0xfff, 0, 0, 0, 0, 0, 0, 0},
+		},
+		// 2^64
+		{
+			[10]uint32{0x04000000, 0x03ffffff, 0x0fff, 0, 0, 0, 0, 0, 0, 0},
+			[10]uint32{0x00000000, 0x00000000, 0x1000, 0, 0, 0, 0, 0, 0, 0},
+		},
+		// 2^64 + 1
+		{
+			[10]uint32{0x04000001, 0x03ffffff, 0x0fff, 0, 0, 0, 0, 0, 0, 0},
+			[10]uint32{0x00000001, 0x00000000, 0x1000, 0, 0, 0, 0, 0, 0, 0},
+		},
+		// 2^96 - 1
+		{
+			[10]uint32{0xffffffff, 0xffffffc0, 0xffffffc0, 0x3ffc0, 0, 0, 0, 0, 0, 0},
+			[10]uint32{0x03ffffff, 0x03ffffff, 0x03ffffff, 0x3ffff, 0, 0, 0, 0, 0, 0},
+		},
+		// 2^96
+		{
+			[10]uint32{0x04000000, 0x03ffffff, 0x03ffffff, 0x3ffff, 0, 0, 0, 0, 0, 0},
+			[10]uint32{0x00000000, 0x00000000, 0x00000000, 0x40000, 0, 0, 0, 0, 0, 0},
+		},
+		// 2^128 - 1
+		{
+			[10]uint32{0xffffffff, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffc0, 0, 0, 0, 0, 0},
+			[10]uint32{0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0xffffff, 0, 0, 0, 0, 0},
+		},
+		// 2^128
+		{
+			[10]uint32{0x04000000, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x0ffffff, 0, 0, 0, 0, 0},
+			[10]uint32{0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x1000000, 0, 0, 0, 0, 0},
+		},
+		// 2^256 - 4294968273 (secp256k1 prime)
+		{
+			[10]uint32{0xfffffc2f, 0xffffff80, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0x3fffc0},
+			[10]uint32{0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x000000},
+		},
+		// 2^256 - 1
+		{
+			[10]uint32{0xffffffff, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0x3fffc0},
+			[10]uint32{0x000003d0, 0x00000040, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x000000},
+		},
+	}
+
+	t.Logf("Running %d tests", len(tests))
+	for i, test := range tests {
+		f := btcec.NewFieldVal().TstSetRawInts(test.raw).Normalize()
+		result := f.TstRawInts()
+		if !reflect.DeepEqual(result, test.normalized) {
+			t.Errorf("fieldVal.Set #%d wrong normalized result\n"+
+				"got: %x\nwant: %x", i, result, test.normalized)
+			continue
+		}
+	}
+}
+
+// TestIsOdd ensures that checking if a field value IsOdd works as expected.
+func TestIsOdd(t *testing.T) {
+	tests := []struct {
+		in       string // hex encoded value
+		expected bool   // expected oddness
+	}{
+		{"0", false},
+		{"1", true},
+		{"2", false},
+		// 2^32 - 1
+		{"ffffffff", true},
+		// 2^64 - 2
+		{"fffffffffffffffe", false},
+		// secp256k1 prime
+		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", true},
+	}
+
+	t.Logf("Running %d tests", len(tests))
+	for i, test := range tests {
+		f := btcec.NewFieldVal().SetHex(test.in)
+		result := f.IsOdd()
+		if result != test.expected {
+			t.Errorf("fieldVal.IsOdd #%d wrong result\n"+
+				"got: %v\nwant: %v", i, result, test.expected)
+			continue
+		}
+	}
+}
+
+// TestEquals ensures that checking two field values for equality via Equals
+// works as expected.
+func TestEquals(t *testing.T) {
+	tests := []struct {
+		in1      string // hex encoded value
+		in2      string // hex encoded value
+		expected bool   // expected equality
+	}{
+		{"0", "0", true},
+		{"0", "1", false},
+		{"1", "0", false},
+		// 2^32 - 1 == 2^32 - 1?
+		{"ffffffff", "ffffffff", true},
+		// 2^64 - 1 == 2^64 - 2?
+		{"ffffffffffffffff", "fffffffffffffffe", false},
+		// 0 == prime (mod prime)?
+		{"0", "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", true},
+		// 1 == prime+1 (mod prime)?
