crypto/rsa: expand on documentation and add some examples.

In some cases the documentation for functions in this package was
lacking from the beginning and, in order cases, the documentation didn't
keep pace as the package grew.

This change somewhat addresses that.

Updates #13711.

Change-Id: I25b2bb1fcd4658c5417671e23cf8e644d08cb9ab
Reviewed-on: https://go-review.googlesource.com/18486Reviewed-by: Rob Pike <r@golang.org>
Reviewed-by: Andrew Gerrand <adg@golang.org>
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>
Run-TryBot: Brad Fitzpatrick <bradfitz@golang.org>

src/crypto/rsa/example_test.go

+// Copyright 2016 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 (
+	"crypto"
+	"crypto/aes"
+	"crypto/cipher"
+	"crypto/rand"
+	"crypto/sha256"
+	"encoding/hex"
+	"fmt"
+	"io"
+	"os"
+)
+
+// RSA is able to encrypt only a very limited amount of data. In order
+// to encrypt reasonable amounts of data a hybrid scheme is commonly
+// used: RSA is used to encrypt a key for a symmetric primitive like
+// AES-GCM.
+//
+// Before encrypting, data is “padded” by embedding it in a known
+// structure. This is done for a number of reasons, but the most
+// obvious is to ensure that the value is large enough that the
+// exponentiation is larger than the modulus. (Otherwise it could be
+// decrypted with a square-root.)
+//
+// In these designs, when using PKCS#1 v1.5, it's vitally important to
+// avoid disclosing whether the received RSA message was well-formed
+// (that is, whether the result of decrypting is a correctly padded
+// message) because this leaks secret information.
+// DecryptPKCS1v15SessionKey is designed for this situation and copies
+// the decrypted, symmetric key (if well-formed) in constant-time over
+// a buffer that contains a random key. Thus, if the RSA result isn't
+// well-formed, the implementation uses a random key in constant time.
+func ExampleDecryptPKCS1v15SessionKey() {
+	// crypto/rand.Reader is a good source of entropy for blinding the RSA
+	// operation.
+	rng := rand.Reader
+
+	// The hybrid scheme should use at least a 16-byte symmetric key. Here
+	// we read the random key that will be used if the RSA decryption isn't
+	// well-formed.
+	key := make([]byte, 32)
+	if _, err := io.ReadFull(rng, key); err != nil {
+		panic("RNG failure")
+	}
+
+	rsaCiphertext, _ := hex.DecodeString("aabbccddeeff")
+
+	if err := DecryptPKCS1v15SessionKey(rng, rsaPrivateKey, rsaCiphertext, key); err != nil {
+		// Any errors that result will be “public” – meaning that they
+		// can be determined without any secret information. (For
+		// instance, if the length of key is impossible given the RSA
+		// public key.)
+		fmt.Fprintf(os.Stderr, "Error from RSA decryption: %s\n", err)
+		return
+	}
+
+	// Given the resulting key, a symmetric scheme can be used to decrypt a
+	// larger ciphertext.
+	block, err := aes.NewCipher(key)
+	if err != nil {
+		panic("aes.NewCipher failed: " + err.Error())
+	}
+
+	// Since the key is random, using a fixed nonce is acceptable as the
+	// (key, nonce) pair will still be unique, as required.
+	var zeroNonce [12]byte
+	aead, err := cipher.NewGCM(block)
+	if err != nil {
+		panic("cipher.NewGCM failed: " + err.Error())
+	}
