mirror of
https://github.com/taigrr/arduinolibs
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ChaCha stream cipher
This commit is contained in:
Rhys Weatherley
parent
46fe4e52fd
commit
07a47cdcf1
@ -31,9 +31,15 @@
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* AES192, or AES256 to create an AES block cipher with a specific
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* key size.
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*
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* \note This AES implementation does not have constant cache behaviour due
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* to the use of table lookups. It may not be safe to use this implementation
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* in an environment where the attacker can observe the timing of encryption
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* and decryption operations. Unless AES compatibility is required,
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* it is recommended that the ChaCha stream cipher be used instead.
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*
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* Reference: http://en.wikipedia.org/wiki/Advanced_Encryption_Standard
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*
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* \sa AES128, AES192, AES256
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* \sa ChaCha, AES128, AES192, AES256
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*/
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// AES S-box (http://en.wikipedia.org/wiki/Rijndael_S-box)
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@ -30,6 +30,7 @@
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* \note While fast and small on 8-bit platforms, Arcfour is a very weak
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* algorithm when used incorrectly. Security can be improved slightly using
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* drop() and good key generation. Never reuse the same key with Arcfour.
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* ChaCha will almost always be a better option than Arcfour.
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*
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* The default key size is 128 bits, but any key size between 40 and
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* 256 bits (5 to 32 bytes) can be used with setKey().
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@ -41,7 +42,7 @@
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*
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* Reference: http://en.wikipedia.org/wiki/RC4
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*
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* \sa Cipher
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* \sa ChaCha
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*/
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/**
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269
libraries/Crypto/ChaCha.cpp
Normal file
269
libraries/Crypto/ChaCha.cpp
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@ -0,0 +1,269 @@
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/*
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* Copyright (C) 2015 Southern Storm Software, Pty Ltd.
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*
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* Permission is hereby granted, free of charge, to any person obtaining a
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* copy of this software and associated documentation files (the "Software"),
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* to deal in the Software without restriction, including without limitation
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* the rights to use, copy, modify, merge, publish, distribute, sublicense,
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* and/or sell copies of the Software, and to permit persons to whom the
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* Software is furnished to do so, subject to the following conditions:
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*
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* The above copyright notice and this permission notice shall be included
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* in all copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
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* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
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* DEALINGS IN THE SOFTWARE.
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*/
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#include "ChaCha.h"
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#include "Crypto.h"
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#include "RotateUtil.h"
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#include "EndianUtil.h"
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#include <string.h>
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/**
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* \class ChaCha ChaCha.h <ChaCha.h>
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* \brief ChaCha stream cipher.
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*
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* ChaCha is a stream cipher that takes a key, an 8-byte nonce/IV, and a
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* counter and hashes them to generate a keystream to XOR with the plaintext.
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* Variations on the ChaCha cipher use 8, 12, or 20 rounds of hashing
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* operations with either 128-bit or 256-bit keys.
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*
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* Reference: http://cr.yp.to/chacha.html
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*/
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/**
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* \brief Constructs a new ChaCha stream cipher.
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*
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* \param numRounds Number of encryption rounds to use; usually 8, 12, or 20.
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*/
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ChaCha::ChaCha(uint8_t numRounds)
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: rounds(numRounds)
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, posn(64)
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{
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}
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ChaCha::~ChaCha()
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{
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clean(block);
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clean(stream);
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}
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size_t ChaCha::keySize() const
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{
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// Default key size is 128-bit, but any key size is allowed.
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return 16;
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}
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size_t ChaCha::ivSize() const
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{
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// We return 8 but we also support 12-byte nonces in setIV().
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return 8;
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}
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/**
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* \fn uint8_t ChaCha::numRounds() const
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* \brief Returns the number of encryption rounds; usually 8, 12, or 20.
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*
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* \sa setNumRounds()
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*/
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/**
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* \fn void ChaCha::setNumRounds(uint8_t numRounds)
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* \brief Sets the number of encryption rounds.
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*
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* \param numRounds The number of encryption rounds; usually 8, 12, or 20.
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*
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* \sa numRounds()
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*/
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bool ChaCha::setKey(const uint8_t *key, size_t len)
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{
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static const char tag128[] = "expand 16-byte k";
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static const char tag256[] = "expand 32-byte k";
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if (len <= 16) {
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memcpy(block, tag128, 16);
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memcpy(block + 16, key, len);
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memcpy(block + 32, key, len);
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if (len < 16) {
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memset(block + 16 + len, 0, 16 - len);
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memset(block + 32 + len, 0, 16 - len);
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}
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} else {
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if (len > 32)
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len = 32;
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memcpy(block, tag256, 16);
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memcpy(block + 16, key, len);
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if (len < 32)
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memset(block + 16 + len, 0, 32 - len);
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}
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posn = 64;
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return true;
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}
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bool ChaCha::setIV(const uint8_t *iv, size_t len)
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{
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// From draft-nir-cfrg-chacha20-poly1305-04.txt, we can use either
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// 64-bit or 96-bit nonces. The 96-bit nonce consists of the high
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// word of the counter prepended to a regular 64-bit nonce for ChaCha.
