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-rw-r--r--libgo/go/crypto/rsa/pkcs1v15.go273
-rw-r--r--libgo/go/crypto/rsa/pkcs1v15_test.go220
-rw-r--r--libgo/go/crypto/rsa/rsa.go445
-rw-r--r--libgo/go/crypto/rsa/rsa_test.go250
4 files changed, 1188 insertions, 0 deletions
diff --git a/libgo/go/crypto/rsa/pkcs1v15.go b/libgo/go/crypto/rsa/pkcs1v15.go
new file mode 100644
index 000000000..714046250
--- /dev/null
+++ b/libgo/go/crypto/rsa/pkcs1v15.go
@@ -0,0 +1,273 @@
+// 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 (
+ "big"
+ "crypto/subtle"
+ "io"
+ "os"
+)
+
+// This file implements encryption and decryption using PKCS#1 v1.5 padding.
+
+// EncryptPKCS1v15 encrypts the given message with RSA and the padding scheme from PKCS#1 v1.5.
+// The message must be no longer than the length of the public modulus minus 11 bytes.
+// WARNING: use of this function to encrypt plaintexts other than session keys
+// is dangerous. Use RSA OAEP in new protocols.
+func EncryptPKCS1v15(rand io.Reader, pub *PublicKey, msg []byte) (out []byte, err os.Error) {
+ k := (pub.N.BitLen() + 7) / 8
+ if len(msg) > k-11 {
+ err = MessageTooLongError{}
+ return
+ }
+
+ // EM = 0x02 || PS || 0x00 || M
+ em := make([]byte, k-1)
+ em[0] = 2
+ ps, mm := em[1:len(em)-len(msg)-1], em[len(em)-len(msg):]
+ err = nonZeroRandomBytes(ps, rand)
+ if err != nil {
+ return
+ }
+ em[len(em)-len(msg)-1] = 0
+ copy(mm, msg)
+
+ m := new(big.Int).SetBytes(em)
+ c := encrypt(new(big.Int), pub, m)
+ out = c.Bytes()
+ return
+}
+
+// DecryptPKCS1v15 decrypts a plaintext using RSA and the padding scheme from PKCS#1 v1.5.
+// If rand != nil, it uses RSA blinding to avoid timing side-channel attacks.
+func DecryptPKCS1v15(rand io.Reader, priv *PrivateKey, ciphertext []byte) (out []byte, err os.Error) {
+ valid, out, err := decryptPKCS1v15(rand, priv, ciphertext)
+ if err == nil && valid == 0 {
+ err = DecryptionError{}
+ }
+
+ return
+}
+
+// DecryptPKCS1v15SessionKey decrypts a session key using RSA and the padding scheme from PKCS#1 v1.5.
+// If rand != nil, it uses RSA blinding to avoid timing side-channel attacks.
+// It returns an error if the ciphertext is the wrong length or if the
+// ciphertext is greater than the public modulus. Otherwise, no error is
+// returned. If the padding is valid, the resulting plaintext message is copied
+// into key. Otherwise, key is unchanged. These alternatives occur in constant
+// time. It is intended that the user of this function generate a random
+// session key beforehand and continue the protocol with the resulting value.
+// This will remove any possibility that an attacker can learn any information
+// about the plaintext.
+// See ``Chosen Ciphertext Attacks Against Protocols Based on the RSA
+// Encryption Standard PKCS #1'', Daniel Bleichenbacher, Advances in Cryptology
+// (Crypto '98),
+func DecryptPKCS1v15SessionKey(rand io.Reader, priv *PrivateKey, ciphertext []byte, key []byte) (err os.Error) {
+ k := (priv.N.BitLen() + 7) / 8
+ if k-(len(key)+3+8) < 0 {
+ err = DecryptionError{}
+ return
+ }
+
+ valid, msg, err := decryptPKCS1v15(rand, priv, ciphertext)
+ if err != nil {
+ return
+ }
+
+ valid &= subtle.ConstantTimeEq(int32(len(msg)), int32(len(key)))
+ subtle.ConstantTimeCopy(valid, key, msg)
+ return
+}
+
+func decryptPKCS1v15(rand io.Reader, priv *PrivateKey, ciphertext []byte) (valid int, msg []byte, err os.Error) {
+ k := (priv.N.BitLen() + 7) / 8
+ if k < 11 {
+ err = DecryptionError{}
+ return
+ }
+
+ c := new(big.Int).SetBytes(ciphertext)
+ m, err := decrypt(rand, priv, c)
+ if err != nil {
+ return
+ }
+
+ em := leftPad(m.Bytes(), k)
+ firstByteIsZero := subtle.ConstantTimeByteEq(em[0], 0)
+ secondByteIsTwo := subtle.ConstantTimeByteEq(em[1], 2)
+
+ // The remainder of the plaintext must be a string of non-zero random
+ // octets, followed by a 0, followed by the message.
