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Diffstat (limited to 'vendor/github.com/keybase/go-crypto/rsa/rsa.go')
| -rw-r--r-- | vendor/github.com/keybase/go-crypto/rsa/rsa.go | 646 |
1 files changed, 646 insertions, 0 deletions
diff --git a/vendor/github.com/keybase/go-crypto/rsa/rsa.go b/vendor/github.com/keybase/go-crypto/rsa/rsa.go new file mode 100644 index 0000000000..ff6b11b3ee --- /dev/null +++ b/vendor/github.com/keybase/go-crypto/rsa/rsa.go @@ -0,0 +1,646 @@ +// 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 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 ( + "crypto" + "crypto/rand" + "crypto/subtle" + "errors" + "hash" + "io" + "math/big" +) + +var bigZero = big.NewInt(0) +var bigOne = big.NewInt(1) + +// A PublicKey represents the public part of an RSA key. +type PublicKey struct { + N *big.Int // modulus + E int64 // public exponent +} + +// OAEPOptions is an interface for passing options to OAEP decryption using the +// crypto.Decrypter interface. +type OAEPOptions struct { + // Hash is the hash function that will be used when generating the mask. + Hash crypto.Hash + // Label is an arbitrary byte string that must be equal to the value + // used when encrypting. + Label []byte +} + +var ( + errPublicModulus = errors.New("crypto/rsa: missing public modulus") + errPublicExponentSmall = errors.New("crypto/rsa: public exponent too small") + errPublicExponentLarge = errors.New("crypto/rsa: public exponent too large") +) + +// checkPub sanity checks the public key before we use it. +// We require pub.E to fit into a 32-bit integer so that we +// do not have different behavior depending on whether +// int is 32 or 64 bits. See also +// http://www.imperialviolet.org/2012/03/16/rsae.html. +func checkPub(pub *PublicKey) error { + if pub.N == nil { + return errPublicModulus + } + if pub.E < 2 { + return errPublicExponentSmall + } + if pub.E > 1<<63-1 { + return errPublicExponentLarge + } + return nil +} + +// A PrivateKey represents an RSA key +type PrivateKey struct { + PublicKey // public part. + D *big.Int // private exponent + Primes []*big.Int // prime factors of N, has >= 2 elements. + + // Precomputed contains precomputed values that speed up private + // operations, if available. + Precomputed PrecomputedValues +} + +// Public returns the public key corresponding to priv. +func (priv *PrivateKey) Public() crypto.PublicKey { + return &priv.PublicKey +} + +// Sign signs msg with priv, reading randomness from rand. If opts is a +// *PSSOptions then the PSS algorithm will be used, otherwise PKCS#1 v1.5 will +// be used. This method is intended to support keys where the private part is +// kept in, for example, a hardware module. Common uses should use the Sign* +// functions in this package. +func (priv *PrivateKey) Sign(rand io.Reader, msg []byte, opts crypto.SignerOpts) ([]byte, error) { + if pssOpts, ok := opts.(*PSSOptions); ok { + return SignPSS(rand, priv, pssOpts.Hash, msg, pssOpts) + } + + return SignPKCS1v15(rand, priv, opts.HashFunc(), msg) +} + +// Decrypt decrypts ciphertext with priv. If opts is nil or of type +// *PKCS1v15DecryptOptions then PKCS#1 v1.5 decryption is performed. Otherwise +// opts must have type *OAEPOptions and OAEP decryption is done. +func (priv *PrivateKey) Decrypt(rand io.Reader, ciphertext []byte, opts crypto.DecrypterOpts) (plaintext []byte, err error) { + if opts == nil { + return DecryptPKCS1v15(rand, priv, ciphertext) + } + + switch opts := opts.