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if (len == 8) {
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memset(block + 48, 0, 8);
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memcpy(block + 56, iv, len);
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posn = 64;
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return true;
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} else if (len == 12) {
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memset(block + 48, 0, 4);
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memcpy(block + 52, iv, len);
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posn = 64;
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return true;
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} else {
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return false;
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}
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}
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/**
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* \brief Sets the starting counter for encryption.
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*
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* \param counter A 4-byte or 8-byte value to use for the starting counter
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* instead of the default value of zero.
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* \param len The length of the counter, which must be 4 or 8.
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* \return Returns false if \a len is not 4 or 8.
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*
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* This function must be called after setIV() and before the first call
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* to encrypt(). It is used to specify a different starting value than
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* zero for the counter portion of the hash input.
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*
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* \sa setIV()
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*/
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bool ChaCha::setCounter(const uint8_t *counter, size_t len)
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{
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// Normally both the IV and the counter are 8 bytes in length.
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// However, if the IV was 12 bytes, then a 4 byte counter can be used.
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if (len == 4 || len == 8) {
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memcpy(block + 48, counter, len);
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posn = 64;
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return true;
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} else {
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return false;
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}
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}
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void ChaCha::encrypt(uint8_t *output, const uint8_t *input, size_t len)
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{
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while (len > 0) {
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if (posn >= 64) {
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// Generate a new encrypted counter block.
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hashCore((uint32_t *)stream, (const uint32_t *)block, rounds);
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posn = 0;
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// Increment the counter, taking care not to reveal
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// any timing information about the starting value.
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// We iterate through the entire counter region even
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// if we could stop earlier because a byte is non-zero.
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uint16_t temp = 1;
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uint8_t index = 48;
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while (index < 56) {
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temp += block[index];
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block[index] = (uint8_t)temp;
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temp >>= 8;
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++index;
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}
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}
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uint8_t templen = 64 - posn;
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if (templen > len)
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templen = len;
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len -= templen;
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while (templen > 0) {
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*output++ = *input++ ^ stream[posn++];
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--templen;
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}
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}
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}
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void ChaCha::decrypt(uint8_t *output, const uint8_t *input, size_t len)
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{
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encrypt(output, input, len);
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}
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void ChaCha::clear()
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{
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clean(block);
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clean(stream);
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posn = 64;
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}
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// On AVR it is faster to rotate left by 16 bits and then right by 4 bits
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// one at a time than to rotate left by 12 bits in a single step.
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#define leftRotate12(a) \
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(__extension__ ({ \
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uint32_t temp = (a); \
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temp = (temp << 16) | (temp >> 16); \
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temp = rightRotate(temp, 1); \
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temp = rightRotate(temp, 1); \
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temp = rightRotate(temp, 1); \
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rightRotate(temp, 1); \
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}))
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// Perform a ChaCha quarter round operation.
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#define quarterRound(a, b, c, d) \
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do { \
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uint32_t _b = (b); \
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uint32_t _a = (a) + _b; \
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uint32_t _d = leftRotate((d) ^ _a, 16); \
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uint32_t _c = (c) + _d; \
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_b = leftRotate12(_b ^ _c); \
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_a += _b; \
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(d) = _d = leftRotate(_d ^ _a, 8); \
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_c += _d; \
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(a) = _a; \
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(b) = leftRotate7(_b ^ _c); \
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(c) = _c; \
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} while (0)
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/**
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* \brief Executes the ChaCha hash core on an input memory block.
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*
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* \param output Output memory block, must be at least 16 words in length
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* and must not overlap with \a input.
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* \param input Input memory block, must be at least 16 words in length.
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* \param rounds Number of ChaCha rounds to perform; usually 8, 12, or 20.
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*
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* This function is provided for the convenience of applications that need
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* access to the ChaCha hash core without the higher-level processing that
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* turns the core into a stream cipher.
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*/
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void ChaCha::hashCore(uint32_t *output, const uint32_t *input, uint8_t rounds)
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{
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uint8_t posn;
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// Copy the input buffer to the output prior to the first round
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// and convert from little-endian to host byte order.
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for (posn = 0; posn < 16; ++posn)
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output[posn] = le32toh(input[posn]);
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// Perform the ChaCha rounds in sets of two.
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for (; rounds >= 2; rounds -= 2) {
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// Column round.
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quarterRound(output[0], output[4], output[8], output[12]);
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quarterRound(output[1], output[5], output[9], output[13]);
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quarterRound(output[2], output[6], output[10], output[14]);
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quarterRound(output[3], output[7], output[11], output[15]);
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// Diagonal round.
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quarterRound(output[0], output[5], output[10], output[15]);
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quarterRound(output[1], output[6], output[11], output[12]);
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quarterRound(output[2], output[7], output[8], output[13]);
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quarterRound(output[3], output[4], output[9], output[14]);
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}
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// Add the original input to the final output, convert back to
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// little-endian, and return the result.
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for (posn = 0; posn < 16; ++posn)
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output[posn] = htole32(output[posn] + le32toh(input[posn]));
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}
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58
libraries/Crypto/ChaCha.h
Normal file
58
libraries/Crypto/ChaCha.h
Normal file
@ -0,0 +1,58 @@
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/*
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* Copyright (C) 2015 Southern Storm Software, Pty Ltd.