+	ciphertext, _ := hex.DecodeString("00112233445566")
+	plaintext, err := aead.Open(nil, zeroNonce[:], ciphertext, nil)
+	if err != nil {
+		// The RSA ciphertext was badly formed; the decryption will
+		// fail here because the AES-GCM key will be incorrect.
+		fmt.Fprintf(os.Stderr, "Error decrypting: %s\n", err)
+		return
+	}
+
+	fmt.Printf("Plaintext: %s\n", string(plaintext))
+}
+
+func ExampleSignPKCS1v15() {
+	// crypto/rand.Reader is a good source of entropy for blinding the RSA
+	// operation.
+	rng := rand.Reader
+
+	message := []byte("message to be signed")
+
+	// Only small messages can be signed directly; thus the hash of a
+	// message, rather than the message itself, is signed. This requires
+	// that the hash function be collision resistant. SHA-256 is the
+	// least-strong hash function that should be used for this at the time
+	// of writing (2016).
+	hashed := sha256.Sum256(message)
+
+	signature, err := SignPKCS1v15(rng, rsaPrivateKey, crypto.SHA256, hashed[:])
+	if err != nil {
+		fmt.Fprintf(os.Stderr, "Error from signing: %s\n", err)
+		return
+	}
+
+	fmt.Printf("Signature: %x\n", signature)
+}
+
+func ExampleVerifyPKCS1v15() {
+	message := []byte("message to be signed")
+	signature, _ := hex.DecodeString("ad2766728615cc7a746cc553916380ca7bfa4f8983b990913bc69eb0556539a350ff0f8fe65ddfd3ebe91fe1c299c2fac135bc8c61e26be44ee259f2f80c1530")
+
+	// Only small messages can be signed directly; thus the hash of a
+	// message, rather than the message itself, is signed. This requires
+	// that the hash function be collision resistant. SHA-256 is the
+	// least-strong hash function that should be used for this at the time
+	// of writing (2016).
+	hashed := sha256.Sum256(message)
+
+	err := VerifyPKCS1v15(&rsaPrivateKey.PublicKey, crypto.SHA256, hashed[:], signature)
+	if err != nil {
+		fmt.Fprintf(os.Stderr, "Error from verification: %s\n", err)
+		return
+	}
+
+	// signature is a valid signature of message from the public key.
+}
+
+func ExampleEncryptOAEP() {
+	secretMessage := []byte("send reinforcements, we're going to advance")
+	label := []byte("orders")
+
+	// crypto/rand.Reader is a good source of entropy for randomizing the
+	// encryption function.
+	rng := rand.Reader
+
+	ciphertext, err := EncryptOAEP(sha256.New(), rng, &test2048Key.PublicKey, secretMessage, label)
+	if err != nil {
+		fmt.Fprintf(os.Stderr, "Error from encryption: %s\n", err)
+		return
+	}
+
+	// Since encryption is a randomized function, ciphertext will be
+	// different each time.
+	fmt.Printf("Ciphertext: %x\n", ciphertext)
+}
+
+func ExampleDecryptOAEP() {
+	ciphertext, _ := hex.DecodeString("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")
+	label := []byte("orders")
+
+	// crypto/rand.Reader is a good source of entropy for blinding the RSA
+	// operation.
+	rng := rand.Reader
+
+	plaintext, err := DecryptOAEP(sha256.New(), rng, test2048Key, ciphertext, label)
+	if err != nil {
+		fmt.Fprintf(os.Stderr, "Error from decryption: %s\n", err)
+		return
+	}
+
+	fmt.Printf("Plaintext: %s\n", string(plaintext))
+
+	// Remember that encryption only provides confidentiality. The
+	// ciphertext should be signed before authenticity is assumed and, even
+	// then, consider that messages might be reordered.
+}

