274149dd14
* Switch to keybase go-crypto (for some elliptic curve key) + test
* Use assert.NoError
and add a little more context to failing test description
* Use assert.(No)Error everywhere 🌈
and assert.Error in place of .Nil/.NotNil
647 lines
19 KiB
Go
647 lines
19 KiB
Go
// Copyright 2009 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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// Package rsa implements RSA encryption as specified in PKCS#1.
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//
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// RSA is a single, fundamental operation that is used in this package to
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// implement either public-key encryption or public-key signatures.
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//
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// The original specification for encryption and signatures with RSA is PKCS#1
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// and the terms "RSA encryption" and "RSA signatures" by default refer to
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// PKCS#1 version 1.5. However, that specification has flaws and new designs
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// should use version two, usually called by just OAEP and PSS, where
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// possible.
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//
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// Two sets of interfaces are included in this package. When a more abstract
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// interface isn't neccessary, there are functions for encrypting/decrypting
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// with v1.5/OAEP and signing/verifying with v1.5/PSS. If one needs to abstract
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// over the public-key primitive, the PrivateKey struct implements the
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// Decrypter and Signer interfaces from the crypto package.
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package rsa
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import (
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"crypto"
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"crypto/rand"
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"crypto/subtle"
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"errors"
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"hash"
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"io"
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"math/big"
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)
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var bigZero = big.NewInt(0)
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var bigOne = big.NewInt(1)
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// A PublicKey represents the public part of an RSA key.
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type PublicKey struct {
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N *big.Int // modulus
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E int64 // public exponent
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}
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// OAEPOptions is an interface for passing options to OAEP decryption using the
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// crypto.Decrypter interface.
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type OAEPOptions struct {
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// Hash is the hash function that will be used when generating the mask.
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Hash crypto.Hash
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// Label is an arbitrary byte string that must be equal to the value
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// used when encrypting.
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Label []byte
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}
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var (
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errPublicModulus = errors.New("crypto/rsa: missing public modulus")
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errPublicExponentSmall = errors.New("crypto/rsa: public exponent too small")
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errPublicExponentLarge = errors.New("crypto/rsa: public exponent too large")
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)
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// checkPub sanity checks the public key before we use it.
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// We require pub.E to fit into a 32-bit integer so that we
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// do not have different behavior depending on whether
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// int is 32 or 64 bits. See also
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// http://www.imperialviolet.org/2012/03/16/rsae.html.
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func checkPub(pub *PublicKey) error {
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if pub.N == nil {
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return errPublicModulus
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}
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if pub.E < 2 {
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return errPublicExponentSmall
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}
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if pub.E > 1<<63-1 {
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return errPublicExponentLarge
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}
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return nil
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}
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// A PrivateKey represents an RSA key
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type PrivateKey struct {
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PublicKey // public part.
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D *big.Int // private exponent
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Primes []*big.Int // prime factors of N, has >= 2 elements.
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// Precomputed contains precomputed values that speed up private
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// operations, if available.
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Precomputed PrecomputedValues
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}
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// Public returns the public key corresponding to priv.
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func (priv *PrivateKey) Public() crypto.PublicKey {
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return &priv.PublicKey
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}
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// Sign signs msg with priv, reading randomness from rand. If opts is a
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// *PSSOptions then the PSS algorithm will be used, otherwise PKCS#1 v1.5 will
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// be used. This method is intended to support keys where the private part is
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// kept in, for example, a hardware module. Common uses should use the Sign*
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// functions in this package.
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func (priv *PrivateKey) Sign(rand io.Reader, msg []byte, opts crypto.SignerOpts) ([]byte, error) {
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if pssOpts, ok := opts.(*PSSOptions); ok {
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return SignPSS(rand, priv, pssOpts.Hash, msg, pssOpts)
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}
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return SignPKCS1v15(rand, priv, opts.HashFunc(), msg)
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}
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// Decrypt decrypts ciphertext with priv. If opts is nil or of type
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// *PKCS1v15DecryptOptions then PKCS#1 v1.5 decryption is performed. Otherwise
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// opts must have type *OAEPOptions and OAEP decryption is done.