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*
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* Permission is hereby granted, free of charge, to any person obtaining a
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* copy of this software and associated documentation files (the "Software"),
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* to deal in the Software without restriction, including without limitation
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* the rights to use, copy, modify, merge, publish, distribute, sublicense,
|
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* and/or sell copies of the Software, and to permit persons to whom the
|
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* Software is furnished to do so, subject to the following conditions:
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*
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* The above copyright notice and this permission notice shall be included
|
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* in all copies or substantial portions of the Software.
|
||||
*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
|
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* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
||||
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
|
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* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
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* DEALINGS IN THE SOFTWARE.
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*/
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#ifndef CRYPTO_CHACHA_h
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#define CRYPTO_CHACHA_h
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#include "Cipher.h"
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class ChaCha : public Cipher
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{
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public:
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explicit ChaCha(uint8_t numRounds = 20);
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virtual ~ChaCha();
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size_t keySize() const;
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size_t ivSize() const;
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uint8_t numRounds() const { return rounds; }
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void setNumRounds(uint8_t numRounds) { rounds = numRounds; }
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bool setKey(const uint8_t *key, size_t len);
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bool setIV(const uint8_t *iv, size_t len);
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bool setCounter(const uint8_t *counter, size_t len);
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void encrypt(uint8_t *output, const uint8_t *input, size_t len);
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void decrypt(uint8_t *output, const uint8_t *input, size_t len);
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void clear();
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static void hashCore(uint32_t *output, const uint32_t *input, uint8_t rounds);
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private:
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uint8_t block[64];
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uint8_t stream[64];
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uint8_t rounds;
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uint8_t posn;
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};
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#endif
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43
libraries/Crypto/EndianUtil.h
Normal file
43
libraries/Crypto/EndianUtil.h
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/*
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* Copyright (C) 2015 Southern Storm Software, Pty Ltd.
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*
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* Permission is hereby granted, free of charge, to any person obtaining a
|
||||
* copy of this software and associated documentation files (the "Software"),
|
||||
* to deal in the Software without restriction, including without limitation
|
||||
* the rights to use, copy, modify, merge, publish, distribute, sublicense,
|
||||
* and/or sell copies of the Software, and to permit persons to whom the
|
||||
* Software is furnished to do so, subject to the following conditions:
|
||||
*
|
||||
* The above copyright notice and this permission notice shall be included
|
||||
* in all copies or substantial portions of the Software.
|
||||
*
|
||||
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
|
||||
* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
||||
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
|
||||
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
||||
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||
* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
|
||||
* DEALINGS IN THE SOFTWARE.
|
||||
*/
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#ifndef CRYPTO_ENDIANUTIL_H
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#define CRYPTO_ENDIANUTIL_H
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#include <inttypes.h>
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// CPU is assumed to be little endian. Edit this file if you
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// need to port this library to a big endian CPU.
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#define htole32(x) (x)
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#define le32toh(x) (x)
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#define htobe32(x) \
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(__extension__ ({ \
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uint32_t _temp = (x); \
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((_temp >> 24) & 0x000000FF) | \
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((_temp >> 8) & 0x0000FF00) | \
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((_temp << 8) & 0x00FF0000) | \
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((_temp << 24) & 0xFF000000); \
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}))
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#define be32toh(x) (htobe32((x)))
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#endif
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174
libraries/Crypto/RotateUtil.h
Normal file
174
libraries/Crypto/RotateUtil.h
Normal file
@ -0,0 +1,174 @@
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/*
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* Copyright (C) 2015 Southern Storm Software, Pty Ltd.
|
||||
*
|
||||
* Permission is hereby granted, free of charge, to any person obtaining a
|
||||
* copy of this software and associated documentation files (the "Software"),
|
||||
* to deal in the Software without restriction, including without limitation
|
||||
* the rights to use, copy, modify, merge, publish, distribute, sublicense,
|
||||
* and/or sell copies of the Software, and to permit persons to whom the
|
||||
* Software is furnished to do so, subject to the following conditions:
|
||||
*
|
||||
* The above copyright notice and this permission notice shall be included
|
||||
* in all copies or substantial portions of the Software.
|
||||
*
|
||||
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
|
||||
* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
||||
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
|
||||
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
||||
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||
* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
|
||||
* DEALINGS IN THE SOFTWARE.
|
||||
*/
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#ifndef CRYPTO_ROTATEUTIL_H
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#define CRYPTO_ROTATEUTIL_H
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#include <inttypes.h>
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// Rotation functions that are optimised for best performance on AVR.
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// The most efficient rotations are where the number of bits is 1 or a
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// multiple of 8, so we compose the efficient rotations to produce all
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// other rotation counts of interest. All macros below assume arguments
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// of 32 bits in size.
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// Generic left rotate - best performance when "bits" is 1 or a multiple of 8.
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#define leftRotate(a, bits) \
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(__extension__ ({ \
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uint32_t _temp = (a); \
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(_temp << (bits)) | (_temp >> (32 - (bits))); \
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}))
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// Generic right rotate - best performance when "bits" is 1 or a multiple of 8.
