Add an RSA-OAEP implementation.

R=rsc
APPROVED=rsc
DELTA=734  (734 added, 0 deleted, 0 changed)
OCL=35738
CL=35879

src/pkg/crypto/rsa/Makefile

+# Copyright 2009 The Go Authors. All rights reserved.
+# Use of this source code is governed by a BSD-style
+# license that can be found in the LICENSE file.
+
+include $(GOROOT)/src/Make.$(GOARCH)
+
+TARG=crypto/rsa
+GOFILES=\
+	rsa.go\
+
+include $(GOROOT)/src/Make.pkg

src/pkg/crypto/rsa/rsa.go

+// Copyright 2009 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// This package implements RSA encryption as specified in PKCS#1.
+package rsa
+
+// TODO(agl): Add support for PSS padding.
+
+import (
+		"bytes";
+	big	"gmp";
+		"hash";
+		"io";
+		"os";
+)
+
+var bigOne = big.NewInt(1)
+
+// randomSafePrime returns a number, p, of the given size, such that p and
+// (p-1)/2 are both prime with high probability.
+func randomSafePrime(rand io.Reader, bits int) (p *big.Int, err os.Error) {
+	if bits < 1 {
+		err = os.EINVAL;
+	}
+
+	bytes := make([]byte, (bits+7)/8);
+	p = new(big.Int);
+	p2 := new(big.Int);
+
+	for {
+		_, err = io.ReadFull(rand, bytes);
+		if err != nil {
+			return;
+		}
+
+		// Don't let the value be too small.
+		bytes[0] |= 0x80;
+		// Make the value odd since an even number this large certainly isn't prime.
+		bytes[len(bytes)-1] |= 1;
+
+		p.SetBytes(bytes);
+		if p.ProbablyPrime(20) {
+			p2.Rsh(p, 1);	// p2 = (p - 1)/2
+			if p2.ProbablyPrime(20) {
+				return;
+			}
+		}
+	}
+
+	return;
+}
+
+// randomNumber returns a uniform random value in [0, max).
+func randomNumber(rand io.Reader, max *big.Int) (n *big.Int, err os.Error) {
+	k := (max.Len() + 7)/8;
+
+	// r is the number of bits in the used in the most significant byte of
+	// max.
+	r := uint(max.Len() % 8);
+	if r == 0 {
+		r = 8;
+	}
+
+	bytes := make([]byte, k);
+	n = new(big.Int);
+
+	for {
+		_, err = io.ReadFull(rand, bytes);
+		if err != nil {
+			return;
+		}
+
+		// Clear bits in the first byte to increase the probability
+		// that the candidate is < max.
+		bytes[0] &= uint8(int(1<<r)-1);
+
+		n.SetBytes(bytes);
+		if big.CmpInt(n, max) < 0 {
+			return;
+		}
+	}
+
+	return;
+}
+
+// A PublicKey represents the public part of an RSA key.
+type PublicKey struct {
+	N	*big.Int;	// modulus
+	E	int;		// public exponent
+}
+
+// A PrivateKey represents an RSA key
+type PrivateKey struct {
+	PublicKey;	// public part.
+	D		*big.Int;	// private exponent
+	P, Q		*big.Int;	// prime factors of N
+}
+
+// GenerateKeyPair generates an RSA keypair of the given bit size.
+func GenerateKey(rand io.Reader, bits int) (priv *PrivateKey, err os.Error) {
+	priv = new(PrivateKey);
+	// Smaller public exponents lead to faster public key
+	// operations. Since the exponent must be coprime to
+	// (p-1)(q-1), the smallest possible value is 3. Some have
+	// suggested that a larger exponent (often 2**16+1) be used
+	// since previous implementation bugs[1] were avoided when this
+	// was the case. However, there are no current reasons not to use
+	// small exponents.