+ // lookingForIndex: 1 iff we are still looking for the zero.
+ // index: the offset of the first zero byte.
+ var lookingForIndex, index int
+ lookingForIndex = 1
+
+ for i := 2; i < len(em); i++ {
+ equals0 := subtle.ConstantTimeByteEq(em[i], 0)
+ index = subtle.ConstantTimeSelect(lookingForIndex&equals0, i, index)
+ lookingForIndex = subtle.ConstantTimeSelect(equals0, 0, lookingForIndex)
+ }
+
+ valid = firstByteIsZero & secondByteIsTwo & (^lookingForIndex & 1)
+ msg = em[index+1:]
+ return
+}
+
+// nonZeroRandomBytes fills the given slice with non-zero random octets.
+func nonZeroRandomBytes(s []byte, rand io.Reader) (err os.Error) {
+ _, err = io.ReadFull(rand, s)
+ if err != nil {
+ return
+ }
+
+ for i := 0; i < len(s); i++ {
+ for s[i] == 0 {
+ _, err = rand.Read(s[i : i+1])
+ if err != nil {
+ return
+ }
+ // In tests, the PRNG may return all zeros so we do
+ // this to break the loop.
+ s[i] ^= 0x42
+ }
+ }
+
+ return
+}
+
+// Due to the design of PKCS#1 v1.5, we need to know the exact hash function in
+// use. A generic hash.Hash will not do.
+type PKCS1v15Hash int
+
+const (
+ HashMD5 PKCS1v15Hash = iota
+ HashSHA1
+ HashSHA256
+ HashSHA384
+ HashSHA512
+ HashMD5SHA1 // combined MD5 and SHA1 hash used for RSA signing in TLS.
+)
+
+// These are ASN1 DER structures:
+// DigestInfo ::= SEQUENCE {
+// digestAlgorithm AlgorithmIdentifier,
+// digest OCTET STRING
+// }
+// For performance, we don't use the generic ASN1 encoder. Rather, we
+// precompute a prefix of the digest value that makes a valid ASN1 DER string
+// with the correct contents.
+var hashPrefixes = [][]byte{
+ // HashMD5
+ {0x30, 0x20, 0x30, 0x0c, 0x06, 0x08, 0x2a, 0x86, 0x48, 0x86, 0xf7, 0x0d, 0x02, 0x05, 0x05, 0x00, 0x04, 0x10},
+ // HashSHA1
+ {0x30, 0x21, 0x30, 0x09, 0x06, 0x05, 0x2b, 0x0e, 0x03, 0x02, 0x1a, 0x05, 0x00, 0x04, 0x14},
+ // HashSHA256
+ {0x30, 0x31, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x01, 0x05, 0x00, 0x04, 0x20},
+ // HashSHA384
+ {0x30, 0x41, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x02, 0x05, 0x00, 0x04, 0x30},
+ // HashSHA512
+ {0x30, 0x51, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x03, 0x05, 0x00, 0x04, 0x40},
+ // HashMD5SHA1
+ {}, // A special TLS case which doesn't use an ASN1 prefix.
+}
+
+// SignPKCS1v15 calcuates the signature of hashed using RSASSA-PSS-SIGN from RSA PKCS#1 v1.5.
+// Note that hashed must be the result of hashing the input message using the
+// given hash function.