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#define rightRotate(a, bits) \
|
||||
(__extension__ ({ \
|
||||
uint32_t _temp = (a); \
|
||||
(_temp >> (bits)) | (_temp << (32 - (bits))); \
|
||||
}))
|
||||
|
||||
// Left rotate by 1.
|
||||
#define leftRotate1(a) (leftRotate((a), 1))
|
||||
|
||||
// Left rotate by 2.
|
||||
#define leftRotate2(a) (leftRotate(leftRotate((a), 1), 1))
|
||||
|
||||
// Left rotate by 3.
|
||||
#define leftRotate3(a) (leftRotate(leftRotate(leftRotate((a), 1), 1), 1))
|
||||
|
||||
// Left rotate by 4.
|
||||
#define leftRotate4(a) (leftRotate(leftRotate(leftRotate(leftRotate((a), 1), 1), 1), 1))
|
||||
|
||||
// Left rotate by 5: Rotate left by 8, then right by 3.
|
||||
#define leftRotate5(a) (rightRotate(rightRotate(rightRotate(leftRotate((a), 8), 1), 1), 1))
|
||||
|
||||
// Left rotate by 6: Rotate left by 8, then right by 2.
|
||||
#define leftRotate6(a) (rightRotate(rightRotate(leftRotate((a), 8), 1), 1))
|
||||
|
||||
// Left rotate by 7: Rotate left by 8, then right by 1.
|
||||
#define leftRotate7(a) (rightRotate(leftRotate((a), 8), 1))
|
||||
|
||||
// Left rotate by 8.
|
||||
#define leftRotate8(a) (leftRotate((a), 8))
|
||||
|
||||
// Left rotate by 9: Rotate left by 8, then left by 1.
|
||||
#define leftRotate9(a) (leftRotate(leftRotate((a), 8), 1))
|
||||
|
||||
// Left rotate by 10: Rotate left by 8, then left by 2.
|
||||
#define leftRotate10(a) (leftRotate(leftRotate(leftRotate((a), 8), 1), 1))
|
||||
|
||||
// Left rotate by 11: Rotate left by 8, then left by 3.
|
||||
#define leftRotate11(a) (leftRotate(leftRotate(leftRotate(leftRotate((a), 8), 1), 1), 1))
|
||||
|
||||
// Left rotate by 12: Rotate left by 8, then left by 4.
|
||||
#define leftRotate12(a) (leftRotate(leftRotate(leftRotate(leftRotate(leftRotate((a), 8), 1), 1), 1), 1))
|
||||
|
||||
// Left rotate by 13: Rotate left by 16, then right by 3.
|
||||
#define leftRotate13(a) (rightRotate(rightRotate(rightRotate(leftRotate((a), 16), 1), 1), 1))
|
||||
|
||||
// Left rotate by 14: Rotate left by 16, then right by 2.
|
||||
#define leftRotate14(a) (rightRotate(rightRotate(leftRotate((a), 16), 1), 1))
|
||||
|
||||
// Left rotate by 15: Rotate left by 16, then right by 1.
|
||||
#define leftRotate15(a) (rightRotate(leftRotate((a), 16), 1))
|
||||
|
||||
// Left rotate by 16.
|
||||
#define leftRotate16(a) (leftRotate((a), 16))
|
||||
|
||||
// Left rotate by 17: Rotate left by 16, then left by 1.
|
||||
#define leftRotate17(a) (leftRotate(leftRotate((a), 16), 1))
|
||||
|
||||
// Left rotate by 18: Rotate left by 16, then left by 2.
|
||||
#define leftRotate18(a) (leftRotate(leftRotate(leftRotate((a), 16), 1), 1))
|
||||
|
||||
// Left rotate by 19: Rotate left by 16, then left by 3.
|
||||
#define leftRotate19(a) (leftRotate(leftRotate(leftRotate(leftRotate((a), 16), 1), 1), 1))
|
||||
|
||||
// Left rotate by 20: Rotate left by 16, then left by 4.
|
||||
#define leftRotate20(a) (leftRotate(leftRotate(leftRotate(leftRotate(leftRotate((a), 16), 1), 1), 1), 1))
|
||||
|
||||
// Left rotate by 21: Rotate left by 24, then right by 3.
|
||||
#define leftRotate21(a) (rightRotate(rightRotate(rightRotate(leftRotate((a), 24), 1), 1), 1))
|
||||
|
||||
// Left rotate by 22: Rotate left by 24, then right by 2.
|
||||
#define leftRotate22(a) (rightRotate(rightRotate(leftRotate((a), 24), 1), 1))
|
||||
|
||||
// Left rotate by 23: Rotate left by 24, then right by 1.
|
||||
#define leftRotate23(a) (rightRotate(leftRotate((a), 24), 1))
|
||||
|
||||
// Left rotate by 24.
|
||||
#define leftRotate24(a) (leftRotate((a), 24))
|
||||
|
||||
// Left rotate by 25: Rotate left by 24, then left by 1.
|
||||
#define leftRotate25(a) (leftRotate(leftRotate((a), 24), 1))
|
||||
|
||||
// Left rotate by 26: Rotate left by 24, then left by 2.
|
||||
#define leftRotate26(a) (leftRotate(leftRotate(leftRotate((a), 24), 1), 1))
|
||||
|
||||
// Left rotate by 27: Rotate left by 24, then left by 3.
|
||||
#define leftRotate27(a) (leftRotate(leftRotate(leftRotate(leftRotate((a), 24), 1), 1), 1))
|
||||
|
||||
// Left rotate by 28: Rotate right by 4.
|
||||
#define leftRotate28(a) (rightRotate(rightRotate(rightRotate(rightRotate((a), 1), 1), 1), 1))
|
||||
|
||||
// Left rotate by 29: Rotate right by 3.
