Hi all,
I've been creating an implementation of SHA-512 in C++ to run on the Arduino Nano 33 IoT for fun, and I've recently run into some really strange behavior that I don't understand. I should note that I am relatively new to both C++ and Arduino, so it is very possible that I am overlooking something obvious.
The program uses an array of eight constant, unsigned, 64-bit integers called hInit:
const uint64_t hInit[HASH_WORDS] = {0x6a09e667f3bcc908, 0xbb67ae8584caa73b, 0x3c6ef372fe94f82b, 0xa54ff53a5f1d36f1, 0x510e527fade682d1, 0x9b05688c2b3e6c1f, 0x1f83d9abfb41bd6b, 0x5be0cd19137e2179};
where static const constexpr unsigned short HASH_WORDS = 8
hInit contains the initial values of a different array, h, which is used in many other places in the program:
uint64_t h[HASH_WORDS];
The first signs that something was off came when testing my program against some known SHA-512 test vectors. When the message length being fed into the program exceeded 811 bytes, the hash that was returned would be incorrect. When I probed further into why this was I discovered that when the array, h, was being initialized with the values of hInit, the last byte of the first 64-bit word was being zeroed out:
In The .ino:
unsigned long long messageLength = 112;
char message[messageLength] = {"abcdefghbcdefghicdefghijdefghijkefghijklfghijklmghijklmnhijklmnoijklmnopjklmnopqklmnopqrlmnopqrsmnopqrstnopqrstu"};
hash.hashBytes(hashOut, message, messageLength);
In The SHA-512 Header File:
void SHA512Hash::hashBytes(char* hashOut, char* messageIn, unsigned long long messageBytes) {
initialize(messageIn, messageBytes);
uint64_t* message = new uint64_t[wordIndex + 1];
buildMessage(message, messageIn, messageBytes);
hashProcess(message);
outputHash(hashOut);
delete[] message;
}
Where The Problem First Shows Itself:
void SHA512Hash::initialize(char* messageIn, unsigned long long messageBytes) {
for(unsigned short i = 0; i < HASH_WORDS; i += 1) {
h[i] = hInit[i];
Serial.print(h[i], HEX);
Serial.print(' ');
}
Serial.println();
...
}
The Serial Printout For h:
6A09E667F3BCC900 BB67AE8584CAA73B 3C6EF372FE94F82B A54FF53A5F1D36F1 510E527FADE682D1 9B05688C2B3E6C1F 1F83D9ABFB41BD6B 5BE0CD19137E2179
As you can see, h is equal to hInit except for the last byte of the first word. 6a09e667f3bcc908 does not equal 6A09E667F3BCC900. I found this rather strange and decided to temporarily fix the problem by hard-coding h = hInit as opposed to copying from an existing variable, as such:
void SHA512Hash::initialize(char* messageIn, unsigned long long messageBytes) {
h[0] = 0x6a09e667f3bcc908;
h[1] = 0xbb67ae8584caa73b;
h[2] = 0x3c6ef372fe94f82b;
h[3] = 0xa54ff53a5f1d36f1;
h[4] = 0x510e527fade682d1;
h[5] = 0x9b05688c2b3e6c1f;
h[6] = 0x1f83d9abfb41bd6b;
h[7] = 0x5be0cd19137e2179;
for(unsigned short i = 0; i < HASH_WORDS; i += 1) {
Serial.print(h[i], HEX);
Serial.print(' ');
}
Serial.println();
...
}
This worked for a time, but when I tried deleting hInit the program would return a false hash, even though it was no longer being used anywhere in the program. With the hard-coded h, and hInit included, the program seems to run as intended. As soon as hInit is commented out, the wrong hash is returned. I am still trying to work out where exactly the program is "messing up," as h will print out the correct initial values when hard-coded, so it is going awry somewhere else.
If anyone knows what is going on here, I'd love to figure out the issue.
I found two other posts which seem to share some similarities to what I am running into:
-
https://forum.arduino.cc/t/strange-problem-need-unused-variable-to-make-blink-like-sketch-run/224807
-
https://forum.arduino.cc/t/due-unused-variable-effects-operation/603974
It should be noted that I tried to update the IDE version I am running but that did not solve the issue.