+		{"1", "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc30", true},
+	}
+
+	t.Logf("Running %d tests", len(tests))
+	for i, test := range tests {
+		f := btcec.NewFieldVal().SetHex(test.in1).Normalize()
+		f2 := btcec.NewFieldVal().SetHex(test.in2).Normalize()
+		result := f.Equals(f2)
+		if result != test.expected {
+			t.Errorf("fieldVal.Equals #%d wrong result\n"+
+				"got: %v\nwant: %v", i, result, test.expected)
+			continue
+		}
+	}
+}
+
+// TestNegate ensures that negating field values via Negate works as expected.
+func TestNegate(t *testing.T) {
+	tests := []struct {
+		in       string // hex encoded value
+		expected string // expected hex encoded value
+	}{
+		// secp256k1 prime (aka 0)
+		{"0", "0"},
+		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", "0"},
+		{"0", "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f"},
+		// secp256k1 prime-1
+		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e", "1"},
+		{"1", "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e"},
+		// secp256k1 prime-2
+		{"2", "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d"},
+		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d", "2"},
+		// Random sampling
+		{
+			"b3d9aac9c5e43910b4385b53c7e78c21d4cd5f8e683c633aed04c233efc2e120",
+			"4c2655363a1bc6ef4bc7a4ac381873de2b32a07197c39cc512fb3dcb103d1b0f",
+		},
+		{
+			"f8a85984fee5a12a7c8dd08830d83423c937d77c379e4a958e447a25f407733f",
+			"757a67b011a5ed583722f77cf27cbdc36c82883c861b56a71bb85d90bf888f0",
+		},
+		{
+			"45ee6142a7fda884211e93352ed6cb2807800e419533be723a9548823ece8312",
+			"ba119ebd5802577bdee16ccad12934d7f87ff1be6acc418dc56ab77cc131791d",
+		},
+		{
+			"53c2a668f07e411a2e473e1c3b6dcb495dec1227af27673761d44afe5b43d22b",
+			"ac3d59970f81bee5d1b8c1e3c49234b6a213edd850d898c89e2bb500a4bc2a04",
+		},
+	}
+
+	t.Logf("Running %d tests", len(tests))
+	for i, test := range tests {
+		f := btcec.NewFieldVal().SetHex(test.in).Normalize()
+		expected := btcec.NewFieldVal().SetHex(test.expected).Normalize()
+		result := f.Negate(1).Normalize()
+		if !result.Equals(expected) {
+			t.Errorf("fieldVal.Negate #%d wrong result\n"+
+				"got: %v\nwant: %v", i, result, expected)
+			continue
+		}
+	}
+}
+
+// TestAddInt ensures that adding an integer to field values via AddInt works as
+// expected.
+func TestAddInt(t *testing.T) {
+	tests := []struct {
+		in1      string // hex encoded value
+		in2      uint   // unsigned integer to add to the value above
+		expected string // expected hex encoded value
+	}{
+		{"0", 1, "1"},
+		{"1", 0, "1"},
+		{"1", 1, "2"},
+		// secp256k1 prime-1 + 1
+		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e", 1, "0"},
+		// secp256k1 prime + 1
+		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", 1, "1"},
+		// Random samples.
+		{
+			"ff95ad9315aff04ab4af0ce673620c7145dc85d03bab5ba4b09ca2c4dec2d6c1",
+			0x10f,
+			"ff95ad9315aff04ab4af0ce673620c7145dc85d03bab5ba4b09ca2c4dec2d7d0",
+		},
+		{
+			"44bdae6b772e7987941f1ba314e6a5b7804a4c12c00961b57d20f41deea9cecf",
+			0x2cf11d41,
+			"44bdae6b772e7987941f1ba314e6a5b7804a4c12c00961b57d20f41e1b9aec10",
+		},
+		{
+			"88c3ecae67b591935fb1f6a9499c35315ffad766adca665c50b55f7105122c9c",
+			0x4829aa2d,
+			"88c3ecae67b591935fb1f6a9499c35315ffad766adca665c50b55f714d3bd6c9",
+		},
+		{
+			"8523e9edf360ca32a95aae4e57fcde5a542b471d08a974d94ea0ee09a015e2a6",
+			0xa21265a5,
+			"8523e9edf360ca32a95aae4e57fcde5a542b471d08a974d94ea0ee0a4228484b",
+		},
+	}
+
+	t.Logf("Running %d tests", len(tests))
+	for i, test := range tests {
+		f := btcec.NewFieldVal().SetHex(test.in1).Normalize()
+		expected := btcec.NewFieldVal().SetHex(test.expected).Normalize()
+		result := f.AddInt(test.in2).Normalize()
+		if !result.Equals(expected) {
+			t.Errorf("fieldVal.AddInt #%d wrong result\n"+
+				"got: %v\nwant: %v", i, result, expected)
+			continue
+		}
+	}
+}
+
+// TestAdd ensures that adding two field values together via Add works as
+// expected.