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func (priv *PrivateKey) Decrypt(rand io.Reader, ciphertext []byte, opts crypto.DecrypterOpts) (plaintext []byte, err error) {
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if opts == nil {
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return DecryptPKCS1v15(rand, priv, ciphertext)
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}
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switch opts := opts.(type) {
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case *OAEPOptions:
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return DecryptOAEP(opts.Hash.New(), rand, priv, ciphertext, opts.Label)
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case *PKCS1v15DecryptOptions:
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if l := opts.SessionKeyLen; l > 0 {
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plaintext = make([]byte, l)
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if _, err := io.ReadFull(rand, plaintext); err != nil {
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return nil, err
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}
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if err := DecryptPKCS1v15SessionKey(rand, priv, ciphertext, plaintext); err != nil {
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return nil, err
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}
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return plaintext, nil
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} else {
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return DecryptPKCS1v15(rand, priv, ciphertext)
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}
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default:
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return nil, errors.New("crypto/rsa: invalid options for Decrypt")
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}
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}
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type PrecomputedValues struct {
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Dp, Dq *big.Int // D mod (P-1) (or mod Q-1)
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Qinv *big.Int // Q^-1 mod P
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// CRTValues is used for the 3rd and subsequent primes. Due to a
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// historical accident, the CRT for the first two primes is handled
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// differently in PKCS#1 and interoperability is sufficiently
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// important that we mirror this.
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CRTValues []CRTValue
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}
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// CRTValue contains the precomputed Chinese remainder theorem values.
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type CRTValue struct {
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Exp *big.Int // D mod (prime-1).
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Coeff *big.Int // R·Coeff ≡ 1 mod Prime.
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R *big.Int // product of primes prior to this (inc p and q).
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}
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// Validate performs basic sanity checks on the key.
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// It returns nil if the key is valid, or else an error describing a problem.
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func (priv *PrivateKey) Validate() error {
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if err := checkPub(&priv.PublicKey); err != nil {
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return err
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}
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// Check that Πprimes == n.
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modulus := new(big.Int).Set(bigOne)
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for _, prime := range priv.Primes {
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// Any primes ≤ 1 will cause divide-by-zero panics later.
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if prime.Cmp(bigOne) <= 0 {
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return errors.New("crypto/rsa: invalid prime value")
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}
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modulus.Mul(modulus, prime)
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}
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if modulus.Cmp(priv.N) != 0 {
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return errors.New("crypto/rsa: invalid modulus")
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}
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// Check that de ≡ 1 mod p-1, for each prime.
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// This implies that e is coprime to each p-1 as e has a multiplicative
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// inverse. Therefore e is coprime to lcm(p-1,q-1,r-1,...) =
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// exponent(ℤ/nℤ). It also implies that a^de ≡ a mod p as a^(p-1) ≡ 1
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// mod p. Thus a^de ≡ a mod n for all a coprime to n, as required.
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congruence := new(big.Int)
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de := new(big.Int).SetInt64(int64(priv.E))
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de.Mul(de, priv.D)
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for _, prime := range priv.Primes {
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pminus1 := new(big.Int).Sub(prime, bigOne)
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congruence.Mod(de, pminus1)
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if congruence.Cmp(bigOne) != 0 {
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return errors.New("crypto/rsa: invalid exponents")
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}
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}
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return nil
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}
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// GenerateKey generates an RSA keypair of the given bit size using the
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// random source random (for example, crypto/rand.Reader).
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func GenerateKey(random io.Reader, bits int) (priv *PrivateKey, err error) {
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return GenerateMultiPrimeKey(random, 2, bits)
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}
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// GenerateMultiPrimeKey generates a multi-prime RSA keypair of the given bit
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// size and the given random source, as suggested in [1]. Although the public
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// keys are compatible (actually, indistinguishable) from the 2-prime case,
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// the private keys are not. Thus it may not be possible to export multi-prime
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// private keys in certain formats or to subsequently import them into other
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// code.
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//
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// Table 1 in [2] suggests maximum numbers of primes for a given size.
