| // 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 necessary, 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. |
| // |
| // The RSA operations in this package are not implemented using constant-time algorithms. |
| package rsa |
| |
| import ( |
| "crypto" |
| "crypto/rand" |
| "crypto/subtle" |
| "errors" |
| "hash" |
| "io" |
| "math" |
| "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 int // 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<<31-1 { |
| 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 digest 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 implements crypto.Signer, which is an interface 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 directly. |
| func (priv *PrivateKey) Sign(rand io.Reader, digest []byte, opts crypto.SignerOpts) ([]byte, error) { |
| if pssOpts, ok := opts.(*PSSOptions); ok { |
| return SignPSS(rand, priv, pssOpts.Hash, digest, pssOpts) |
| } |
| |
| return SignPKCS1v15(rand, priv, opts.HashFunc(), digest) |
| } |
| |
| // 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) (*PrivateKey, 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) (*PrivateKey, error) { |
| priv := new(PrivateKey) |
| priv.E = 65537 |
| |
| if nprimes < 2 { |
| return nil, errors.New("crypto/rsa: GenerateMultiPrimeKey: nprimes must be >= 2") |
| } |
| |
| if bits < 64 { |
| primeLimit := float64(uint64(1) << uint(bits/nprimes)) |
| // pi approximates the number of primes less than primeLimit |
| pi := primeLimit / (math.Log(primeLimit) - 1) |
| // Generated primes start with 11 (in binary) so we can only |
| // use a quarter of them. |
| pi /= 4 |
| // Use a factor of two to ensure that key generation terminates |
| // in a reasonable amount of time. |
| pi /= 2 |
| if pi <= float64(nprimes) { |
| return nil, errors.New("crypto/rsa: too few primes of given length to generate an RSA key") |
| } |
| } |
| |
| 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++ { |
| var err error |
| 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) |
| e := big.NewInt(int64(priv.E)) |
| g.GCD(priv.D, nil, 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 priv, nil |
| } |
| |
| // 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 minus |
| // twice the hash length, minus a further 2. |
| func EncryptOAEP(hash hash.Hash, random io.Reader, pub *PublicKey, msg []byte, label []byte) ([]byte, 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 { |
| return nil, ErrMessageTooLong |
| } |
| |
| 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 nil, err |
| } |
| |
| 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 out, nil |
| } |
| |
| // 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) |
| g.GCD(x, nil, 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 |
| } |
| if priv.N.Sign() == 0 { |
| return nil, ErrDecryption |
| } |
| |
| 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) // N != 0 |
| 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) ([]byte, 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 { |
| return nil, ErrDecryption |
| } |
| |
| c := new(big.Int).SetBytes(ciphertext) |
| |
| m, err := decrypt(random, priv, c) |
| if err != nil { |
| return nil, err |
| } |
| |
| 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 { |
| return nil, ErrDecryption |
| } |
| |
| return rest[index+1:], nil |
| } |
| |
| // 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 |
| } |