+func TestAdd(t *testing.T) {
+	tests := []struct {
+		in1      string // first hex encoded value
+		in2      string // second hex encoded value to add
+		expected string // expected hex encoded value
+	}{
+		{"0", "1", "1"},
+		{"1", "0", "1"},
+		{"1", "1", "2"},
+		// secp256k1 prime-1 + 1
+		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e", "1", "0"},
+		// secp256k1 prime + 1
+		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", "1", "1"},
+		// Random samples.
+		{
+			"2b2012f975404e5065b4292fb8bed0a5d315eacf24c74d8b27e73bcc5430edcc",
+			"2c3cefa4e4753e8aeec6ac4c12d99da4d78accefda3b7885d4c6bab46c86db92",
+			"575d029e59b58cdb547ad57bcb986e4aaaa0b7beff02c610fcadf680c0b7c95e",
+		},
+		{
+			"8131e8722fe59bb189692b96c9f38de92885730f1dd39ab025daffb94c97f79c",
+			"ff5454b765f0aab5f0977dcc629becc84cabeb9def48e79c6aadb2622c490fa9",
+			"80863d2995d646677a00a9632c8f7ab175315ead0d1c824c9088b21c78e10b16",
+		},
+		{
+			"c7c95e93d0892b2b2cdd77e80eb646ea61be7a30ac7e097e9f843af73fad5c22",
+			"3afe6f91a74dfc1c7f15c34907ee981656c37236d946767dd53ccad9190e437c",
+			"02c7ce2577d72747abf33b3116a4df00b881ec6785c47ffc74c105d158bba36f",
+		},
+		{
+			"fd1c26f6a23381e5d785ba889494ec059369b888ad8431cd67d8c934b580dbe1",
+			"a475aa5a31dcca90ef5b53c097d9133d6b7117474b41e7877bb199590fc0489c",
+			"a191d150d4104c76c6e10e492c6dff42fedacfcff8c61954e38a628ec541284e",
+		},
+	}
+
+	t.Logf("Running %d tests", len(tests))
+	for i, test := range tests {
+		f := btcec.NewFieldVal().SetHex(test.in1).Normalize()
+		f2 := btcec.NewFieldVal().SetHex(test.in2).Normalize()
+		expected := btcec.NewFieldVal().SetHex(test.expected).Normalize()
+		result := f.Add(f2).Normalize()
+		if !result.Equals(expected) {
+			t.Errorf("fieldVal.Add #%d wrong result\n"+
+				"got: %v\nwant: %v", i, result, expected)
+			continue
+		}
+	}
+}
+
+// TestAdd2 ensures that adding two field values together via Add2 works as
+// expected.
+func TestAdd2(t *testing.T) {
+	tests := []struct {
+		in1      string // first hex encoded value
+		in2      string // second hex encoded value to add
+		expected string // expected hex encoded value
+	}{
+		{"0", "1", "1"},
+		{"1", "0", "1"},
+		{"1", "1", "2"},
+		// secp256k1 prime-1 + 1
+		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e", "1", "0"},
+		// secp256k1 prime + 1
+		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", "1", "1"},
+		// Random samples.