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//
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// [1] US patent 4405829 (1972, expired)
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// [2] http://www.cacr.math.uwaterloo.ca/techreports/2006/cacr2006-16.pdf
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func GenerateMultiPrimeKey(random io.Reader, nprimes int, bits int) (priv *PrivateKey, err error) {
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priv = new(PrivateKey)
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priv.E = 65537
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if nprimes < 2 {
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return nil, errors.New("crypto/rsa: GenerateMultiPrimeKey: nprimes must be >= 2")
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}
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primes := make([]*big.Int, nprimes)
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NextSetOfPrimes:
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for {
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todo := bits
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// crypto/rand should set the top two bits in each prime.
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// Thus each prime has the form
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// p_i = 2^bitlen(p_i) × 0.11... (in base 2).
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// And the product is:
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// P = 2^todo × α
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// where α is the product of nprimes numbers of the form 0.11...
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//
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// If α < 1/2 (which can happen for nprimes > 2), we need to
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// shift todo to compensate for lost bits: the mean value of 0.11...
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// is 7/8, so todo + shift - nprimes * log2(7/8) ~= bits - 1/2
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// will give good results.
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if nprimes >= 7 {
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todo += (nprimes - 2) / 5
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}
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for i := 0; i < nprimes; i++ {
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primes[i], err = rand.Prime(random, todo/(nprimes-i))
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if err != nil {
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return nil, err
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}
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todo -= primes[i].BitLen()
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}
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// Make sure that primes is pairwise unequal.
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for i, prime := range primes {
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for j := 0; j < i; j++ {
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if prime.Cmp(primes[j]) == 0 {
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continue NextSetOfPrimes
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}
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}
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}
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n := new(big.Int).Set(bigOne)
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totient := new(big.Int).Set(bigOne)
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pminus1 := new(big.Int)
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for _, prime := range primes {
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n.Mul(n, prime)
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pminus1.Sub(prime, bigOne)
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totient.Mul(totient, pminus1)
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}
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if n.BitLen() != bits {
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// This should never happen for nprimes == 2 because
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// crypto/rand should set the top two bits in each prime.
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// For nprimes > 2 we hope it does not happen often.
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continue NextSetOfPrimes
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}
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g := new(big.Int)
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priv.D = new(big.Int)
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y := new(big.Int)
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e := big.NewInt(int64(priv.E))
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g.GCD(priv.D, y, e, totient)
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if g.Cmp(bigOne) == 0 {
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if priv.D.Sign() < 0 {
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priv.D.Add(priv.D, totient)
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}
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priv.Primes = primes
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priv.N = n
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break
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}
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}
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priv.Precompute()
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return
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}
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// incCounter increments a four byte, big-endian counter.
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func incCounter(c *[4]byte) {
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if c[3]++; c[3] != 0 {
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return
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}
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if c[2]++; c[2] != 0 {
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return
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}
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if c[1]++; c[1] != 0 {
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return
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}
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c[0]++
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}
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// mgf1XOR XORs the bytes in out with a mask generated using the MGF1 function
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// specified in PKCS#1 v2.1.
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func mgf1XOR(out []byte, hash hash.Hash, seed []byte) {
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var counter [4]byte
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var digest []byte
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done := 0
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for done < len(out) {
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hash.Write(seed)
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hash.Write(counter[0:4])
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digest = hash.Sum(digest[:0])
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hash.Reset()
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for i := 0; i < len(digest) && done < len(out); i++ {
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out[done] ^= digest[i]
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done++
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}
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incCounter(&counter)
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}
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}
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// ErrMessageTooLong is returned when attempting to encrypt a message which is
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// too large for the size of the public key.
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var ErrMessageTooLong = errors.New("crypto/rsa: message too long for RSA public key size")
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func encrypt(c *big.Int, pub *PublicKey, m *big.Int) *big.Int {
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e := big.NewInt(int64(pub.E))
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c.Exp(m, e, pub.N)
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return c
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}
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// EncryptOAEP encrypts the given message with RSA-OAEP.
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//
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// OAEP is parameterised by a hash function that is used as a random oracle.
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// Encryption and decryption of a given message must use the same hash function
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// and sha256.New() is a reasonable choice.
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//
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// The random parameter is used as a source of entropy to ensure that
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// encrypting the same message twice doesn't result in the same ciphertext.