+func SignPKCS1v15(rand io.Reader, priv *PrivateKey, hash PKCS1v15Hash, hashed []byte) (s []byte, err os.Error) {
+ hashLen, prefix, err := pkcs1v15HashInfo(hash, len(hashed))
+ if err != nil {
+ return
+ }
+
+ tLen := len(prefix) + hashLen
+ k := (priv.N.BitLen() + 7) / 8
+ if k < tLen+11 {
+ return nil, MessageTooLongError{}
+ }
+
+ // EM = 0x00 || 0x01 || PS || 0x00 || T
+ em := make([]byte, k)
+ em[1] = 1
+ for i := 2; i < k-tLen-1; i++ {
+ em[i] = 0xff
+ }
+ copy(em[k-tLen:k-hashLen], prefix)
+ copy(em[k-hashLen:k], hashed)
+
+ m := new(big.Int).SetBytes(em)
+ c, err := decrypt(rand, priv, m)
+ if err == nil {
+ s = c.Bytes()
+ }
+ return
+}
+
+// VerifyPKCS1v15 verifies an RSA PKCS#1 v1.5 signature.
+// hashed is the result of hashing the input message using the given hash
+// function and sig is the signature. A valid signature is indicated by
+// returning a nil error.
+func VerifyPKCS1v15(pub *PublicKey, hash PKCS1v15Hash, hashed []byte, sig []byte) (err os.Error) {
+ hashLen, prefix, err := pkcs1v15HashInfo(hash, len(hashed))
+ if err != nil {
+ return
+ }
+
+ tLen := len(prefix) + hashLen
+ k := (pub.N.BitLen() + 7) / 8
+ if k < tLen+11 {
+ err = VerificationError{}
+ return
+ }
+
+ c := new(big.Int).SetBytes(sig)
+ m := encrypt(new(big.Int), pub, c)
+ em := leftPad(m.Bytes(), k)
+ // EM = 0x00 || 0x01 || PS || 0x00 || T
+
+ ok := subtle.ConstantTimeByteEq(em[0], 0)
+ ok &= subtle.ConstantTimeByteEq(em[1], 1)
+ ok &= subtle.ConstantTimeCompare(em[k-hashLen:k], hashed)
+ ok &= subtle.ConstantTimeCompare(em[k-tLen:k-hashLen], prefix)
+ ok &= subtle.ConstantTimeByteEq(em[k-tLen-1], 0)
+
+ for i := 2; i < k-tLen-1; i++ {
+ ok &= subtle.ConstantTimeByteEq(em[i], 0xff)
+ }
+
+ if ok != 1 {
+ return VerificationError{}
+ }
+
+ return nil
+}
+
+func pkcs1v15HashInfo(hash PKCS1v15Hash, inLen int) (hashLen int, prefix []byte, err os.Error) {
+ switch hash {
+ case HashMD5:
+ hashLen = 16
+ case HashSHA1:
+ hashLen = 20
+ case HashSHA256:
+ hashLen = 32
+ case HashSHA384:
+ hashLen = 48
+ case HashSHA512:
+ hashLen = 64
+ case HashMD5SHA1:
+ hashLen = 36
+ default:
+ return 0, nil, os.ErrorString("unknown hash function")
+ }
+
+ if inLen != hashLen {
+ return 0, nil, os.ErrorString("input must be hashed message")
+ }
+
+ prefix = hashPrefixes[int(hash)]
+ return
+}
diff --git a/libgo/go/crypto/rsa/pkcs1v15_test.go b/libgo/go/crypto/rsa/pkcs1v15_test.go
new file mode 100644
index 000000000..bf6306dc2
--- /dev/null
+++ b/libgo/go/crypto/rsa/pkcs1v15_test.go
@@ -0,0 +1,220 @@
+// 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 (
+ "big"
+ "bytes"
+ "crypto/rand"
+ "crypto/sha1"
+ "encoding/base64"
+ "encoding/hex"
+ "io"
+ "testing"
+ "testing/quick"
+)
+
+func decodeBase64(in string) []byte {
+ out := make([]byte, base64.StdEncoding.DecodedLen(len(in)))
+ n, err := base64.StdEncoding.Decode(out, []byte(in))
+ if err != nil {
+ return nil
+ }
+ return out[0:n]
+}
+
+type DecryptPKCS1v15Test struct {
+ in, out string