+		{
+			"ad82b8d1cc136e23e9fd77fe2c7db1fe5a2ecbfcbde59ab3529758334f862d28",
+			"4d6a4e95d6d61f4f46b528bebe152d408fd741157a28f415639347a84f6f574b",
+			"faed0767a2e98d7330b2a0bcea92df3eea060d12380e8ec8b62a9fdb9ef58473",
+		},
+		{
+			"f3f43a2540054a86e1df98547ec1c0e157b193e5350fb4a3c3ea214b228ac5e7",
+			"25706572592690ea3ddc951a1b48b504a4c83dc253756e1b96d56fdfb3199522",
+			"19649f97992bdb711fbc2d6e9a0a75e5fc79d1a7888522bf5abf912bd5a45eda",
+		},
+		{
+			"6915bb94eef13ff1bb9b2633d997e13b9b1157c713363cc0e891416d6734f5b8",
+			"11f90d6ac6fe1c4e8900b1c85fb575c251ec31b9bc34b35ada0aea1c21eded22",
+			"7b0ec8ffb5ef5c40449bd7fc394d56fdecfd8980cf6af01bc29c2b898922e2da",
+		},
+		{
+			"48b0c9eae622eed9335b747968544eb3e75cb2dc8128388f948aa30f88cabde4",
+			"0989882b52f85f9d524a3a3061a0e01f46d597839d2ba637320f4b9510c8d2d5",
+			"523a5216391b4e7685a5aea9c9f52ed32e324a601e53dec6c699eea4999390b9",
+		},
+	}
+
+	t.Logf("Running %d tests", len(tests))
+	for i, test := range tests {
+		f := btcec.NewFieldVal().SetHex(test.in1).Normalize()
+		f2 := btcec.NewFieldVal().SetHex(test.in2).Normalize()
+		expected := btcec.NewFieldVal().SetHex(test.expected).Normalize()
+		result := f.Add2(f, f2).Normalize()
+		if !result.Equals(expected) {
+			t.Errorf("fieldVal.Add2 #%d wrong result\n"+
+				"got: %v\nwant: %v", i, result, expected)
+			continue
+		}
+	}
+}
+
+// TestMulInt ensures that adding an integer to field values via MulInt works as
+// expected.
+func TestMulInt(t *testing.T) {
+	tests := []struct {
+		in1      string // hex encoded value
+		in2      uint   // unsigned integer to multiply with value above
+		expected string // expected hex encoded value
+	}{
+		{"0", 0, "0"},
+		{"1", 0, "0"},
+		{"0", 1, "0"},
+		{"1", 1, "1"},
+		// secp256k1 prime-1 * 2
+		{
+			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
+			2,
+			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d",
+		},
+		// secp256k1 prime * 3
+		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", 3, "0"},
+		// secp256k1 prime-1 * 8
+		{
+			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
+			8,
+			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc27",
+		},
+		// Random samples for first value.  The second value is limited
+		// to 8 since that is the maximum int used in the elliptic curve
+		// calculations.
+		{
+			"b75674dc9180d306c692163ac5e089f7cef166af99645c0c23568ab6d967288a",
+			6,
+			"4c06bd2b6904f228a76c8560a3433bced9a8681d985a2848d407404d186b0280",
+		},
+		{
+			"54873298ac2b5ba8591c125ae54931f5ea72040aee07b208d6135476fb5b9c0e",
+			3,
+			"fd9597ca048212f90b543710afdb95e1bf560c20ca17161a8239fd64f212d42a",
+		},
+		{
+			"7c30fbd363a74c17e1198f56b090b59bbb6c8755a74927a6cba7a54843506401",
+			5,
+			"6cf4eb20f2447c77657fccb172d38c0aa91ea4ac446dc641fa463a6b5091fba7",
+		},
+		{
+			"fb4529be3e027a3d1587d8a500b72f2d312e3577340ef5175f96d113be4c2ceb",
+			8,
+			"da294df1f013d1e8ac3ec52805b979698971abb9a077a8bafcb688a4f261820f",
+		},
+	}
+
+	t.Logf("Running %d tests", len(tests))
+	for i, test := range tests {
+		f := btcec.NewFieldVal().SetHex(test.in1).Normalize()
+		expected := btcec.NewFieldVal().SetHex(test.expected).Normalize()
+		result := f.MulInt(test.in2).Normalize()
+		if !result.Equals(expected) {
+			t.Errorf("fieldVal.MulInt #%d wrong result\n"+
+				"got: %v\nwant: %v", i, result, expected)
+			continue
+		}
+	}
+}
+
+// TestMul ensures that multiplying two field valuess via Mul works as expected.
+func TestMul(t *testing.T) {
+	tests := []struct {
+		in1      string // first hex encoded value
+		in2      string // second hex encoded value to multiply with
+		expected string // expected hex encoded value
+	}{
+		{"0", "0", "0"},
+		{"1", "0", "0"},
+		{"0", "1", "0"},
+		{"1", "1", "1"},
+		// secp256k1 prime-1 * 2
+		{
+			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
+			"2",
+			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d",
+		},
+		// secp256k1 prime * 3
+		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", "3", "0"},
+		// secp256k1 prime-1 * 8
+		{
+			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
+			"8",
+			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc27",
+		},
+		// Random samples.