+	// [1] http://marc.info/?l=cryptography&m=115694833312008&w=2
+	priv.E = 3;
+
+	pminus1 := new(big.Int);
+	qminus1 := new(big.Int);
+	totient := new(big.Int);
+
+	for {
+		p, err := randomSafePrime(rand, bits/2);
+		if err != nil {
+			return;
+		}
+
+		q, err := randomSafePrime(rand, bits/2);
+		if err != nil {
+			return;
+		}
+
+		if big.CmpInt(p, q) == 0 {
+			continue;
+		}
+
+		n := new(big.Int).Mul(p, q);
+		pminus1.Sub(p, bigOne);
+		qminus1.Sub(q, bigOne);
+		totient.Mul(pminus1, qminus1);
+
+		g := new(big.Int);
+		priv.D = new(big.Int);
+		y := new(big.Int);
+		e := big.NewInt(int64(priv.E));
+		big.GcdInt(g, priv.D, y, e, totient);
+
+		if big.CmpInt(g, bigOne) == 0 {
+			priv.D.Add(priv.D, totient);
+			priv.P = p;
+			priv.Q = q;
+			priv.N = n;
+
+			break;
+		}
+	}
+
+	return;
+}
+
+// incCounter increments a four byte, big-endian counter.
+func incCounter(c *[4]byte) {
+	if c[3]++; c[3] != 0 {
+		return;
+	}
+	if c[2]++; c[2] != 0 {
+		return;
+	}
+	if c[1]++; c[1] != 0 {
+		return;
+	}
+	c[0]++;
+}
+
+// mgf1XOR XORs the bytes in out with a mask generated using the MGF1 function
+// specified in PKCS#1 v2.1.
+func mgf1XOR(out []byte, hash hash.Hash, seed []byte) {
+	var counter [4]byte;
+
+	done := 0;
+	for done < len(out) {
+		hash.Write(seed);
+		hash.Write(counter[0:4]);
+		digest := hash.Sum();
+		hash.Reset();
+
+		for i := 0; i < len(digest) && done < len(out); i++ {
+			out[done] ^= digest[i];
+			done++;
+		}
+		incCounter(&counter);
+	}
+}
+
+// MessageTooLongError is returned when attempting to encrypt a message which
+// is too large for the size of the public key.
+type MessageTooLongError struct{}
+
+func (MessageTooLongError) String() string {
+	return "message too long for RSA public key size";
+}
+
+func encrypt(c *big.Int, pub *PublicKey, m *big.Int) *big.Int {
+	e := big.NewInt(int64(pub.E));
+	c.Exp(m, e, pub.N);
+	return c;
+}
+
+// EncryptOAEP encrypts the given message with RSA-OAEP.
+// The message must be no longer than the length of the public modulus less
+// twice the hash length plus 2.
+func EncryptOAEP(hash hash.Hash, rand io.Reader, pub *PublicKey, msg []byte, label []byte) (out []byte, err os.Error) {
+	hash.Reset();
+	k := (pub.N.Len() + 7)/8;
+	if len(msg) > k - 2 * hash.Size() - 2 {
+		err = MessageTooLongError{};
+		return;
+	}
+
+	hash.Write(label);
+	lHash := hash.Sum();
+	hash.Reset();
+
+	em := make([]byte, k);
+	seed := em[1 : 1 + hash.Size()];
+	db := em[1 + hash.Size() : len(em)];
+
+	bytes.Copy(db[0 : hash.Size()], lHash);
+	db[len(db)-len(msg)-1] = 1;
+	bytes.Copy(db[len(db)-len(msg) : len(db)], msg);
+
+	_, err = io.ReadFull(rand, seed);
+	if err != nil {
+		return;
+	}
+
+	mgf1XOR(db, hash, seed);
+	mgf1XOR(seed, hash, db);
+
+	m := new(big.Int);
+	m.SetBytes(em);
+	c := encrypt(new(big.Int), pub, m);
+	out = c.Bytes();
+	return;
+}
+
+// A DecryptionError represents a failure to decrypt a message.
+// It is deliberately vague to avoid adaptive attacks.
+type DecryptionError struct{}
+
+func (DecryptionError) String() string {
+	return "RSA decryption error";
+}
+
+// modInverse returns ia, the inverse of a in the multiplicative group of prime
+// order n. It requires that a be a member of the group (i.e. less than n).
+func modInverse(a, n *big.Int) (ia *big.Int) {
+	g := new(big.Int);
+	x := new(big.Int);
+	y := new(big.Int);
+	big.GcdInt(g, x, y, a, n);
+	if big.CmpInt(x, bigOne) < 0 {
+		// 0 is not the multiplicative inverse of any element so, if x
+		// < 1, then x is negative.
+		x.Add(x, n);
+	}
+
+	return x;
+}
+
+// constantTimeCompare returns 1 iff the two equal length slices, x
+// and y, have equal contents. The time taken is a function of the length of
+// the slices and is independent of the contents.