+}
+
+// These test vectors were generated with `openssl rsautl -pkcs -encrypt`
+var decryptPKCS1v15Tests = []DecryptPKCS1v15Test{
+ {
+ "gIcUIoVkD6ATMBk/u/nlCZCCWRKdkfjCgFdo35VpRXLduiKXhNz1XupLLzTXAybEq15juc+EgY5o0DHv/nt3yg==",
+ "x",
+ },
+ {
+ "Y7TOCSqofGhkRb+jaVRLzK8xw2cSo1IVES19utzv6hwvx+M8kFsoWQm5DzBeJCZTCVDPkTpavUuEbgp8hnUGDw==",
+ "testing.",
+ },
+ {
+ "arReP9DJtEVyV2Dg3dDp4c/PSk1O6lxkoJ8HcFupoRorBZG+7+1fDAwT1olNddFnQMjmkb8vxwmNMoTAT/BFjQ==",
+ "testing.\n",
+ },
+ {
+ "WtaBXIoGC54+vH0NH0CHHE+dRDOsMc/6BrfFu2lEqcKL9+uDuWaf+Xj9mrbQCjjZcpQuX733zyok/jsnqe/Ftw==",
+ "01234567890123456789012345678901234567890123456789012",
+ },
+}
+
+func TestDecryptPKCS1v15(t *testing.T) {
+ for i, test := range decryptPKCS1v15Tests {
+ out, err := DecryptPKCS1v15(nil, rsaPrivateKey, decodeBase64(test.in))
+ if err != nil {
+ t.Errorf("#%d error decrypting", i)
+ }
+ want := []byte(test.out)
+ if bytes.Compare(out, want) != 0 {
+ t.Errorf("#%d got:%#v want:%#v", i, out, want)
+ }
+ }
+}
+
+func TestEncryptPKCS1v15(t *testing.T) {
+ random := rand.Reader
+ k := (rsaPrivateKey.N.BitLen() + 7) / 8
+
+ tryEncryptDecrypt := func(in []byte, blind bool) bool {
+ if len(in) > k-11 {
+ in = in[0 : k-11]
+ }
+
+ ciphertext, err := EncryptPKCS1v15(random, &rsaPrivateKey.PublicKey, in)
+ if err != nil {
+ t.Errorf("error encrypting: %s", err)
+ return false
+ }
+
+ var rand io.Reader
+ if !blind {
+ rand = nil
+ } else {
+ rand = random
+ }
+ plaintext, err := DecryptPKCS1v15(rand, rsaPrivateKey, ciphertext)
+ if err != nil {
+ t.Errorf("error decrypting: %s", err)
+ return false
+ }
+
+ if bytes.Compare(plaintext, in) != 0 {
+ t.Errorf("output mismatch: %#v %#v", plaintext, in)
+ return false
+ }
+ return true
+ }
+
+ quick.Check(tryEncryptDecrypt, nil)
+}
+
+// These test vectors were generated with `openssl rsautl -pkcs -encrypt`
+var decryptPKCS1v15SessionKeyTests = []DecryptPKCS1v15Test{
+ {
+ "e6ukkae6Gykq0fKzYwULpZehX+UPXYzMoB5mHQUDEiclRbOTqas4Y0E6nwns1BBpdvEJcilhl5zsox/6DtGsYg==",
+ "1234",
+ },
+ {
+ "Dtis4uk/q/LQGGqGk97P59K03hkCIVFMEFZRgVWOAAhxgYpCRG0MX2adptt92l67IqMki6iVQyyt0TtX3IdtEw==",
+ "FAIL",
+ },
+ {
+ "LIyFyCYCptPxrvTxpol8F3M7ZivlMsf53zs0vHRAv+rDIh2YsHS69ePMoPMe3TkOMZ3NupiL3takPxIs1sK+dw==",
+ "abcd",
+ },
+ {
+ "bafnobel46bKy76JzqU/RIVOH0uAYvzUtauKmIidKgM0sMlvobYVAVQPeUQ/oTGjbIZ1v/6Gyi5AO4DtHruGdw==",
+ "FAIL",
+ },
+}
+
+func TestEncryptPKCS1v15SessionKey(t *testing.T) {
+ for i, test := range decryptPKCS1v15SessionKeyTests {
+ key := []byte("FAIL")
+ err := DecryptPKCS1v15SessionKey(nil, rsaPrivateKey, decodeBase64(test.in), key)
+ if err != nil {
+ t.Errorf("#%d error decrypting", i)
+ }
+ want := []byte(test.out)
+ if bytes.Compare(key, want) != 0 {
+ t.Errorf("#%d got:%#v want:%#v", i, key, want)
+ }
+ }
+}
+
+func TestNonZeroRandomBytes(t *testing.T) {
+ random := rand.Reader
+
+ b := make([]byte, 512)
+ err := nonZeroRandomBytes(b, random)
+ if err != nil {
+ t.Errorf("returned error: %s", err)
+ }
+ for _, b := range b {