|
||||
#define leftRotate29(a) (rightRotate(rightRotate(rightRotate((a), 1), 1), 1))
|
||||
|
||||
// Left rotate by 30: Rotate right by 2.
|
||||
#define leftRotate30(a) (rightRotate(rightRotate((a), 1), 1))
|
||||
|
||||
// Left rotate by 31: Rotate right by 1.
|
||||
#define leftRotate31(a) (rightRotate((a), 1))
|
||||
|
||||
// Define the right rotations in terms of left rotations.
|
||||
#define rightRotate1(a) (leftRotate31((a)))
|
||||
#define rightRotate2(a) (leftRotate30((a)))
|
||||
#define rightRotate3(a) (leftRotate29((a)))
|
||||
#define rightRotate4(a) (leftRotate28((a)))
|
||||
#define rightRotate5(a) (leftRotate27((a)))
|
||||
#define rightRotate6(a) (leftRotate26((a)))
|
||||
#define rightRotate7(a) (leftRotate25((a)))
|
||||
#define rightRotate8(a) (leftRotate24((a)))
|
||||
#define rightRotate9(a) (leftRotate23((a)))
|
||||
#define rightRotate10(a) (leftRotate22((a)))
|
||||
#define rightRotate11(a) (leftRotate21((a)))
|
||||
#define rightRotate12(a) (leftRotate20((a)))
|
||||
#define rightRotate13(a) (leftRotate19((a)))
|
||||
#define rightRotate14(a) (leftRotate18((a)))
|
||||
#define rightRotate15(a) (leftRotate17((a)))
|
||||
#define rightRotate16(a) (leftRotate16((a)))
|
||||
#define rightRotate17(a) (leftRotate15((a)))
|
||||
#define rightRotate18(a) (leftRotate14((a)))
|
||||
#define rightRotate19(a) (leftRotate13((a)))
|
||||
#define rightRotate20(a) (leftRotate12((a)))
|
||||
#define rightRotate21(a) (leftRotate11((a)))
|
||||
#define rightRotate22(a) (leftRotate10((a)))
|
||||
#define rightRotate23(a) (leftRotate9((a)))
|
||||
#define rightRotate24(a) (leftRotate8((a)))
|
||||
#define rightRotate25(a) (leftRotate7((a)))
|
||||
#define rightRotate26(a) (leftRotate6((a)))
|
||||
#define rightRotate27(a) (leftRotate5((a)))
|
||||
#define rightRotate28(a) (leftRotate4((a)))
|
||||
#define rightRotate29(a) (leftRotate3((a)))
|
||||
#define rightRotate30(a) (leftRotate2((a)))
|
||||
#define rightRotate31(a) (leftRotate1((a)))
|
||||
|
||||
#endif
|
||||
375
libraries/Crypto/examples/TestChaCha/TestChaCha.ino
Normal file
375
libraries/Crypto/examples/TestChaCha/TestChaCha.ino
Normal file
@ -0,0 +1,375 @@
|
||||
/*
|
||||
* Copyright (C) 2015 Southern Storm Software, Pty Ltd.
|
||||
*
|
||||
* Permission is hereby granted, free of charge, to any person obtaining a
|
||||
* copy of this software and associated documentation files (the "Software"),
|
||||
* to deal in the Software without restriction, including without limitation
|
||||
* the rights to use, copy, modify, merge, publish, distribute, sublicense,
|
||||
* and/or sell copies of the Software, and to permit persons to whom the
|
||||
* Software is furnished to do so, subject to the following conditions:
|
||||
*
|
||||
* The above copyright notice and this permission notice shall be included
|
||||
* in all copies or substantial portions of the Software.
|
||||
*
|
||||
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
|
||||
* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
||||
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
|
||||
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
||||
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||
* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
|
||||
* DEALINGS IN THE SOFTWARE.
|
||||
*/
|
||||
|
||||
/*
|
||||
This example runs tests on the ChaCha implementation to verify correct behaviour.
|
||||
*/
|
||||
|
||||
#include <Crypto.h>
|
||||
#include <ChaCha.h>
|
||||
#include <string.h>
|
||||
|
||||
#define MAX_PLAINTEXT_SIZE 64
|
||||
#define MAX_CIPHERTEXT_SIZE 64
|
||||
|
||||
struct TestVector
|
||||
{
|
||||
const char *name;
|
||||
byte key[32];
|
||||
size_t keySize;
|
||||
uint8_t rounds;
|
||||
byte plaintext[MAX_PLAINTEXT_SIZE];
|
||||
byte ciphertext[MAX_CIPHERTEXT_SIZE];
|
||||
byte iv[8];
|
||||
byte counter[8];
|
||||
size_t size;
|
||||
};
|
||||
|
||||
// Use the test vectors from section 9 of the Salsa20 specification,
|
||||
// http://cr.yp.to/snuffle/spec.pdf, but modify the ciphertext to
|
||||
// the expected output from ChaCha20/12/8. Unfortunately the ChaCha
|
||||
// specification doesn't contain test vectors - these were generated
|
||||
// using the reference implementation from http://cr.yp.to/chacha.html.