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//
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// The label parameter may contain arbitrary data that will not be encrypted,
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// but which gives important context to the message. For example, if a given
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// public key is used to decrypt two types of messages then distinct label
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// values could be used to ensure that a ciphertext for one purpose cannot be
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// used for another by an attacker. If not required it can be empty.
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//
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// The message must be no longer than the length of the public modulus less
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// twice the hash length plus 2.
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func EncryptOAEP(hash hash.Hash, random io.Reader, pub *PublicKey, msg []byte, label []byte) (out []byte, err error) {
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if err := checkPub(pub); err != nil {
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return nil, err
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}
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hash.Reset()
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k := (pub.N.BitLen() + 7) / 8
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if len(msg) > k-2*hash.Size()-2 {
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err = ErrMessageTooLong
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return
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}
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hash.Write(label)
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lHash := hash.Sum(nil)
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hash.Reset()
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em := make([]byte, k)
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seed := em[1 : 1+hash.Size()]
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db := em[1+hash.Size():]
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copy(db[0:hash.Size()], lHash)
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db[len(db)-len(msg)-1] = 1
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copy(db[len(db)-len(msg):], msg)
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_, err = io.ReadFull(random, seed)
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if err != nil {
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return
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}
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mgf1XOR(db, hash, seed)
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mgf1XOR(seed, hash, db)
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m := new(big.Int)
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m.SetBytes(em)
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c := encrypt(new(big.Int), pub, m)
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out = c.Bytes()
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if len(out) < k {
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// If the output is too small, we need to left-pad with zeros.
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t := make([]byte, k)
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copy(t[k-len(out):], out)
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out = t
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}
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return
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}
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// ErrDecryption represents a failure to decrypt a message.
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// It is deliberately vague to avoid adaptive attacks.
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var ErrDecryption = errors.New("crypto/rsa: decryption error")
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// ErrVerification represents a failure to verify a signature.
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// It is deliberately vague to avoid adaptive attacks.
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var ErrVerification = errors.New("crypto/rsa: verification error")
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// modInverse returns ia, the inverse of a in the multiplicative group of prime
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// order n. It requires that a be a member of the group (i.e. less than n).
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func modInverse(a, n *big.Int) (ia *big.Int, ok bool) {
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g := new(big.Int)
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x := new(big.Int)
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y := new(big.Int)
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g.GCD(x, y, a, n)
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if g.Cmp(bigOne) != 0 {
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// In this case, a and n aren't coprime and we cannot calculate
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// the inverse. This happens because the values of n are nearly
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// prime (being the product of two primes) rather than truly
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// prime.
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return
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}
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if x.Cmp(bigOne) < 0 {
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// 0 is not the multiplicative inverse of any element so, if x
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// < 1, then x is negative.
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x.Add(x, n)
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}
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return x, true
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}
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|
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// Precompute performs some calculations that speed up private key operations
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// in the future.
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func (priv *PrivateKey) Precompute() {
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if priv.Precomputed.Dp != nil {
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return
|
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}
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priv.Precomputed.Dp = new(big.Int).Sub(priv.Primes[0], bigOne)
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priv.Precomputed.Dp.Mod(priv.D, priv.Precomputed.Dp)
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priv.Precomputed.Dq = new(big.Int).Sub(priv.Primes[1], bigOne)
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priv.Precomputed.Dq.Mod(priv.D, priv.Precomputed.Dq)
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priv.Precomputed.Qinv = new(big.Int).ModInverse(priv.Primes[1], priv.Primes[0])
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r := new(big.Int).Mul(priv.Primes[0], priv.Primes[1])
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priv.Precomputed.CRTValues = make([]CRTValue, len(priv.Primes)-2)
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for i := 2; i < len(priv.Primes); i++ {
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prime := priv.Primes[i]
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values := &priv.Precomputed.CRTValues[i-2]
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values.Exp = new(big.Int).Sub(prime, bigOne)
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values.Exp.Mod(priv.D, values.Exp)
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values.R = new(big.Int).Set(r)
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values.Coeff = new(big.Int).ModInverse(r, prime)
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r.Mul(r, prime)
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}
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}
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// decrypt performs an RSA decryption, resulting in a plaintext integer. If a
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// random source is given, RSA blinding is used.