+func constantTimeCompare(x, y []byte) int {
+	var v byte;
+
+	for i := 0; i < len(x); i++ {
+		v |= x[i]^y[i];
+	}
+
+	return constantTimeByteEq(v, 0);
+}
+
+// constantTimeSelect returns a if mask is 1 and b if mask is 0.
+// Its behaviour is undefined if mask takes any other value.
+func constantTimeSelect(mask, a, b int) int {
+	return ^(mask-1)&a | (mask-1)&b;
+}
+
+// constantTimeByteEq returns 1 if a == b and 0 otherwise.
+func constantTimeByteEq(a, b uint8) (mask int) {
+	x := ^(a^b);
+	x &= x>>4;
+	x &= x>>2;
+	x &= x>>1;
+
+	return int(x);
+}
+
+// decrypt performs an RSA decryption, resulting in a plaintext integer. If a
+// random source is given, RSA blinding is used.
+func decrypt(rand io.Reader, priv *PrivateKey, c *big.Int) (m *big.Int, err os.Error) {
+	// TODO(agl): can we get away with reusing blinds?
+	if big.CmpInt(c, priv.N) > 0 {
+		err = DecryptionError{};
+		return;
+	}
+
+	var ir *big.Int;
+	if rand != nil {
+		// Blinding enabled. Blinding involves multiplying c by r^e.
+		// Then the decryption operation performs (m^e * r^e)^d mod n
+		// which equals mr mod n. The factor of r can then be removed
+		// by multipling by the multiplicative inverse of r.
+
+		r, err := randomNumber(rand, priv.N);
+		if err != nil {
+			return;
+		}
+		ir = modInverse(r, priv.N);
+		bigE := big.NewInt(int64(priv.E));
+		rpowe := new(big.Int).Exp(r, bigE, priv.N);
+		c.Mul(c, rpowe);
+		c.Mod(c, priv.N);
+	}
+
+	m = new(big.Int).Exp(c, priv.D, priv.N);
+
+	if ir != nil {
+		// Unblind.
+		m.Mul(m, ir);
+		m.Mod(m, priv.N);
+	}
+
+	return;
+}
+
+// DecryptOAEP decrypts ciphertext using RSA-OAEP.
+// If rand != nil, DecryptOAEP uses RSA blinding to avoid timing side-channel attacks.
+func DecryptOAEP(hash hash.Hash, rand io.Reader, priv *PrivateKey, ciphertext []byte, label []byte) (msg []byte, err os.Error) {
+	k := (priv.N.Len() + 7)/8;
+	if len(ciphertext) > k ||
+		k < hash.Size() * 2 + 2 {
+		err = DecryptionError{};
+		return;
+	}
+
+	c := new(big.Int).SetBytes(ciphertext);
+
+	m, err := decrypt(rand, priv, c);
+	if err != nil {
+		return;
+	}
+
+	hash.Write(label);
+	lHash := hash.Sum();
+	hash.Reset();
+
+	// Converting the plaintext number to bytes will strip any
+	// leading zeros so we may have to left pad. We do this unconditionally
+	// to avoid leaking timing information. (Although we still probably
+	// leak the number of leading zeros. It's not clear that we can do
+	// anything about this.)
+	em := leftPad(m.Bytes(), k);
+
+	firstByteIsZero := constantTimeByteEq(em[0], 0);
+
+	seed := em[1 : hash.Size() + 1];
+	db := em[hash.Size() + 1 : len(em)];
+
+	mgf1XOR(seed, hash, db);
+	mgf1XOR(db, hash, seed);
+
+	lHash2 := db[0 : hash.Size()];
+
+	// We have to validate the plaintext in contanst time in order to avoid
+	// attacks like: J. Manger. A Chosen Ciphertext Attack on RSA Optimal
+	// Asymmetric Encryption Padding (OAEP) as Standardized in PKCS #1
+	// v2.0. In J. Kilian, editor, Advances in Cryptology.
+	lHash2Good := constantTimeCompare(lHash, lHash2);
+
+	// The remainder of the plaintext must be zero or more 0x00, followed
+	// by 0x01, followed by the message.
+	//   lookingForIndex: 1 iff we are still looking for the 0x01
+	//   index: the offset of the first 0x01 byte
+	//   invalid: 1 iff we saw a non-zero byte before the 0x01.