|
||||
|
||||
static TestVector const testVectorChaCha20_128 = {
|
||||
.name = "ChaCha20 128-bit",
|
||||
.key = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16},
|
||||
.keySize = 16,
|
||||
.rounds = 20,
|
||||
.plaintext = {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
|
||||
.ciphertext = {0x1C, 0x91, 0xE7, 0x99, 0x71, 0xC0, 0x1C, 0x2A,
|
||||
0xEC, 0xE9, 0x24, 0x35, 0xB1, 0x6E, 0xBF, 0xFD,
|
||||
0x33, 0x05, 0xCC, 0x17, 0x24, 0x9D, 0x66, 0xA7,
|
||||
0xA0, 0xCA, 0xB8, 0x36, 0x03, 0xA6, 0x9D, 0x93,
|
||||
0x9A, 0x4C, 0x10, 0x40, 0xD9, 0x2A, 0x86, 0x78,
|
||||
0x3A, 0xAD, 0x71, 0x87, 0x55, 0x9F, 0x5B, 0x9A,
|
||||
0x68, 0x52, 0xA0, 0xAD, 0x59, 0xAE, 0x04, 0x10,
|
||||
0x25, 0x74, 0x5C, 0x05, 0x62, 0x78, 0xF4, 0x8A},
|
||||
.iv = {101,102,103,104,105,106,107,108},
|
||||
.counter = {109, 110, 111, 112, 113, 114, 115, 116},
|
||||
.size = 64
|
||||
};
|
||||
|
||||
static TestVector const testVectorChaCha20_256 = {
|
||||
.name = "ChaCha20 256-bit",
|
||||
.key = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
|
||||
201, 202, 203, 204, 205, 206, 207, 208, 209, 210,
|
||||
211, 212, 213, 214, 215, 216},
|
||||
.keySize = 32,
|
||||
.rounds = 20,
|
||||
.plaintext = {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
|
||||
.ciphertext = {0x2A, 0x7E, 0x73, 0xC2, 0x2A, 0xE5, 0xCF, 0x4E,
|
||||
0x21, 0x75, 0xB1, 0x26, 0x38, 0x3F, 0x60, 0x84,
|
||||
0x11, 0x25, 0xFC, 0xAD, 0xFD, 0x16, 0x54, 0xF2,
|
||||
0xD7, 0x8C, 0x5D, 0x49, 0x8D, 0x96, 0xBE, 0x15,
|
||||
0xC9, 0x00, 0x12, 0x09, 0x14, 0x43, 0x2D, 0x6D,
|
||||
0x64, 0x33, 0x88, 0xA6, 0x16, 0x39, 0x86, 0xFD,
|
||||
0xD8, 0x85, 0x4D, 0x76, 0x42, 0xEC, 0x0A, 0x0C,
|
||||
0x8A, 0xF2, 0x99, 0x2E, 0x54, 0xAE, 0xB4, 0xD9},
|
||||
.iv = {101,102,103,104,105,106,107,108},
|
||||
.counter = {109, 110, 111, 112, 113, 114, 115, 116},
|
||||
.size = 64
|
||||
};
|
||||
|
||||
static TestVector const testVectorChaCha12_128 = {
|
||||
.name = "ChaCha12 128-bit",
|
||||
.key = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16},
|
||||
.keySize = 16,
|
||||
.rounds = 12,
|
||||
.plaintext = {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
|
||||
.ciphertext = {0xCB, 0xC1, 0xCF, 0x63, 0xE8, 0xD0, 0x62, 0x83,
|
||||
0xFC, 0x12, 0x87, 0x8C, 0x62, 0x09, 0x5B, 0xF8,
|
||||
0x84, 0x93, 0x30, 0xC6, 0xE6, 0x26, 0x87, 0x99,
|
||||
0xB0, 0xD9, 0xC1, 0xE1, 0xD7, 0x58, 0xCA, 0x05,
|
||||
0xFE, 0x46, 0x40, 0xD1, 0xDC, 0x14, 0x68, 0x3C,
|
||||
0xFF, 0x25, 0xF7, 0x70, 0x5F, 0xBF, 0x37, 0xC5,
|
||||
0x29, 0x8F, 0x3C, 0x55, 0x74, 0xDF, 0xF7, 0x49,
|
||||
0x8D, 0xD8, 0xE9, 0xBA, 0x5D, 0xF1, 0x9F, 0xA5},
|
||||
.iv = {101,102,103,104,105,106,107,108},
|
||||
.counter = {109, 110, 111, 112, 113, 114, 115, 116},
|
||||
.size = 64
|
||||
};
|
||||
|
||||
static TestVector const testVectorChaCha12_256 = {
|
||||
.name = "ChaCha12 256-bit",
|
||||
.key = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
|
||||
201, 202, 203, 204, 205, 206, 207, 208, 209, 210,
|
||||
211, 212, 213, 214, 215, 216},
|
||||
.keySize = 32,
|
||||
.rounds = 12,
|
||||
.plaintext = {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
|
||||
.ciphertext = {0xB8, 0x49, 0xD4, 0x70, 0xE0, 0xFF, 0x57, 0x12,
|
||||
0x95, 0xBF, 0xD9, 0xCD, 0x26, 0xFD, 0x4D, 0x6E,
|
||||
0x70, 0xA2, 0xBC, 0x58, 0x63, 0xF6, 0x2C, 0xC3,
|
||||
0xC7, 0x1C, 0x9B, 0x1A, 0x54, 0xDC, 0xF9, 0xF8,
|
||||
0xFD, 0x59, 0xEA, 0xC9, 0xC3, 0x10, 0xA1, 0xDE,
|
||||
0xD1, 0x53, 0x84, 0xD6, 0x8D, 0xC6, 0x61, 0x09,
|
||||
0x2E, 0x62, 0x14, 0xC5, 0x77, 0x4B, 0x6B, 0x5B,