(type) { + case *OAEPOptions: + return DecryptOAEP(opts.Hash.New(), rand, priv, ciphertext, opts.Label) + + case *PKCS1v15DecryptOptions: + if l := opts.SessionKeyLen; l > 0 { + plaintext = make([]byte, l) + if _, err := io.ReadFull(rand, plaintext); err != nil { + return nil, err + } + if err := DecryptPKCS1v15SessionKey(rand, priv, ciphertext, plaintext); err != nil { + return nil, err + } + return plaintext, nil + } else { + return DecryptPKCS1v15(rand, priv, ciphertext) + } + + default: + return nil, errors.New("crypto/rsa: invalid options for Decrypt") + } +} + +type PrecomputedValues struct { + Dp, Dq *big.Int // D mod (P-1) (or mod Q-1) + Qinv *big.Int // Q^-1 mod P + + // CRTValues is used for the 3rd and subsequent primes. Due to a + // historical accident, the CRT for the first two primes is handled + // differently in PKCS#1 and interoperability is sufficiently + // important that we mirror this. + CRTValues []CRTValue +} + +// CRTValue contains the precomputed Chinese remainder theorem values. +type CRTValue struct { + Exp *big.Int // D mod (prime-1). + Coeff *big.Int // R·Coeff ≡ 1 mod Prime. + R *big.Int // product of primes prior to this (inc p and q). +} + +// Validate performs basic sanity checks on the key. +// It returns nil if the key is valid, or else an error describing a problem. +func (priv *PrivateKey) Validate() error { + if err := checkPub(&priv.PublicKey); err != nil { + return err + } + + // Check that Πprimes == n. + modulus := new(big.Int).Set(bigOne) + for _, prime := range priv.Primes { + // Any primes ≤ 1 will cause divide-by-zero panics later. + if prime.Cmp(bigOne) <= 0 { + return errors.New("crypto/rsa: invalid prime value") + } + modulus.Mul(modulus, prime) + } + if modulus.Cmp(priv.N) != 0 { + return errors.New("crypto/rsa: invalid modulus") + } + + // Check that de ≡ 1 mod p-1, for each prime. + // This implies that e is coprime to each p-1 as e has a multiplicative + // inverse. Therefore e is coprime to lcm(p-1,q-1,r-1,...) = + // exponent(ℤ/nℤ). It also implies that a^de ≡ a mod p as a^(p-1) ≡ 1 + // mod p. Thus a^de ≡ a mod n for all a coprime to n, as required. + congruence := new(big.Int) + de := new(big.Int).SetInt64(int64(priv.E)) + de.Mul(de, priv.D) + for _, prime := range priv.Primes { + pminus1 := new(big.Int).Sub(prime, bigOne) + congruence.Mod(de, pminus1) + if congruence.Cmp(bigOne) != 0 { + return errors.New("crypto/rsa: invalid exponents") + } + } + return nil +} + +// GenerateKey generates an RSA keypair of the given bit size using the +// random source random (for example, crypto/rand.Reader). +func GenerateKey(random io.Reader, bits int) (priv *PrivateKey, err error) { + return GenerateMultiPrimeKey(random, 2, bits) +} + +// GenerateMultiPrimeKey generates a multi-prime RSA keypair of the given bit +// size and the given random source, as suggested in [1]. Although the public +// keys are compatible (actually, indistinguishable) from the 2-prime case, +// the private keys are not. Thus it may not be possible to export multi-prime +// private keys in certain formats or to subsequently import them into other +// code. +// +// Table 1 in [2] suggests maximum numbers of primes for a given size. +// +// [1] US patent 4405829 (1972, expired) +// [2] http://www.cacr.math.uwaterloo.ca/techreports/2006/cacr2006-16.pdf +func GenerateMultiPrimeKey(random io.Reader, nprimes int, bits int) (priv *PrivateKey, err error) { + priv = new(PrivateKey) + priv.E = 65537 + + if nprimes < 2 { + return nil, errors.New("crypto/rsa: GenerateMultiPrimeKey: nprimes must be >= 2") + } + + primes := make([]*big.Int, nprimes) + +NextSetOfPrimes: + for { + todo := bits + // crypto/rand should set the top two bits in each prime. + // Thus each prime has the form + // p_i = 2^bitlen(p_i) × 0.11... (in base 2). + // And the product is: + // P = 2^todo × α + // where α is the product of nprimes numbers of the form 0.11... + // + // If α < 1/2 (which can happen for nprimes > 2), we need to + // shift todo to compensate for lost bits: the mean value of 0.11... + // is 7/8, so todo + shift - nprimes * log2(7/8) ~= bits - 1/2 + // will give good results. + if nprimes >= 7 { + todo += (nprimes - 2) / 5 + } + for i := 0; i < nprimes; i++ { + primes[i], err = rand.Prime(random, todo/(nprimes-i)) + if err != nil { + return nil, err + } + todo -= primes[i].BitLen() + } + + // Make sure that primes is pairwise unequal. + for i, prime := range primes { + for j := 0; j < i; j++ { + if prime.Cmp(primes[j]) == 