Below is a copy of the entirety of the program:
The Header File:
#ifndef SHA512_H
#define SHA512_H
#include "Arduino.h" // DELETE ME!!
#include "HardwareSerial.h" // DELETE ME!!
#include <stdint.h>
class SHA512Hash {
private:
static const constexpr unsigned short HASH_BYTES = 64;
static const constexpr unsigned short WORD_CONVERSION = 8; // 8 bytes/1 word, 1 word/8 bytes.
static const constexpr unsigned short HALF_WORD_CONVERSION = WORD_CONVERSION/2;
static const constexpr unsigned short HASH_WORDS = HASH_BYTES/WORD_CONVERSION;
static const constexpr unsigned short ROUNDS = 80;
static const constexpr unsigned short BLOCK_BITS = 1024;
static const constexpr unsigned short BIT_CONVERSION = 8; // 8 bits/1 byte, 1 byte/8 bits.
static const constexpr unsigned short BLOCK_BYTES = BLOCK_BITS/BIT_CONVERSION;
static const constexpr unsigned short APPEND_BIT = 1;
static const constexpr unsigned short MESSAGE_LENGTH_BITS = 128;
static const constexpr unsigned short WORD_BITS = 64;
static const constexpr unsigned short HALF_WORD_BITS = WORD_BITS/2;
static const constexpr unsigned short MESSAGE_LENGTH_WORDS = MESSAGE_LENGTH_BITS/WORD_BITS;
static const constexpr unsigned short WORD_SHIFT = WORD_BITS - BIT_CONVERSION;
static const constexpr unsigned short HALF_WORD_SHIFT = 24;
static const constexpr unsigned short BLOCK_WORDS = BLOCK_BITS/WORD_BITS;
const uint64_t hInit[HASH_WORDS] = {0x6a09e667f3bcc908, 0xbb67ae8584caa73b, 0x3c6ef372fe94f82b, 0xa54ff53a5f1d36f1, 0x510e527fade682d1, 0x9b05688c2b3e6c1f, 0x1f83d9abfb41bd6b, 0x5be0cd19137e2179}; // Derived from the first 64 bits of the fractional parts of the square roots of the first 8 primes.
const uint64_t k[ROUNDS] = {
0x428a2f98d728ae22, 0x7137449123ef65cd, 0xb5c0fbcfec4d3b2f, 0xe9b5dba58189dbbc, 0x3956c25bf348b538, 0x59f111f1b605d019, 0x923f82a4af194f9b, 0xab1c5ed5da6d8118,
0xd807aa98a3030242, 0x12835b0145706fbe, 0x243185be4ee4b28c, 0x550c7dc3d5ffb4e2, 0x72be5d74f27b896f, 0x80deb1fe3b1696b1, 0x9bdc06a725c71235, 0xc19bf174cf692694,
0xe49b69c19ef14ad2, 0xefbe4786384f25e3, 0x0fc19dc68b8cd5b5, 0x240ca1cc77ac9c65, 0x2de92c6f592b0275, 0x4a7484aa6ea6e483, 0x5cb0a9dcbd41fbd4, 0x76f988da831153b5,
0x983e5152ee66dfab, 0xa831c66d2db43210, 0xb00327c898fb213f, 0xbf597fc7beef0ee4, 0xc6e00bf33da88fc2, 0xd5a79147930aa725, 0x06ca6351e003826f, 0x142929670a0e6e70,