|
||||
0x0D, 0x35, 0xE6, 0x17, 0x41, 0x51, 0xA6, 0xA4},
|
||||
.iv = {101,102,103,104,105,106,107,108},
|
||||
.counter = {109, 110, 111, 112, 113, 114, 115, 116},
|
||||
.size = 64
|
||||
};
|
||||
|
||||
static TestVector const testVectorChaCha8_128 = {
|
||||
.name = "ChaCha8 128-bit",
|
||||
.key = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16},
|
||||
.keySize = 16,
|
||||
.rounds = 8,
|
||||
.plaintext = {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
|
||||
.ciphertext = {0x76, 0x42, 0x84, 0xB4, 0x87, 0x1F, 0x54, 0xAE,
|
||||
0x33, 0xBF, 0x79, 0x3C, 0xE2, 0x78, 0x5B, 0x4D,
|
||||
0xE7, 0x90, 0xF3, 0x8C, 0xB8, 0xF4, 0xA1, 0x56,
|
||||
0x87, 0x8B, 0x54, 0x06, 0xBE, 0x5A, 0x1B, 0x1C,
|
||||
0x30, 0x31, 0xD3, 0xCD, 0x90, 0x34, 0xC8, 0x93,
|
||||
0x2C, 0x0A, 0x5E, 0xC9, 0x4A, 0x1A, 0x66, 0x4C,
|
||||
0x28, 0x94, 0xA9, 0x61, 0xBB, 0xB4, 0xF0, 0x2D,
|
||||
0x59, 0x73, 0x9F, 0xC9, 0xF1, 0xF0, 0x66, 0x05},
|
||||
.iv = {101,102,103,104,105,106,107,108},
|
||||
.counter = {109, 110, 111, 112, 113, 114, 115, 116},
|
||||
.size = 64
|
||||
};
|
||||
|
||||
static TestVector const testVectorChaCha8_256 = {
|
||||
.name = "ChaCha8 256-bit",
|
||||
.key = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
|
||||
201, 202, 203, 204, 205, 206, 207, 208, 209, 210,
|
||||
211, 212, 213, 214, 215, 216},
|
||||
.keySize = 32,
|
||||
.rounds = 8,
|
||||
.plaintext = {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
|
||||
.ciphertext = {0x38, 0x0F, 0x75, 0xD6, 0x32, 0xF8, 0xBB, 0x2C,
|
||||
0x44, 0x81, 0xF4, 0x27, 0x90, 0xB8, 0xAA, 0xE3,
|
||||
0x09, 0xD1, 0xB9, 0x55, 0xC2, 0xF5, 0x85, 0x27,
|
||||
0xBB, 0x8F, 0x43, 0x00, 0x68, 0x2B, 0x2A, 0x1B,
|
||||
0x7A, 0xC1, 0x5B, 0xC3, 0xA3, 0xFF, 0x29, 0xC9,
|
||||
0xD2, 0x95, 0x98, 0xF6, 0x3C, 0xAC, 0x9B, 0x2C,
|
||||
0xA3, 0xF1, 0x40, 0x1E, 0xFA, 0x7C, 0xAC, 0xA3,
|
||||
0xB1, 0x61, 0x27, 0x50, 0xBB, 0x03, 0x24, 0x36},
|
||||
.iv = {101,102,103,104,105,106,107,108},
|
||||
.counter = {109, 110, 111, 112, 113, 114, 115, 116},
|
||||
.size = 64
|
||||
};
|
||||
|
||||
ChaCha chacha;
|
||||
|
||||
byte buffer[128];
|
||||
|
||||
bool testCipher_N(ChaCha *cipher, const struct TestVector *test, size_t inc)
|
||||
{
|
||||
byte output[MAX_CIPHERTEXT_SIZE];
|
||||
size_t posn, len;
|
||||
|
||||
cipher->clear();
|
||||
if (!cipher->setKey(test->key, test->keySize)) {
|
||||
Serial.print("setKey ");
|
||||
return false;
|
||||
}
|
||||
if (!cipher->setIV(test->iv, cipher->ivSize())) {
|
||||
Serial.print("setIV ");
|
||||
return false;
|
||||
}
|
||||
if (!cipher->setCounter(test->counter, 8)) {
|
||||
Serial.print("setCounter ");
|
||||
return false;
|
||||
}
|
||||
|
||||
memset(output, 0xBA, sizeof(output));
|
||||
|
||||
for (posn = 0; posn < test->size; posn += inc) {
|
||||
len = test->size - posn;
|
||||
if (len > inc)
|
||||
len = inc;
|
||||
cipher->encrypt(output + posn, test->plaintext + posn, len);
|
||||
}
|
||||
|
||||
if (memcmp(output, test->ciphertext, test->size) != 0) {
|
||||
Serial.print(output[0], HEX);
|
||||
Serial.print("->");
|
||||
Serial.print(test->ciphertext[0], HEX);
|
||||
return false;
|
||||
}
|
||||
|
||||
cipher->setKey(test->key, test->keySize);
|
||||
cipher->setIV(test->iv, cipher->ivSize());
|
||||
cipher->setCounter(test->counter, 8);
|
||||
|
||||
for (posn = 0; posn < test->size; posn += inc) {
|
||||
len = test->size - posn;
|
||||
if (len > inc)
|
||||
len = inc;
|
||||
cipher->decrypt(output + posn, test->ciphertext + posn, len);
|
||||
}