0 { + continue NextSetOfPrimes + } + } + } + + n := new(big.Int).Set(bigOne) + totient := new(big.Int).Set(bigOne) + pminus1 := new(big.Int) + for _, prime := range primes { + n.Mul(n, prime) + pminus1.Sub(prime, bigOne) + totient.Mul(totient, pminus1) + } + if n.BitLen() != bits { + // This should never happen for nprimes == 2 because + // crypto/rand should set the top two bits in each prime. + // For nprimes > 2 we hope it does not happen often. + continue NextSetOfPrimes + } + + g := new(big.Int) + priv.D = new(big.Int) + y := new(big.Int) + e := big.NewInt(int64(priv.E)) + g.GCD(priv.D, y, e, totient) + + if g.Cmp(bigOne) == 0 { + if priv.D.Sign() < 0 { + priv.D.Add(priv.D, totient) + } + priv.Primes = primes + priv.N = n + + break + } + } + + priv.Precompute() + 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 + var digest []byte + + done := 0 + for done < len(out) { + hash.Write(seed) + hash.Write(counter[0:4]) + digest = hash.Sum(digest[:0]) + hash.Reset() + + for i := 0; i < len(digest) && done < len(out); i++ { + out[done] ^= digest[i] + done++ + } + incCounter(&counter) + } +} + +// ErrMessageTooLong is returned when attempting to encrypt a message which is +// too large for the size of the public key. +var ErrMessageTooLong = errors.New("crypto/rsa: 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. +// +// 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) { + if err := checkPub(pub); err != nil { + return nil, err + } + hash.Reset() + k := (pub.N.BitLen() + 7) / 8 + if len(msg) > k-2*hash.Size()-2 { + err = ErrMessageTooLong + return + } + + hash.Write(label) + lHash := hash.Sum(nil) + 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(random, 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() + + if len(out) < k { + // If the output is too small, we need to left-pad with zeros. + t := make([]byte, k) + copy(t[k-len(out):], out) + out = t + } + + return +} + +// ErrDecryption represents a failure to decrypt a message. +// It is deliberately vague to avoid adaptive attacks. +var ErrDecryption = errors.New("crypto/rsa: decryption error") + +// ErrVerification represents a failure to verify a signature. +// It is deliberately vague to avoid adaptive attacks. +var ErrVerification = errors.New("crypto/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) + g.GCD(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 +} + +// Precompute performs some calculations that speed up private key operations +// in the future. +func (priv *PrivateKey) Precompute() { + if priv.Precomputed.Dp != nil { + return + } + + priv.Precomputed.Dp = new(big.Int).Sub(priv.Primes[0], bigOne) + priv.Precomputed.Dp.Mod(priv.D, priv.Precomputed.Dp) + + priv.Precomputed.Dq = new(big.Int).Sub(priv.Primes[1], bigOne) + priv.Precomputed.Dq.Mod(priv.D, priv.Precomputed.Dq) + + priv.Precomputed.Qinv = new(big.Int).ModInverse(priv.Primes[1], priv.Primes[0]) + + r := new(big.Int).Mul(priv.Primes[0], priv.Primes[1]) + priv.Precomputed.CRTValues = make([]CRTValue, len(priv.Primes)-2) + for i := 2; i < len(priv.Primes); i++ { + prime := priv.Primes[i] + values := &priv.Precomputed.CRTValues[i-2] + + values.Exp = new(big.Int).Sub(prime, bigOne) + values.Exp.Mod(priv.D, values.Exp) + + values.R = new(big.Int).Set(r) + values.Coeff = new(big.Int).ModInverse(r, prime) + + r.Mul(r, prime) + } +} + +// decrypt performs an RSA decryption, resulting in a plaintext integer. If a +// random source is given, RSA blinding is used. +func decrypt(random io.Reader, priv *PrivateKey, c *big.Int) (m *big.Int, err error) { + // TODO(agl): can we get away with reusing blinds? + if c.Cmp(priv.N) > 0 { + err = ErrDecryption + return + } + + var ir *big.Int + if random != 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 multiplying by the multiplicative inverse of r. + + var r *big.Int + + for { + r, err = rand.Int(random, 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) + 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 +} |