0x27b70a8546d22ffc, 0x2e1b21385c26c926, 0x4d2c6dfc5ac42aed, 0x53380d139d95b3df, 0x650a73548baf63de, 0x766a0abb3c77b2a8, 0x81c2c92e47edaee6, 0x92722c851482353b,
0xa2bfe8a14cf10364, 0xa81a664bbc423001, 0xc24b8b70d0f89791, 0xc76c51a30654be30, 0xd192e819d6ef5218, 0xd69906245565a910, 0xf40e35855771202a, 0x106aa07032bbd1b8,
0x19a4c116b8d2d0c8, 0x1e376c085141ab53, 0x2748774cdf8eeb99, 0x34b0bcb5e19b48a8, 0x391c0cb3c5c95a63, 0x4ed8aa4ae3418acb, 0x5b9cca4f7763e373, 0x682e6ff3d6b2b8a3,
0x748f82ee5defb2fc, 0x78a5636f43172f60, 0x84c87814a1f0ab72, 0x8cc702081a6439ec, 0x90befffa23631e28, 0xa4506cebde82bde9, 0xbef9a3f7b2c67915, 0xc67178f2e372532b,
0xca273eceea26619c, 0xd186b8c721c0c207, 0xeada7dd6cde0eb1e, 0xf57d4f7fee6ed178, 0x06f067aa72176fba, 0x0a637dc5a2c898a6, 0x113f9804bef90dae, 0x1b710b35131c471b,
0x28db77f523047d84, 0x32caab7b40c72493, 0x3c9ebe0a15c9bebc, 0x431d67c49c100d4c, 0x4cc5d4becb3e42b6, 0x597f299cfc657e2a, 0x5fcb6fab3ad6faec, 0x6c44198c4a475817
}; // Derived from the first 64 bits of the fractional parts of the cube roots of the first 80 primes.
uint64_t h[HASH_WORDS];
uint64_t a[HASH_WORDS]; // Working variables.
unsigned short messageRemainderBits;
unsigned short zeroBits;
unsigned short zeroWords;
unsigned long long messageWords;
unsigned short wordRemainder;
unsigned long long wordIndex;
unsigned long long blockCount;
uint32_t buildBuffer;
uint64_t rotRBuffer;
uint64_t w[ROUNDS]; // Message schedule array.
uint64_t s0;
uint64_t s1;
uint64_t t0;
uint64_t t1;
void initialize(char*, unsigned long long);
void buildMessage(uint64_t*, char*, unsigned long long);
void rotR(uint64_t, unsigned short);
void hashProcess(uint64_t*);
void outputHash(char[HASH_BYTES]);
public:
SHA512Hash();
~SHA512Hash();
void hashBytes(char[HASH_BYTES], char*, unsigned long long);
};
SHA512Hash::SHA512Hash() {
}
SHA512Hash::~SHA512Hash() {
}
void SHA512Hash::initialize(char* messageIn, unsigned long long messageBytes) {
/* for(unsigned short i = 0; i < HASH_WORDS; i += 1) {
h[i] = hInit[i];
Serial.print(h[i], HEX);
Serial.print(' ');
}
Serial.println();*/
// 0x6a09e667f3bcc908, 0xbb67ae8584caa73b, 0x3c6ef372fe94f82b, 0xa54ff53a5f1d36f1,
// 0x510e527fade682d1, 0x9b05688c2b3e6c1f, 0x1f83d9abfb41bd6b, 0x5be0cd19137e2179
h[0] = 0x6a09e667f3bcc908; // Why does this work, when the previous method failed? Maybe try the previous method without error messages?