+	var lookingForIndex, index, invalid int;
+	lookingForIndex = 1;
+	rest := db[hash.Size() : len(db)];
+
+	for i := 0; i < len(rest); i++ {
+		equals0 := constantTimeByteEq(rest[i], 0);
+		equals1 := constantTimeByteEq(rest[i], 1);
+		index = constantTimeSelect(lookingForIndex & equals1, i, index);
+		lookingForIndex = constantTimeSelect(equals1, 0, lookingForIndex);
+		invalid = constantTimeSelect(lookingForIndex & ^equals0, 1, invalid);
+	}
+
+	if firstByteIsZero & lHash2Good & ^invalid & ^lookingForIndex != 1 {
+		err = DecryptionError{};
+		return;
+	}
+
+	msg = rest[index+1 : len(rest)];
+	return;
+}
+
+// leftPad returns a new slice of length size. The contents of input are right
+// aligned in the new slice.
+func leftPad(input []byte, size int) (out []byte) {
+	n := len(input);
+	if n > size {
+		n = size;
+	}
+	out = make([]byte, size);
+	bytes.Copy(out[len(out)-n : len(out)], input);
+	return;
+}

src/pkg/crypto/rsa/rsa_test.go

+// Copyright 2009 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package rsa
+
+import (
+		"bytes";
+		"crypto/sha1";
+	big	"gmp";
+		"os";
+		"testing";
+)
+
+func TestKeyGeneration(t *testing.T) {
+	urandom, err := os.Open("/dev/urandom", os.O_RDONLY, 0);
+	if err != nil {
+		t.Errorf("failed to open /dev/urandom");
+	}
+
+	priv, err := GenerateKey(urandom, 16);
+	if err != nil {
+		t.Errorf("failed to generate key");
+	}
+	pub := &priv.PublicKey;
+	m := big.NewInt(42);
+	c := encrypt(new(big.Int), pub, m);
+	m2, err := decrypt(nil, priv, c);
+	if err != nil {
+		t.Errorf("error while decrypting: %s", err);
+	}
+	if big.CmpInt(m, m2) != 0 {
+		t.Errorf("got:%v, want:%v (%s)", m2, m, priv);
+	}
+
+	m3, err := decrypt(urandom, priv, c);
+	if err != nil {
+		t.Errorf("error while decrypting (blind): %s", err);
+	}
+	if big.CmpInt(m, m3) != 0 {
+		t.Errorf("(blind) got:%v, want:%v", m3, m);
+	}
+}
+
+type SliceReader struct {
+	s	[]byte;
+	offset	int;
+}
+
+func (s SliceReader) Read(out []byte) (n int, err os.Error) {
+	if s.offset == len(s.s) {
+		err = os.EOF;
+		return;
+	}
+	n = bytes.Copy(out, s.s[s.offset : len(s.s)]);
+	s.offset += n;
+	return;
+}
+
+type testEncryptOAEPMessage struct {
+	in	[]byte;
+	seed	[]byte;
+	out	[]byte;
+}
+
+type testEncryptOAEPStruct struct {
+	modulus	string;
+	e	int;
+	d	string;
+	msgs	[]testEncryptOAEPMessage;
+}
+
+func TestEncryptOAEP(t *testing.T) {
+	sha1 := sha1.New();
+	n := new(big.Int);
+	for i, test := range testEncryptOAEPData {
+		n.SetString(test.modulus, 16);
+		public := PublicKey{n, test.e};
+
+		for j, message := range test.msgs {
+			randomSource := SliceReader{message.seed, 0};
+			out, err := EncryptOAEP(sha1, randomSource, &public, message.in, nil);
+			if err != nil {
+				t.Errorf("#%d,%d error: %s", i, j, err);
+			}
+			if bytes.Compare(out, message.out) != 0 {
+				t.Errorf("#%d,%d bad result: %s (want %s)", i, j, out, message.out);
+			}
+		}
+	}
+}
+
+func TestDecryptOAEP(t *testing.T) {
+	urandom, err := os.Open("/dev/urandom", os.O_RDONLY, 0);
+	if err != nil {
+		t.Errorf("Failed to open /dev/urandom");
+	}
+
+	sha1 := sha1.New();
+	n := new(big.Int);
+	d := new(big.Int);
+	for i, test := range testEncryptOAEPData {
+		n.SetString(test.modulus, 16);
+		d.SetString(test.d, 16);
+		private := PrivateKey{PublicKey{n, test.e}, d, nil, nil};
+
+		for j, message := range test.msgs {
+			out, err := DecryptOAEP(sha1, nil, &private, message.out, nil);
+			if err != nil {
+				t.Errorf("#%d,%d error: %s", i, j, err);
+			} else if bytes.Compare(out, message.in) != 0 {
+				t.Errorf("#%d,%d bad result: %#v (want %#v)", i, j, out, message.in);
+			}
+
+			// Decrypt with blinding.