+ if b == 0 {
+ t.Errorf("Zero octet found")
+ return
+ }
+ }
+}
+
+type signPKCS1v15Test struct {
+ in, out string
+}
+
+// These vectors have been tested with
+// `openssl rsautl -verify -inkey pk -in signature | hexdump -C`
+var signPKCS1v15Tests = []signPKCS1v15Test{
+ {"Test.\n", "a4f3fa6ea93bcdd0c57be020c1193ecbfd6f200a3d95c409769b029578fa0e336ad9a347600e40d3ae823b8c7e6bad88cc07c1d54c3a1523cbbb6d58efc362ae"},
+}
+
+func TestSignPKCS1v15(t *testing.T) {
+ for i, test := range signPKCS1v15Tests {
+ h := sha1.New()
+ h.Write([]byte(test.in))
+ digest := h.Sum()
+
+ s, err := SignPKCS1v15(nil, rsaPrivateKey, HashSHA1, digest)
+ if err != nil {
+ t.Errorf("#%d %s", i, err)
+ }
+
+ expected, _ := hex.DecodeString(test.out)
+ if bytes.Compare(s, expected) != 0 {
+ t.Errorf("#%d got: %x want: %x", i, s, expected)
+ }
+ }
+}
+
+func TestVerifyPKCS1v15(t *testing.T) {
+ for i, test := range signPKCS1v15Tests {
+ h := sha1.New()
+ h.Write([]byte(test.in))
+ digest := h.Sum()
+
+ sig, _ := hex.DecodeString(test.out)
+
+ err := VerifyPKCS1v15(&rsaPrivateKey.PublicKey, HashSHA1, digest, sig)
+ if err != nil {
+ t.Errorf("#%d %s", i, err)
+ }
+ }
+}
+
+func bigFromString(s string) *big.Int {
+ ret := new(big.Int)
+ ret.SetString(s, 10)
+ return ret
+}
+
+// In order to generate new test vectors you'll need the PEM form of this key:
+// -----BEGIN RSA PRIVATE KEY-----
+// MIIBOgIBAAJBALKZD0nEffqM1ACuak0bijtqE2QrI/KLADv7l3kK3ppMyCuLKoF0
+// fd7Ai2KW5ToIwzFofvJcS/STa6HA5gQenRUCAwEAAQJBAIq9amn00aS0h/CrjXqu
+// /ThglAXJmZhOMPVn4eiu7/ROixi9sex436MaVeMqSNf7Ex9a8fRNfWss7Sqd9eWu
+// RTUCIQDasvGASLqmjeffBNLTXV2A5g4t+kLVCpsEIZAycV5GswIhANEPLmax0ME/
+// EO+ZJ79TJKN5yiGBRsv5yvx5UiHxajEXAiAhAol5N4EUyq6I9w1rYdhPMGpLfk7A
+// IU2snfRJ6Nq2CQIgFrPsWRCkV+gOYcajD17rEqmuLrdIRexpg8N1DOSXoJ8CIGlS
+// tAboUGBxTDq3ZroNism3DaMIbKPyYrAqhKov1h5V
+// -----END RSA PRIVATE KEY-----
+
+var rsaPrivateKey = &PrivateKey{
+ PublicKey: PublicKey{
+ N: bigFromString("9353930466774385905609975137998169297361893554149986716853295022578535724979677252958524466350471210367835187480748268864277464700638583474144061408845077"),
+ E: 65537,
+ },
+ D: bigFromString("7266398431328116344057699379749222532279343923819063639497049039389899328538543087657733766554155839834519529439851673014800261285757759040931985506583861"),
+ P: bigFromString("98920366548084643601728869055592650835572950932266967461790948584315647051443"),
+ Q: bigFromString("94560208308847015747498523884063394671606671904944666360068158221458669711639"),
+}
diff --git a/libgo/go/crypto/rsa/rsa.go b/libgo/go/crypto/rsa/rsa.go
new file mode 100644
index 000000000..c7a8d2053
--- /dev/null
+++ b/libgo/go/crypto/rsa/rsa.go
@@ -0,0 +1,445 @@
+// 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 (
+ "big"
+ "crypto/subtle"
+ "hash"
+ "io"
+ "os"
+)
+
+var bigZero = big.NewInt(0)
+var bigOne = big.NewInt(1)
+
+// randomPrime returns a number, p, of the given size, such that p is prime
+// with high probability.