+		{
+			"cfb81753d5ef499a98ecc04c62cb7768c2e4f1740032946db1c12e405248137e",
+			"58f355ad27b4d75fb7db0442452e732c436c1f7c5a7c4e214fa9cc031426a7d3",
+			"1018cd2d7c2535235b71e18db9cd98027386328d2fa6a14b36ec663c4c87282b",
+		},
+		{
+			"26e9d61d1cdf3920e9928e85fa3df3e7556ef9ab1d14ec56d8b4fc8ed37235bf",
+			"2dfc4bbe537afee979c644f8c97b31e58be5296d6dbc460091eae630c98511cf",
+			"da85f48da2dc371e223a1ae63bd30b7e7ee45ae9b189ac43ff357e9ef8cf107a",
+		},
+		{
+			"5db64ed5afb71646c8b231585d5b2bf7e628590154e0854c4c29920b999ff351",
+			"279cfae5eea5d09ade8e6a7409182f9de40981bc31c84c3d3dfe1d933f152e9a",
+			"2c78fbae91792dd0b157abe3054920049b1879a7cc9d98cfda927d83be411b37",
+		},
+		{
+			"b66dfc1f96820b07d2bdbd559c19319a3a73c97ceb7b3d662f4fe75ecb6819e6",
+			"bf774aba43e3e49eb63a6e18037d1118152568f1a3ac4ec8b89aeb6ff8008ae1",
+			"c4f016558ca8e950c21c3f7fc15f640293a979c7b01754ee7f8b3340d4902ebb",
+		},
+	}
+
+	t.Logf("Running %d tests", len(tests))
+	for i, test := range tests {
+		f := btcec.NewFieldVal().SetHex(test.in1).Normalize()
+		f2 := btcec.NewFieldVal().SetHex(test.in2).Normalize()
+		expected := btcec.NewFieldVal().SetHex(test.expected).Normalize()
+		result := f.Mul(f2).Normalize()
+		if !result.Equals(expected) {
+			t.Errorf("fieldVal.Mul #%d wrong result\n"+
+				"got: %v\nwant: %v", i, result, expected)
+			continue
+		}
+	}
+}
+
+// TestSquare ensures that squaring field values via Square works as expected.
+func TestSquare(t *testing.T) {
+	tests := []struct {
+		in       string // hex encoded value
+		expected string // expected hex encoded value
+	}{
+		// secp256k1 prime (aka 0)
+		{"0", "0"},
+		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", "0"},
+		{"0", "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f"},
+		// secp256k1 prime-1
+		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e", "1"},
+		// secp256k1 prime-2
+		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d", "4"},
+		// Random sampling
+		{
+			"b0ba920360ea8436a216128047aab9766d8faf468895eb5090fc8241ec758896",
+			"133896b0b69fda8ce9f648b9a3af38f345290c9eea3cbd35bafcadf7c34653d3",
+		},
+		{
+			"c55d0d730b1d0285a1599995938b042a756e6e8857d390165ffab480af61cbd5",
+			"cd81758b3f5877cbe7e5b0a10cebfa73bcbf0957ca6453e63ee8954ab7780bee",
+		},
+		{
+			"e89c1f9a70d93651a1ba4bca5b78658f00de65a66014a25544d3365b0ab82324",
+			"39ffc7a43e5dbef78fd5d0354fb82c6d34f5a08735e34df29da14665b43aa1f",
+		},
+		{
+			"7dc26186079d22bcbe1614aa20ae627e62d72f9be7ad1e99cac0feb438956f05",
+			"bf86bcfc4edb3d81f916853adfda80c07c57745b008b60f560b1912f95bce8ae",
+		},
+	}
+
+	t.Logf("Running %d tests", len(tests))
+	for i, test := range tests {
+		f := btcec.NewFieldVal().SetHex(test.in).Normalize()
+		expected := btcec.NewFieldVal().SetHex(test.expected).Normalize()
+		result := f.Square().Normalize()
+		if !result.Equals(expected) {
+			t.Errorf("fieldVal.Square #%d wrong result\n"+
+				"got: %v\nwant: %v", i, result, expected)
+			continue
+		}
+	}
+}
+
+// TestInverse ensures that finding the multiplicative inverse via Inverse works
+// as expected.