+			out, err = DecryptOAEP(sha1, urandom, &private, message.out, nil);
+			if err != nil {
+				t.Errorf("#%d,%d (blind) error: %s", i, j, err);
+			} else if bytes.Compare(out, message.in) != 0 {
+				t.Errorf("#%d,%d (blind) bad result: %#v (want %#v)", i, j, out, message.in);
+			}
+		}
+	}
+}
+
+type TestConstantTimeCompareStruct struct {
+	a, b	[]byte;
+	out	int;
+}
+
+var testConstandTimeCompareData = []TestConstantTimeCompareStruct{
+	TestConstantTimeCompareStruct{[]byte{}, []byte{}, 1},
+	TestConstantTimeCompareStruct{[]byte{0x11}, []byte{0x11}, 1},
+	TestConstantTimeCompareStruct{[]byte{0x12}, []byte{0x11}, 0},
+}
+
+func TestConstantTimeCompare(t *testing.T) {
+	for i, test := range testConstandTimeCompareData {
+		if r := constantTimeCompare(test.a, test.b); r != test.out {
+			t.Errorf("#%d bad result (got %x, want %x)", i, r, test.out);
+		}
+	}
+}
+
+type TestConstantTimeByteEqStruct struct {
+	a, b	uint8;
+	out	int;
+}
+
+var testConstandTimeByteEqData = []TestConstantTimeByteEqStruct{
+	TestConstantTimeByteEqStruct{0, 0, 1},
+	TestConstantTimeByteEqStruct{0, 1, 0},
+	TestConstantTimeByteEqStruct{1, 0, 0},
+	TestConstantTimeByteEqStruct{0xff, 0xff, 1},
+	TestConstantTimeByteEqStruct{0xff, 0xfe, 0},
+}
+
+func TestConstantTimeByteEq(t *testing.T) {
+	for i, test := range testConstandTimeByteEqData {
+		if r := constantTimeByteEq(test.a, test.b); r != test.out {
+			t.Errorf("#%d bad result (got %x, want %x)", i, r, test.out);
+		}
+	}
+}
+
+// testEncryptOAEPData contains a subset of the vectors from RSA's "Test vectors for RSA-OAEP".
+var testEncryptOAEPData = []testEncryptOAEPStruct{
+	// Key 1
+	testEncryptOAEPStruct{"a8b3b284af8eb50b387034a860f146c4919f318763cd6c5598c8ae4811a1e0abc4c7e0b082d693a5e7fced675cf4668512772c0cbc64a742c6c630f533c8cc72f62ae833c40bf25842e984bb78bdbf97c0107d55bdb662f5c4e0fab9845cb5148ef7392dd3aaff93ae1e6b667bb3d4247616d4f5ba10d4cfd226de88d39f16fb",
+		65537,
+		"53339cfdb79fc8466a655c7316aca85c55fd8f6dd898fdaf119517ef4f52e8fd8e258df93fee180fa0e4ab29693cd83b152a553d4ac4d1812b8b9fa5af0e7f55fe7304df41570926f3311f15c4d65a732c483116ee3d3d2d0af3549ad9bf7cbfb78ad884f84d5beb04724dc7369b31def37d0cf539e9cfcdd3de653729ead5d1",
+		[]testEncryptOAEPMessage{
+			// Example 1.1