+func randomPrime(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)
+
+ 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 big.ProbablyPrime(p, 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.BitLen() + 7) / 8
+
+ // r is the number of bits in the used in the most significant byte of
+ // max.
+ r := uint(max.BitLen() % 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 n.Cmp(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
+}
+
+// Validate performs basic sanity checks on the key.
+// It returns nil if the key is valid, or else an os.Error describing a problem.
+
+func (priv PrivateKey) Validate() os.Error {
+ // Check that p and q are prime. Note that this is just a sanity
+ // check. Since the random witnesses chosen by ProbablyPrime are
+ // deterministic, given the candidate number, it's easy for an attack
+ // to generate composites that pass this test.
+ if !big.ProbablyPrime(priv.P, 20) {
+ return os.ErrorString("P is composite")
+ }
+ if !big.ProbablyPrime(priv.Q, 20) {
+ return os.ErrorString("Q is composite")
+ }
+
+ // Check that p*q == n.
+ modulus := new(big.Int).Mul(priv.P, priv.Q)
+ if modulus.Cmp(priv.N) != 0 {
+ return os.ErrorString("invalid modulus")
+ }
+ // Check that e and totient(p, q) are coprime.
+ pminus1 := new(big.Int).Sub(priv.P, bigOne)
+ qminus1 := new(big.Int).Sub(priv.Q, bigOne)
+ totient := new(big.Int).Mul(pminus1, qminus1)
+ e := big.NewInt(int64(priv.E))
+ gcd := new(big.Int)
+ x := new(big.Int)
+ y := new(big.Int)
+ big.GcdInt(gcd, x, y, totient, e)
+ if gcd.Cmp(bigOne) != 0 {
+ return os.ErrorString("invalid public exponent E")
+ }
+ // Check that de ≡ 1 (mod totient(p, q))
+ de := new(big.Int).Mul(priv.D, e)
+ de.Mod(de, totient)
+ if de.Cmp(bigOne) != 0 {
+ return os.ErrorString("invalid private exponent D")
+ }
+ return nil
+}
+
+// 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 := randomPrime(rand, bits/2)
+ if err != nil {
+ return nil, err
+ }
+
+ q, err := randomPrime(rand, bits/2)
+ if err != nil {
+ return nil, err
+ }
+
+ if p.Cmp(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 g.Cmp(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.BitLen() + 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():]
+
+ copy(db[0:hash.Size()], lHash)
+ db[len(db)-len(msg)-1] = 1
+ copy(db[len(db)-len(msg):], 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" }
+
+// A VerificationError represents a failure to verify a signature.
+// It is deliberately vague to avoid adaptive attacks.
+type VerificationError struct{}
+
+func (VerificationError) String() string { return "RSA verification 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, ok bool) {
+ g := new(big.Int)
+ x := new(big.Int)
+ y := new(big.Int)
+ big.GcdInt(g, x, y, a, n)
+ if g.Cmp(bigOne) != 0 {
+ // In this case, a and n aren't coprime and we cannot calculate
+ // the inverse. This happens because the values of n are nearly
+ // prime (being the product of two primes) rather than truly
+ // prime.
+ return
+ }
+
+ if x.Cmp(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, true
+}
+
+// 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 c.Cmp(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.