+func TestInverse(t *testing.T) {
+	tests := []struct {
+		in       string // hex encoded value
+		expected string // expected hex encoded value
+	}{
+		// secp256k1 prime (aka 0)
+		{"0", "0"},
+		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", "0"},
+		{"0", "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f"},
+		// secp256k1 prime-1
+		{
+			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
+			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
+		},
+		// secp256k1 prime-2
+		{
+			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d",
+			"7fffffffffffffffffffffffffffffffffffffffffffffffffffffff7ffffe17",
+		},
+		// Random sampling
+		{
+			"16fb970147a9acc73654d4be233cc48b875ce20a2122d24f073d29bd28805aca",
+			"987aeb257b063df0c6d1334051c47092b6d8766c4bf10c463786d93f5bc54354",
+		},
+		{
+			"69d1323ce9f1f7b3bd3c7320b0d6311408e30281e273e39a0d8c7ee1c8257919",
+			"49340981fa9b8d3dad72de470b34f547ed9179c3953797d0943af67806f4bb6",
+		},
+		{
+			"e0debf988ae098ecda07d0b57713e97c6d213db19753e8c95aa12a2fc1cc5272",
+			"64f58077b68af5b656b413ea366863f7b2819f8d27375d9c4d9804135ca220c2",
+		},
+		{
+			"dcd394f91f74c2ba16aad74a22bb0ed47fe857774b8f2d6c09e28bfb14642878",
+			"fb848ec64d0be572a63c38fe83df5e7f3d032f60bf8c969ef67d36bf4ada22a9",
+		},
+	}
+
+	t.Logf("Running %d tests", len(tests))
+	for i, test := range tests {
+		f := btcec.NewFieldVal().SetHex(test.in).Normalize()
+		expected := btcec.NewFieldVal().SetHex(test.expected).Normalize()
+		result := f.Inverse().Normalize()
+		if !result.Equals(expected) {
+			t.Errorf("fieldVal.Inverse #%d wrong result\n"+
+				"got: %v\nwant: %v", i, result, expected)
+			continue
+		}
+	}
+}
diff --git a/internal_test.go b/internal_test.go
index 6615fd36..c388225b 100644
--- a/internal_test.go
+++ b/internal_test.go
@@ -4,8 +4,62 @@
 
 package btcec
 
+import (
+	"math/big"
+)
+
 const (
 	TstPubkeyUncompressed = pubkeyUncompressed
 	TstPubkeyCompressed   = pubkeyCompressed
 	TstPubkeyHybrid       = pubkeyHybrid
 )
+
+// TstRawInts allows the test package to get the integers from the internal
+// field representation for ensuring correctness.  It is only available during
+// the tests.
+func (f *fieldVal) TstRawInts() [10]uint32 {
+	return f.n
+}
+
+// TstSetRawInts allows the test package to directly set the integers used by
+// the internal field representation.  It is only available during the tests.
+func (f *fieldVal) TstSetRawInts(raw [10]uint32) *fieldVal {
+	for i := 0; i < len(raw); i++ {
+		f.n[i] = raw[i]
+	}
+	return f
+}
+
+// TstFieldJacobianToBigAffine makes the internal fieldJacobianToBigAffine
+// function available to the test package.
+func (curve *KoblitzCurve) TstFieldJacobianToBigAffine(x, y, z *fieldVal) (*big.Int, *big.Int) {
+	return curve.fieldJacobianToBigAffine(x, y, z)
+}
+
+// TstIsJacobianOnCurve returns boolean if the point (x,y,z) is on the curve.
+func (curve *KoblitzCurve) TstIsJacobianOnCurve(x, y, z *fieldVal) bool {
+	// Elliptic curve equation for secp256k1 is: y^2 = x^3 + 7
+	// In Jacobian coordinates, Y = y/z^3 and X = x/z^2
+	// Thus:
+	// (y/z^3)^2 = (x/z^2)^3 + 7
+	// y^2/z^6 = x^3/z^6 + 7
+	// y^2 = x^3 + 7*z^6
+	var y2, z2, x3, result fieldVal
+	y2.SquareVal(y).Normalize()
+	z2.SquareVal(z)
+	x3.SquareVal(x).Mul(x)
+	result.SquareVal(&z2).Mul(&z2).MulInt(7).Add(&x3).Normalize()
+	return y2.Equals(&result)
+}
+
+// TstAddJacobian makes the internal addJacobian function available to the test
+// package.