+			testEncryptOAEPMessage{
+				[]byte{0x66, 0x28, 0x19, 0x4e, 0x12, 0x07, 0x3d, 0xb0,
+					0x3b, 0xa9, 0x4c, 0xda, 0x9e, 0xf9, 0x53, 0x23, 0x97,
+					0xd5, 0x0d, 0xba, 0x79, 0xb9, 0x87, 0x00, 0x4a, 0xfe,
+					0xfe, 0x34,
+				},
+				[]byte{0x18, 0xb7, 0x76, 0xea, 0x21, 0x06, 0x9d, 0x69,
+					0x77, 0x6a, 0x33, 0xe9, 0x6b, 0xad, 0x48, 0xe1, 0xdd,
+					0xa0, 0xa5, 0xef,
+				},
+				[]byte{0x35, 0x4f, 0xe6, 0x7b, 0x4a, 0x12, 0x6d, 0x5d,
+					0x35, 0xfe, 0x36, 0xc7, 0x77, 0x79, 0x1a, 0x3f, 0x7b,
+					0xa1, 0x3d, 0xef, 0x48, 0x4e, 0x2d, 0x39, 0x08, 0xaf,
+					0xf7, 0x22, 0xfa, 0xd4, 0x68, 0xfb, 0x21, 0x69, 0x6d,
+					0xe9, 0x5d, 0x0b, 0xe9, 0x11, 0xc2, 0xd3, 0x17, 0x4f,
+					0x8a, 0xfc, 0xc2, 0x01, 0x03, 0x5f, 0x7b, 0x6d, 0x8e,
+					0x69, 0x40, 0x2d, 0xe5, 0x45, 0x16, 0x18, 0xc2, 0x1a,
+					0x53, 0x5f, 0xa9, 0xd7, 0xbf, 0xc5, 0xb8, 0xdd, 0x9f,
+					0xc2, 0x43, 0xf8, 0xcf, 0x92, 0x7d, 0xb3, 0x13, 0x22,
+					0xd6, 0xe8, 0x81, 0xea, 0xa9, 0x1a, 0x99, 0x61, 0x70,
+					0xe6, 0x57, 0xa0, 0x5a, 0x26, 0x64, 0x26, 0xd9, 0x8c,
+					0x88, 0x00, 0x3f, 0x84, 0x77, 0xc1, 0x22, 0x70, 0x94,
+					0xa0, 0xd9, 0xfa, 0x1e, 0x8c, 0x40, 0x24, 0x30, 0x9c,
+					0xe1, 0xec, 0xcc, 0xb5, 0x21, 0x00, 0x35, 0xd4, 0x7a,
+					0xc7, 0x2e, 0x8a,
+				},
+			},
+			// Example 1.2
+			testEncryptOAEPMessage{
+				[]byte{0x75, 0x0c, 0x40, 0x47, 0xf5, 0x47, 0xe8, 0xe4,
+					0x14, 0x11, 0x85, 0x65, 0x23, 0x29, 0x8a, 0xc9, 0xba,
+					0xe2, 0x45, 0xef, 0xaf, 0x13, 0x97, 0xfb, 0xe5, 0x6f,
+					0x9d, 0xd5,
+				},
+				[]byte{0x0c, 0xc7, 0x42, 0xce, 0x4a, 0x9b, 0x7f, 0x32,
+					0xf9, 0x51, 0xbc, 0xb2, 0x51, 0xef, 0xd9, 0x25, 0xfe,
+					0x4f, 0xe3, 0x5f,
+				},
+				[]byte{0x64, 0x0d, 0xb1, 0xac, 0xc5, 0x8e, 0x05, 0x68,
+					0xfe, 0x54, 0x07, 0xe5, 0xf9, 0xb7, 0x01, 0xdf, 0xf8,
+					0xc3, 0xc9, 0x1e, 0x71, 0x6c, 0x53, 0x6f, 0xc7, 0xfc,
+					0xec, 0x6c, 0xb5, 0xb7, 0x1c, 0x11, 0x65, 0x98, 0x8d,
+					0x4a, 0x27, 0x9e, 0x15, 0x77, 0xd7, 0x30, 0xfc, 0x7a,
+					0x29, 0x93, 0x2e, 0x3f, 0x00, 0xc8, 0x15, 0x15, 0x23,
+					0x6d, 0x8d, 0x8e, 0x31, 0x01, 0x7a, 0x7a, 0x09, 0xdf,
+					0x43, 0x52, 0xd9, 0x04, 0xcd, 0xeb, 0x79, 0xaa, 0x58,
+					0x3a, 0xdc, 0xc3, 0x1e, 0xa6, 0x98, 0xa4, 0xc0, 0x52,
+					0x83, 0xda, 0xba, 0x90, 0x89, 0xbe, 0x54, 0x91, 0xf6,