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func decrypt(random io.Reader, priv *PrivateKey, c *big.Int) (m *big.Int, err error) {
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// TODO(agl): can we get away with reusing blinds?
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if c.Cmp(priv.N) > 0 {
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err = ErrDecryption
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return
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}
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var ir *big.Int
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if random != nil {
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// Blinding enabled. Blinding involves multiplying c by r^e.
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// Then the decryption operation performs (m^e * r^e)^d mod n
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// which equals mr mod n. The factor of r can then be removed
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// by multiplying by the multiplicative inverse of r.
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|
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var r *big.Int
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|
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for {
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r, err = rand.Int(random, priv.N)
|
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if err != nil {
|
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return
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}
|
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if r.Cmp(bigZero) == 0 {
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r = bigOne
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}
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var ok bool
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ir, ok = modInverse(r, priv.N)
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if ok {
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break
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||
}
|
||
}
|
||
bigE := big.NewInt(int64(priv.E))
|
||
rpowe := new(big.Int).Exp(r, bigE, priv.N)
|
||
cCopy := new(big.Int).Set(c)
|
||
cCopy.Mul(cCopy, rpowe)
|
||
cCopy.Mod(cCopy, priv.N)
|
||
c = cCopy
|
||
}
|
||
|
||
if priv.Precomputed.Dp == nil {
|
||
m = new(big.Int).Exp(c, priv.D, priv.N)
|
||
} else {
|
||
// We have the precalculated values needed for the CRT.
|
||
m = new(big.Int).Exp(c, priv.Precomputed.Dp, priv.Primes[0])
|
||
m2 := new(big.Int).Exp(c, priv.Precomputed.Dq, priv.Primes[1])
|
||
m.Sub(m, m2)
|
||
if m.Sign() < 0 {
|
||
m.Add(m, priv.Primes[0])
|
||
}
|
||
m.Mul(m, priv.Precomputed.Qinv)
|
||
m.Mod(m, priv.Primes[0])
|
||
m.Mul(m, priv.Primes[1])
|
||
m.Add(m, m2)
|
||
|
||
for i, values := range priv.Precomputed.CRTValues {
|
||
prime := priv.Primes[2+i]
|
||
m2.Exp(c, values.Exp, prime)
|
||
m2.Sub(m2, m)
|
||
m2.Mul(m2, values.Coeff)
|
||
m2.Mod(m2, prime)
|
||
if m2.Sign() < 0 {
|
||
m2.Add(m2, prime)
|
||
}
|
||
m2.Mul(m2, values.R)
|
||
m.Add(m, m2)
|
||
}
|
||
}
|
||
|
||
if ir != nil {
|
||
// Unblind.
|
||
m.Mul(m, ir)
|
||
m.Mod(m, priv.N)
|
||
}
|
||
|
||
return
|
||
}
|
||
|
||
func decryptAndCheck(random io.Reader, priv *PrivateKey, c *big.Int) (m *big.Int, err error) {
|
||
m, err = decrypt(random, priv, c)
|
||
if err != nil {
|
||
return nil, err
|
||
}
|
||
|
||
// In order to defend against errors in the CRT computation, m^e is
|
||
// calculated, which should match the original ciphertext.
|
||
check := encrypt(new(big.Int), &priv.PublicKey, m)
|
||
if c.Cmp(check) != 0 {
|
||
return nil, errors.New("rsa: internal error")
|
||
}
|
||
return m, nil
|
||
}
|
||
|
||
// DecryptOAEP decrypts ciphertext using 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, 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
|
||
}
|
||
k := (priv.N.BitLen() + 7) / 8
|
||
if len(ciphertext) > k ||
|
||
k < hash.Size()*2+2 {
|
||
err = ErrDecryption
|
||
return
|
||
}
|
||
|
||
c := new(big.Int).SetBytes(ciphertext)
|
||
|
||
m, err := decrypt(random, priv, c)
|
||
if err != nil {
|
||
return
|
||
}
|
||
|
||
hash.Write(label)
|
||
lHash := hash.Sum(nil)
|
||
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 = ErrDecryption
|
||
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
|
||
}
|