+
+ var r *big.Int
+
+ for {
+ r, err = randomNumber(rand, priv.N)
+ if err != nil {
+ return
+ }
+ if r.Cmp(bigZero) == 0 {
+ r = bigOne
+ }
+ var ok bool
+ ir, ok = modInverse(r, priv.N)
+ if ok {
+ break
+ }
+ }
+ 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.BitLen() + 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 := subtle.ConstantTimeByteEq(em[0], 0)
+
+ seed := em[1 : hash.Size()+1]
+ db := em[hash.Size()+1:]
+
+ mgf1XOR(seed, hash, db)
+ mgf1XOR(db, hash, seed)
+
+ lHash2 := db[0:hash.Size()]
+
+ // We have to validate the plaintext in constant 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 := subtle.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():]
+
+ for i := 0; i < len(rest); i++ {
+ equals0 := subtle.ConstantTimeByteEq(rest[i], 0)
+ equals1 := subtle.ConstantTimeByteEq(rest[i], 1)
+ index = subtle.ConstantTimeSelect(lookingForIndex&equals1, i, index)
+ lookingForIndex = subtle.ConstantTimeSelect(equals1, 0, lookingForIndex)
+ invalid = subtle.ConstantTimeSelect(lookingForIndex&^equals0, 1, invalid)
+ }
+
+ if firstByteIsZero&lHash2Good&^invalid&^lookingForIndex != 1 {
+ err = DecryptionError{}
+ return
+ }
+
+ msg = rest[index+1:]
+ 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)
+ copy(out[len(out)-n:], input)
+ return
+}
diff --git a/libgo/go/crypto/rsa/rsa_test.go b/libgo/go/crypto/rsa/rsa_test.go
new file mode 100644
index 000000000..df1f17f17
--- /dev/null
+++ b/libgo/go/crypto/rsa/rsa_test.go
@@ -0,0 +1,250 @@
+// 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 (
+ "big"
+ "bytes"
+ "crypto/rand"
+ "crypto/sha1"
+ "testing"
+)
+
+func TestKeyGeneration(t *testing.T) {
+ random := rand.Reader
+
+ priv, err := GenerateKey(random, 1024)
+ 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 m.Cmp(m2) != 0 {
+ t.Errorf("got:%v, want:%v (%s)", m2, m, priv)
+ }
+
+ m3, err := decrypt(random, priv, c)
+ if err != nil {
+ t.Errorf("error while decrypting (blind): %s", err)
+ }
+ if m.Cmp(m3) != 0 {
+ t.Errorf("(blind) got:%v, want:%v", m3, m)
+ }
+}
+
+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 := bytes.NewBuffer(message.seed)
+ 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) {
+ random := rand.Reader
+
+ 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, random, &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)
+ }
+ }
+ }
+}
+
+// testEncryptOAEPData contains a subset of the vectors from RSA's "Test vectors for RSA-OAEP".
+var testEncryptOAEPData = []testEncryptOAEPStruct{
+ // Key 1
+ {"a8b3b284af8eb50b387034a860f146c4919f318763cd6c5598c8ae4811a1e0abc4c7e0b082d693a5e7fced675cf4668512772c0cbc64a742c6c630f533c8cc72f62ae833c40bf25842e984bb78bdbf97c0107d55bdb662f5c4e0fab9845cb5148ef7392dd3aaff93ae1e6b667bb3d4247616d4f5ba10d4cfd226de88d39f16fb",
+ 65537,
+ "53339cfdb79fc8466a655c7316aca85c55fd8f6dd898fdaf119517ef4f52e8fd8e258df93fee180fa0e4ab29693cd83b152a553d4ac4d1812b8b9fa5af0e7f55fe7304df41570926f3311f15c4d65a732c483116ee3d3d2d0af3549ad9bf7cbfb78ad884f84d5beb04724dc7369b31def37d0cf539e9cfcdd3de653729ead5d1",
+ []testEncryptOAEPMessage{
+ // Example 1.1
+ {
+ []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
+ {
+ []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
+ {
+ []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
+ {"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",
+ 65537,
+ "056b04216fe5f354ac77250a4b6b0c8525a85c59b0bd80c56450a22d5f438e596a333aa875e291dd43f48cb88b9d5fc0d499f9fcd1c397f9afc070cd9e398c8d19e61db7c7410a6b2675dfbf5d345b804d201add502d5ce2dfcb091ce9997bbebe57306f383e4d588103f036f7e85d1934d152a323e4a8db451d6f4a5b1b0f102cc150e02feee2b88dea4ad4c1baccb24d84072d14e1d24a6771f7408ee30564fb86d4393a34bcf0b788501d193303f13a2284b001f0f649eaf79328d4ac5c430ab4414920a9460ed1b7bc40ec653e876d09abc509ae45b525190116a0c26101848298509c1c3bf3a483e7274054e15e97075036e989f60932807b5257751e79",
+ []testEncryptOAEPMessage{
+ // Example 10.1
+ {
+ []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,
+ },
+ },
+ },
+ },
+}