+					0x7c, 0x1a, 0x4e, 0xe4, 0x8d, 0xc7, 0x4b, 0xbb, 0xe6,
+					0x64, 0x3a, 0xef, 0x84, 0x66, 0x79, 0xb4, 0xcb, 0x39,
+					0x5a, 0x35, 0x2d, 0x5e, 0xd1, 0x15, 0x91, 0x2d, 0xf6,
+					0x96, 0xff, 0xe0, 0x70, 0x29, 0x32, 0x94, 0x6d, 0x71,
+					0x49, 0x2b, 0x44,
+				},
+			},
+			// Example 1.3
+			testEncryptOAEPMessage{
+				[]byte{0xd9, 0x4a, 0xe0, 0x83, 0x2e, 0x64, 0x45, 0xce,
+					0x42, 0x33, 0x1c, 0xb0, 0x6d, 0x53, 0x1a, 0x82, 0xb1,
+					0xdb, 0x4b, 0xaa, 0xd3, 0x0f, 0x74, 0x6d, 0xc9, 0x16,
+					0xdf, 0x24, 0xd4, 0xe3, 0xc2, 0x45, 0x1f, 0xff, 0x59,
+					0xa6, 0x42, 0x3e, 0xb0, 0xe1, 0xd0, 0x2d, 0x4f, 0xe6,
+					0x46, 0xcf, 0x69, 0x9d, 0xfd, 0x81, 0x8c, 0x6e, 0x97,
+					0xb0, 0x51,
+				},
+				[]byte{0x25, 0x14, 0xdf, 0x46, 0x95, 0x75, 0x5a, 0x67,
+					0xb2, 0x88, 0xea, 0xf4, 0x90, 0x5c, 0x36, 0xee, 0xc6,
+					0x6f, 0xd2, 0xfd,
+				},
+				[]byte{0x42, 0x37, 0x36, 0xed, 0x03, 0x5f, 0x60, 0x26,
+					0xaf, 0x27, 0x6c, 0x35, 0xc0, 0xb3, 0x74, 0x1b, 0x36,
+					0x5e, 0x5f, 0x76, 0xca, 0x09, 0x1b, 0x4e, 0x8c, 0x29,
+					0xe2, 0xf0, 0xbe, 0xfe, 0xe6, 0x03, 0x59, 0x5a, 0xa8,
+					0x32, 0x2d, 0x60, 0x2d, 0x2e, 0x62, 0x5e, 0x95, 0xeb,
+					0x81, 0xb2, 0xf1, 0xc9, 0x72, 0x4e, 0x82, 0x2e, 0xca,
+					0x76, 0xdb, 0x86, 0x18, 0xcf, 0x09, 0xc5, 0x34, 0x35,
+					0x03, 0xa4, 0x36, 0x08, 0x35, 0xb5, 0x90, 0x3b, 0xc6,
+					0x37, 0xe3, 0x87, 0x9f, 0xb0, 0x5e, 0x0e, 0xf3, 0x26,
+					0x85, 0xd5, 0xae, 0xc5, 0x06, 0x7c, 0xd7, 0xcc, 0x96,
+					0xfe, 0x4b, 0x26, 0x70, 0xb6, 0xea, 0xc3, 0x06, 0x6b,
+					0x1f, 0xcf, 0x56, 0x86, 0xb6, 0x85, 0x89, 0xaa, 0xfb,
+					0x7d, 0x62, 0x9b, 0x02, 0xd8, 0xf8, 0x62, 0x5c, 0xa3,
+					0x83, 0x36, 0x24, 0xd4, 0x80, 0x0f, 0xb0, 0x81, 0xb1,
+					0xcf, 0x94, 0xeb,
+				},
+			},
+		},
+	},
+	// Key 10
+	testEncryptOAEPStruct{"ae45ed5601cec6b8cc05f803935c674ddbe0d75c4c09fd7951fc6b0caec313a8df39970c518bffba5ed68f3f0d7f22a4029d413f1ae07e4ebe9e4177ce23e7f5404b569e4ee1bdcf3c1fb03ef113802d4f855eb9b5134b5a7c8085adcae6fa2fa1417ec3763be171b0c62b760ede23c12ad92b980884c641f5a8fac26bdad4a03381a22fe1b754885094c82506d4019a535a286afeb271bb9ba592de18dcf600c2aeeae56e02f7cf79fc14cf3bdc7cd84febbbf950ca90304b2219a7aa063aefa2c3c1980e560cd64afe779585b6107657b957857efde6010988ab7de417fc88d8f384c4e6e72c3f943e0c31c0c4a5cc36f879d8a3ac9d7d59860eaada6b83bb",