|
||||
|
||||
if (memcmp(output, test->plaintext, test->size) != 0)
|
||||
return false;
|
||||
|
||||
return true;
|
||||
}
|
||||
|
||||
void testCipher(ChaCha *cipher, const struct TestVector *test)
|
||||
{
|
||||
bool ok;
|
||||
|
||||
Serial.print(test->name);
|
||||
Serial.print(" ... ");
|
||||
|
||||
cipher->setNumRounds(test->rounds);
|
||||
|
||||
ok = testCipher_N(cipher, test, test->size);
|
||||
ok &= testCipher_N(cipher, test, 1);
|
||||
ok &= testCipher_N(cipher, test, 2);
|
||||
ok &= testCipher_N(cipher, test, 5);
|
||||
ok &= testCipher_N(cipher, test, 8);
|
||||
ok &= testCipher_N(cipher, test, 13);
|
||||
ok &= testCipher_N(cipher, test, 16);
|
||||
|
||||
if (ok)
|
||||
Serial.println("Passed");
|
||||
else
|
||||
Serial.println("Failed");
|
||||
}
|
||||
|
||||
void perfCipherEncrypt(ChaCha *cipher, const struct TestVector *test)
|
||||
{
|
||||
unsigned long start;
|
||||
unsigned long elapsed;
|
||||
int count;
|
||||
|
||||
Serial.print(test->name);
|
||||
Serial.print(" Encrypt ... ");
|
||||
|
||||
cipher->setNumRounds(test->rounds);
|
||||
cipher->setKey(test->key, test->keySize);
|
||||
cipher->setIV(test->iv, cipher->ivSize());
|
||||
start = micros();
|
||||
for (count = 0; count < 500; ++count) {
|
||||
cipher->encrypt(buffer, buffer, sizeof(buffer));
|
||||
}
|
||||
elapsed = micros() - start;
|
||||
|
||||
Serial.print(elapsed / (sizeof(buffer) * 500.0));
|
||||
Serial.print("us per byte, ");
|
||||
Serial.print((sizeof(buffer) * 500.0 * 1000000.0) / elapsed);
|
||||
Serial.println(" bytes per second");
|
||||
}
|
||||
|
||||
void perfCipherDecrypt(ChaCha *cipher, const struct TestVector *test)
|
||||
{
|
||||
unsigned long start;
|
||||
unsigned long elapsed;
|
||||
int count;
|
||||
|
||||
Serial.print(test->name);
|
||||
Serial.print(" Decrypt ... ");
|
||||
|
||||
cipher->setNumRounds(test->rounds);
|
||||
cipher->setKey(test->key, test->keySize);
|
||||
cipher->setIV(test->iv, cipher->ivSize());
|
||||
start = micros();
|
||||
for (count = 0; count < 500; ++count) {
|
||||
cipher->decrypt(buffer, buffer, sizeof(buffer));
|
||||
}
|
||||
elapsed = micros() - start;
|
||||
|
||||
Serial.print(elapsed / (sizeof(buffer) * 500.0));
|
||||
Serial.print("us per byte, ");
|
||||
Serial.print((sizeof(buffer) * 500.0 * 1000000.0) / elapsed);
|
||||
Serial.println(" bytes per second");
|
||||
}
|
||||
|
||||
void perfCipher(ChaCha *cipher, const struct TestVector *test)
|
||||
{
|
||||
perfCipherEncrypt(cipher, test);
|
||||
perfCipherDecrypt(cipher, test);
|
||||
}
|
||||
|
||||
void setup()
|
||||
{
|
||||
Serial.begin(9600);
|
||||
|
||||
Serial.println();
|
||||
|
||||
Serial.println("Test Vectors:");
|
||||
testCipher(&chacha, &testVectorChaCha20_128);
|
||||
testCipher(&chacha, &testVectorChaCha20_256);
|
||||
testCipher(&chacha, &testVectorChaCha12_128);
|
||||
testCipher(&chacha, &testVectorChaCha12_256);
|
||||
testCipher(&chacha, &testVectorChaCha8_128);
|
||||
testCipher(&chacha, &testVectorChaCha8_256);
|
||||
|
||||
Serial.println();
|
||||
|
||||
Serial.println("Performance Tests:");
|
||||
perfCipher(&chacha, &testVectorChaCha20_128);
|
||||
perfCipher(&chacha, &testVectorChaCha20_256);
|
||||
perfCipher(&chacha, &testVectorChaCha12_128);
|
||||
perfCipher(&chacha, &testVectorChaCha12_256);
|
||||
perfCipher(&chacha, &testVectorChaCha8_128);
|
||||
perfCipher(&chacha, &testVectorChaCha8_256);
|
||||
}
|
||||
|
||||
void loop()
|
||||
{
|
||||
}
|
||||
Loading…
x
Reference in New Issue
Block a user