src/crypto/rsa/pkcs1v15.go

@@ -26,6 +26,10 @@ type PKCS1v15DecryptOptions struct {
 
 // 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.
+//
+// The rand parameter is used as a source of entropy to ensure that encrypting
+// the same message twice doesn't result in the same ciphertext.
+//
 // 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 error) {
@@ -59,6 +63,12 @@ func EncryptPKCS1v15(rand io.Reader, pub *PublicKey, msg []byte) (out []byte, er
 
 // 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.
+//
+// Note that whether this function returns an error or not discloses secret
+// information. If an attacker can cause this function to run repeatedly and
+// learn whether each instance returned an error then they can decrypt and
+// forge signatures as if they had the private key. See
+// DecryptPKCS1v15SessionKey for a way of solving this problem.
 func DecryptPKCS1v15(rand io.Reader, priv *PrivateKey, ciphertext []byte) (out []byte, err error) {
 	if err := checkPub(&priv.PublicKey); err != nil {
 		return nil, err
@@ -87,6 +97,12 @@ func DecryptPKCS1v15(rand io.Reader, priv *PrivateKey, ciphertext []byte) (out [
 // See ``Chosen Ciphertext Attacks Against Protocols Based on the RSA
 // Encryption Standard PKCS #1'', Daniel Bleichenbacher, Advances in Cryptology
 // (Crypto '98).
+//
+// Note that if the session key is too small then it may be possible for an
+// attacker to brute-force it. If they can do that then they can learn whether
+// a random value was used (because it'll be different for the same ciphertext)
+// and thus whether the padding was correct. This defeats the point of this
+// function. Using at least a 16-byte key will protect against this attack.
 func DecryptPKCS1v15SessionKey(rand io.Reader, priv *PrivateKey, ciphertext []byte, key []byte) (err error) {
 	if err := checkPub(&priv.PublicKey); err != nil {
 		return err
@@ -201,6 +217,13 @@ var hashPrefixes = map[crypto.Hash][]byte{
 // Note that hashed must be the result of hashing the input message using the
 // given hash function. If hash is zero, hashed is signed directly. This isn't
 // advisable except for interoperability.
+//
+// If rand is not nil then RSA blinding will be used to avoid timing side-channel attacks.
+//
+// This function is deterministic. Thus, if the set of possible messages is
+// small, an attacker may be able to build a map from messages to signatures
+// and identify the signed messages. As ever, signatures provide authenticity,
+// not confidentiality.
 func SignPKCS1v15(rand io.Reader, priv *PrivateKey, hash crypto.Hash, hashed []byte) (s []byte, err error) {
 	hashLen, prefix, err := pkcs1v15HashInfo(hash, len(hashed))
 	if err != nil {

src/crypto/rsa/rsa.go

@@ -3,6 +3,21 @@
 // license that can be found in the LICENSE file.
 
 // Package rsa implements RSA encryption as specified in PKCS#1.
+//
+// RSA is a single, fundamental operation that is used in this package to
+// implement either public-key encryption or public-key signatures.
+//
+// The original specification for encryption and signatures with RSA is PKCS#1
+// and the terms "RSA encryption" and "RSA signatures" by default refer to
+// PKCS#1 version 1.5. However, that specification has flaws and new designs
+// should use version two, usually called by just OAEP and PSS, where
+// possible.
+//
+// Two sets of interfaces are included in this package. When a more abstract
+// interface isn't neccessary, there are functions for encrypting/decrypting
+// with v1.5/OAEP and signing/verifying with v1.5/PSS. If one needs to abstract
+// over the public-key primitive, the PrivateKey struct implements the
+// Decrypter and Signer interfaces from the crypto package.
 package rsa
 
 import (
@@ -317,6 +332,20 @@ func encrypt(c *big.Int, pub *PublicKey, m *big.Int) *big.Int {
 }
 
 // EncryptOAEP encrypts the given message with RSA-OAEP.
+//
+// OAEP is parameterised by a hash function that is used as a random oracle.
+// Encryption and decryption of a given message must use the same hash function
+// and sha256.New() is a reasonable choice.
+//
+// The random parameter is used as a source of entropy to ensure that
+// encrypting the same message twice doesn't result in the same ciphertext.
+//
+// The label parameter may contain arbitrary data that will not be encrypted,
+// but which gives important context to the message. For example, if a given
+// public key is used to decrypt two types of messages then distinct label
+// values could be used to ensure that a ciphertext for one purpose cannot be
+// used for another by an attacker. If not required it can be empty.
+//
 // 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, random io.Reader, pub *PublicKey, msg []byte, label []byte) (out []byte, err error) {
@@ -522,7 +551,17 @@ func decryptAndCheck(random io.Reader, priv *PrivateKey, c *big.Int) (m *big.Int
 }
 
 // DecryptOAEP decrypts ciphertext using RSA-OAEP.
-// If random != nil, DecryptOAEP uses RSA blinding to avoid timing side-channel attacks.
+
+// OAEP is parameterised by a hash function that is used as a random oracle.
+// Encryption and decryption of a given message must use the same hash function
+// and sha256.New() is a reasonable choice.
+//
+// The random parameter, if not nil, is used to blind the private-key operation
+// and avoid timing side-channel attacks. Blinding is purely internal to this
+// function – the random data need not match that used when encrypting.
+//
+// The label parameter must match the value given when encrypting. See
+// EncryptOAEP for details.
 func DecryptOAEP(hash hash.Hash, random io.Reader, priv *PrivateKey, ciphertext []byte, label []byte) (msg []byte, err error) {
 	if err := checkPub(&priv.PublicKey); err != nil {
 		return nil, err