+func (curve *KoblitzCurve) TstAddJacobian(x1, y1, z1, x2, y2, z2, x3, y3, z3 *fieldVal) {
+	curve.addJacobian(x1, y1, z1, x2, y2, z2, x3, y3, z3)
+}
+
+// TstDoubleJacobian makes the internal doubleJacobian function available to the test
+// package.
+func (curve *KoblitzCurve) TstDoubleJacobian(x1, y1, z1, x3, y3, z3 *fieldVal) {
+	curve.doubleJacobian(x1, y1, z1, x3, y3, z3)
+}
diff --git a/test_coverage.txt b/test_coverage.txt
index 316be9bd..2295eefc 100644
--- a/test_coverage.txt
+++ b/test_coverage.txt
@@ -1,26 +1,58 @@
 
-github.com/conformal/btcec/signature.go	 parseSig			 100.00% (51/51)
-github.com/conformal/btcec/btcec.go	 KoblitzCurve.doubleJacobian	 100.00% (21/21)
-github.com/conformal/btcec/btcec.go	 KoblitzCurve.ScalarMult	 100.00% (9/9)
-github.com/conformal/btcec/pubkey.go	 PublicKey.SerializeHybrid	 100.00% (8/8)
-github.com/conformal/btcec/btcec.go	 initS256			 100.00% (7/7)
-github.com/conformal/btcec/pubkey.go	 PublicKey.SerializeCompressed	 100.00% (7/7)
-github.com/conformal/btcec/btcec.go	 KoblitzCurve.IsOnCurve		 100.00% (7/7)
-github.com/conformal/btcec/pubkey.go	 PublicKey.SerializeUncompressed 100.00% (5/5)
-github.com/conformal/btcec/btcec.go	 zForAffine			 100.00% (4/4)
-github.com/conformal/btcec/signature.go	 canonicalPadding		 100.00% (4/4)
-github.com/conformal/btcec/btcec.go	 KoblitzCurve.QPlus1Div4	 100.00% (3/3)
-github.com/conformal/btcec/btcec.go	 KoblitzCurve.Add		 100.00% (3/3)
-github.com/conformal/btcec/btcec.go	 S256				 100.00% (2/2)
-github.com/conformal/btcec/btcec.go	 initAll			 100.00% (1/1)
-github.com/conformal/btcec/btcec.go	 KoblitzCurve.ScalarBaseMult	 100.00% (1/1)
-github.com/conformal/btcec/pubkey.go	 isOdd				 100.00% (1/1)
-github.com/conformal/btcec/signature.go	 ParseSignature			 100.00% (1/1)
-github.com/conformal/btcec/signature.go	 ParseDERSignature		 100.00% (1/1)
-github.com/conformal/btcec/btcec.go	 KoblitzCurve.Params		 100.00% (1/1)
-github.com/conformal/btcec/pubkey.go	 ParsePubKey			 96.88% (31/32)
-github.com/conformal/btcec/btcec.go	 KoblitzCurve.addJacobian	 91.67% (55/60)
-github.com/conformal/btcec/btcec.go	 KoblitzCurve.affineFromJacobian 90.00% (9/10)
-github.com/conformal/btcec/btcec.go	 KoblitzCurve.Double		 0.00% (0/2)
-github.com/conformal/btcec		 ------------------------------- 96.27% (232/241)
+github.com/conformal/btcec/field.go	 fieldVal.Normalize			 100.00% (93/93)
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+github.com/conformal/btcec/signature.go	 parseSig				 100.00% (51/51)
+github.com/conformal/btcec/btcec.go	 KoblitzCurve.addGeneric		 100.00% (35/35)
+github.com/conformal/btcec/btcec.go	 KoblitzCurve.addZ2EqualsOne		 100.00% (35/35)
+github.com/conformal/btcec/field.go	 fieldVal.PutBytes			 100.00% (32/32)
+github.com/conformal/btcec/btcec.go	 KoblitzCurve.addZ1EqualsZ2		 100.00% (30/30)
+github.com/conformal/btcec/btcec.go	 KoblitzCurve.addZ1AndZ2EqualsOne	 100.00% (29/29)
+github.com/conformal/btcec/btcec.go	 KoblitzCurve.addJacobian		 100.00% (22/22)
+github.com/conformal/btcec/btcec.go	 KoblitzCurve.doubleZ1EqualsOne		 100.00% (18/18)
+github.com/conformal/btcec/btcec.go	 KoblitzCurve.doubleGeneric		 100.00% (18/18)