+		65537,
+		"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",
+		[]testEncryptOAEPMessage{
+		// Example 10.1
+		testEncryptOAEPMessage{
+			[]byte{0x8b, 0xba, 0x6b, 0xf8, 0x2a, 0x6c, 0x0f, 0x86,
+				0xd5, 0xf1, 0x75, 0x6e, 0x97, 0x95, 0x68, 0x70, 0xb0,
+				0x89, 0x53, 0xb0, 0x6b, 0x4e, 0xb2, 0x05, 0xbc, 0x16,
+				0x94, 0xee,
+			},
+			[]byte{0x47, 0xe1, 0xab, 0x71, 0x19, 0xfe, 0xe5, 0x6c,
+				0x95, 0xee, 0x5e, 0xaa, 0xd8, 0x6f, 0x40, 0xd0, 0xaa,
+				0x63, 0xbd, 0x33,
+			},
+			[]byte{0x53, 0xea, 0x5d, 0xc0, 0x8c, 0xd2, 0x60, 0xfb,
+				0x3b, 0x85, 0x85, 0x67, 0x28, 0x7f, 0xa9, 0x15, 0x52,
+				0xc3, 0x0b, 0x2f, 0xeb, 0xfb, 0xa2, 0x13, 0xf0, 0xae,
+				0x87, 0x70, 0x2d, 0x06, 0x8d, 0x19, 0xba, 0xb0, 0x7f,
+				0xe5, 0x74, 0x52, 0x3d, 0xfb, 0x42, 0x13, 0x9d, 0x68,
+				0xc3, 0xc5, 0xaf, 0xee, 0xe0, 0xbf, 0xe4, 0xcb, 0x79,
+				0x69, 0xcb, 0xf3, 0x82, 0xb8, 0x04, 0xd6, 0xe6, 0x13,
+				0x96, 0x14, 0x4e, 0x2d, 0x0e, 0x60, 0x74, 0x1f, 0x89,
+				0x93, 0xc3, 0x01, 0x4b, 0x58, 0xb9, 0xb1, 0x95, 0x7a,
+				0x8b, 0xab, 0xcd, 0x23, 0xaf, 0x85, 0x4f, 0x4c, 0x35,
+				0x6f, 0xb1, 0x66, 0x2a, 0xa7, 0x2b, 0xfc, 0xc7, 0xe5,
+				0x86, 0x55, 0x9d, 0xc4, 0x28, 0x0d, 0x16, 0x0c, 0x12,
+				0x67, 0x85, 0xa7, 0x23, 0xeb, 0xee, 0xbe, 0xff, 0x71,
+				0xf1, 0x15, 0x94, 0x44, 0x0a, 0xae, 0xf8, 0x7d, 0x10,
+				0x79, 0x3a, 0x87, 0x74, 0xa2, 0x39, 0xd4, 0xa0, 0x4c,
+				0x87, 0xfe, 0x14, 0x67, 0xb9, 0xda, 0xf8, 0x52, 0x08,
+				0xec, 0x6c, 0x72, 0x55, 0x79, 0x4a, 0x96, 0xcc, 0x29,
+				0x14, 0x2f, 0x9a, 0x8b, 0xd4, 0x18, 0xe3, 0xc1, 0xfd,
+				0x67, 0x34, 0x4b, 0x0c, 0xd0, 0x82, 0x9d, 0xf3, 0xb2,
+				0xbe, 0xc6, 0x02, 0x53, 0x19, 0x62, 0x93, 0xc6, 0xb3,
+				0x4d, 0x3f, 0x75, 0xd3, 0x2f, 0x21, 0x3d, 0xd4, 0x5c,
+				0x62, 0x73, 0xd5, 0x05, 0xad, 0xf4, 0xcc, 0xed, 0x10,
+				0x57, 0xcb, 0x75, 0x8f, 0xc2, 0x6a, 0xee, 0xfa, 0x44,
+				0x12, 0x55, 0xed, 0x4e, 0x64, 0xc1, 0x99, 0xee, 0x07,
+				0x5e, 0x7f, 0x16, 0x64, 0x61, 0x82, 0xfd, 0xb4, 0x64,
+				0x73, 0x9b, 0x68, 0xab, 0x5d, 0xaf, 0xf0, 0xe6, 0x3e,
+				0x95, 0x52, 0x01, 0x68, 0x24, 0xf0, 0x54, 0xbf, 0x4d,
+				0x3c, 0x8c, 0x90, 0xa9, 0x7b, 0xb6, 0xb6, 0x55, 0x32,
+				0x84, 0xeb, 0x42, 0x9f, 0xcc,
+			},
+		}},
+	},
+}