+github.com/conformal/btcec/field.go	 fieldVal.MulInt			 100.00% (12/12)
+github.com/conformal/btcec/btcec.go	 KoblitzCurve.fieldJacobianToBigAffine	 100.00% (12/12)
+github.com/conformal/btcec/field.go	 fieldVal.Add				 100.00% (11/11)
+github.com/conformal/btcec/field.go	 fieldVal.Add2				 100.00% (11/11)
+github.com/conformal/btcec/field.go	 fieldVal.SetBytes			 100.00% (11/11)
+github.com/conformal/btcec/field.go	 fieldVal.NegateVal			 100.00% (11/11)
+github.com/conformal/btcec/btcec.go	 KoblitzCurve.ScalarMult		 100.00% (10/10)
+github.com/conformal/btcec/field.go	 fieldVal.Zero				 100.00% (10/10)
+github.com/conformal/btcec/btcec.go	 KoblitzCurve.doubleJacobian		 100.00% (9/9)
+github.com/conformal/btcec/btcec.go	 KoblitzCurve.Add			 100.00% (9/9)
+github.com/conformal/btcec/btcec.go	 initS256				 100.00% (8/8)
+github.com/conformal/btcec/pubkey.go	 PublicKey.SerializeHybrid		 100.00% (8/8)
+github.com/conformal/btcec/pubkey.go	 PublicKey.SerializeCompressed		 100.00% (7/7)
+github.com/conformal/btcec/btcec.go	 KoblitzCurve.Double			 100.00% (6/6)
+github.com/conformal/btcec/field.go	 fieldVal.SetByteSlice			 100.00% (5/5)
+github.com/conformal/btcec/pubkey.go	 PublicKey.SerializeUncompressed	 100.00% (5/5)
+github.com/conformal/btcec/signature.go	 canonicalPadding			 100.00% (4/4)
+github.com/conformal/btcec/field.go	 fieldVal.SetHex			 100.00% (4/4)
+github.com/conformal/btcec/btcec.go	 KoblitzCurve.bigAffineToField		 100.00% (4/4)
+github.com/conformal/btcec/btcec.go	 KoblitzCurve.IsOnCurve			 100.00% (4/4)
+github.com/conformal/btcec/field.go	 fieldVal.SetInt			 100.00% (3/3)
+github.com/conformal/btcec/field.go	 fieldVal.Bytes				 100.00% (3/3)
+github.com/conformal/btcec/field.go	 fieldVal.Set				 100.00% (2/2)
+github.com/conformal/btcec/field.go	 fieldVal.String			 100.00% (2/2)
+github.com/conformal/btcec/btcec.go	 S256					 100.00% (2/2)
+github.com/conformal/btcec/field.go	 fieldVal.IsZero			 100.00% (2/2)
+github.com/conformal/btcec/field.go	 fieldVal.Equals			 100.00% (2/2)
+github.com/conformal/btcec/field.go	 fieldVal.AddInt			 100.00% (2/2)
+github.com/conformal/btcec/field.go	 fieldVal.Square			 100.00% (1/1)
+github.com/conformal/btcec/btcec.go	 KoblitzCurve.ScalarBaseMult		 100.00% (1/1)
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+github.com/conformal/btcec/field.go	 NewFieldVal				 100.00% (1/1)
+github.com/conformal/btcec/pubkey.go	 isOdd					 100.00% (1/1)
+github.com/conformal/btcec/signature.go	 ParseDERSignature			 100.00% (1/1)
+github.com/conformal/btcec/field.go	 fieldVal.Mul				 100.00% (1/1)
+github.com/conformal/btcec/btcec.go	 KoblitzCurve.QPlus1Div4		 100.00% (1/1)
+github.com/conformal/btcec/btcec.go	 initAll				 100.00% (1/1)
+github.com/conformal/btcec/field.go	 fieldVal.Negate			 100.00% (1/1)
+github.com/conformal/btcec/field.go	 fieldVal.IsOdd				 100.00% (1/1)
+github.com/conformal/btcec/signature.go	 ParseSignature				 100.00% (1/1)
+github.com/conformal/btcec/pubkey.go	 ParsePubKey				 96.88% (31/32)
+github.com/conformal/btcec/pubkey.go	 pad					 80.00% (4/5)
+github.com/conformal/btcec		 -------------------------------------	 99.76% (823/825)