h[1] = 0xbb67ae8584caa73b;
h[2] = 0x3c6ef372fe94f82b;
h[3] = 0xa54ff53a5f1d36f1;
h[4] = 0x510e527fade682d1;
h[5] = 0x9b05688c2b3e6c1f;
h[6] = 0x1f83d9abfb41bd6b;
h[7] = 0x5be0cd19137e2179;
for(unsigned short i = 0; i < 8; i += 1) {
Serial.print(h[i], HEX);
Serial.print(' ');
}
Serial.println();
messageRemainderBits = (messageBytes % BLOCK_BYTES)*BIT_CONVERSION;
zeroBits = BLOCK_BITS - ((((messageRemainderBits + APPEND_BIT + MESSAGE_LENGTH_BITS) - 1) % BLOCK_BITS) + 1); // 7 (messageBytes = 111) to 1023 (messageBytes = 112)
zeroWords = zeroBits/WORD_BITS;
messageWords = messageBytes/WORD_CONVERSION;
wordRemainder = messageBytes % WORD_CONVERSION;
wordIndex = messageWords + zeroWords + MESSAGE_LENGTH_WORDS;
blockCount = (wordIndex + 1)/BLOCK_WORDS;
}
void SHA512Hash::buildMessage(uint64_t* message, char* messageIn, unsigned long long messageBytes) {
for(unsigned long long i = 0; i < messageWords; i += 1) {
message[i] = 0x0000000000000000;
for(unsigned short j = 0; j < HALF_WORD_CONVERSION; j += 1) {
message[i] |= (messageIn[(WORD_CONVERSION*i) + j] << (HALF_WORD_SHIFT - (BIT_CONVERSION*j)));
}
message[i] = message[i] << HALF_WORD_BITS;
buildBuffer = 0x00000000;
for(unsigned short j = HALF_WORD_CONVERSION; j < WORD_CONVERSION; j += 1) {
buildBuffer |= (messageIn[(WORD_CONVERSION*i) + j] << (HALF_WORD_SHIFT - (BIT_CONVERSION*(j - HALF_WORD_CONVERSION))));
}
message[i] |= buildBuffer;
}
if(wordRemainder == 0) {
message[messageWords] = 0x8000000000000000;
} else {
message[messageWords] = 0x0000000000000000;
if(wordRemainder < HALF_WORD_CONVERSION) {
for(unsigned short i = 0; i < wordRemainder; i += 1) {
message[messageWords] |= (messageIn[(WORD_CONVERSION*messageWords) + i] << (HALF_WORD_SHIFT - (BIT_CONVERSION*i)));
}
message[messageWords] |= (0x80 << (HALF_WORD_SHIFT - (BIT_CONVERSION*wordRemainder)));
message[messageWords] = message[messageWords] << HALF_WORD_BITS;
} else if(wordRemainder == HALF_WORD_CONVERSION) {
for(unsigned short i = 0; i < wordRemainder; i += 1) {
message[messageWords] |= (messageIn[(WORD_CONVERSION*messageWords) + i] << (HALF_WORD_SHIFT - (BIT_CONVERSION*i)));
}
message[messageWords] = message[messageWords] << HALF_WORD_BITS;
buildBuffer = 0x80000000;
message[messageWords] |= buildBuffer;
} else {
for(unsigned short i = 0; i < HALF_WORD_CONVERSION; i += 1) {
message[messageWords] |= (messageIn[(WORD_CONVERSION*messageWords) + i] << (HALF_WORD_SHIFT - (BIT_CONVERSION*i)));
}
message[messageWords] = message[messageWords] << HALF_WORD_BITS;
buildBuffer = 0x00000000;
for(unsigned short i = HALF_WORD_CONVERSION; i < wordRemainder; i += 1) {
buildBuffer |= (messageIn[(WORD_CONVERSION*messageWords) + i] << (HALF_WORD_SHIFT - (BIT_CONVERSION*(i - HALF_WORD_CONVERSION))));
}
buildBuffer |= (0x80 << (HALF_WORD_SHIFT - (BIT_CONVERSION*(wordRemainder % HALF_WORD_CONVERSION))));
message[messageWords] |= buildBuffer;
}
}
for(unsigned long long i = 0; i < zeroWords; i += 1) {
message[(messageWords + 1) + i] = 0x0000000000000000;
}
message[wordIndex - 1] = (uint64_t)messageBytes >> 61; // Has the effect of multiplying messageBytes by 8 (to convert from bytes to bits).
message[wordIndex] = (uint64_t)messageBytes << 3;
for(unsigned long long i = 0; i < (wordIndex + 1); i += 1) {
if(message[i] == 0) {
Serial.print('0');
} else {
Serial.print(message[i], HEX);
}
Serial.print(' ');
}
Serial.println();
}
void SHA512Hash::rotR(uint64_t n, unsigned short c) {
rotRBuffer = ((n >> c) | (n << (WORD_BITS - c)));
}
void SHA512Hash::hashProcess(uint64_t* message) {
for(unsigned long long b = 0; b < blockCount; b += 1) {
for(unsigned short i = 0; i < BLOCK_WORDS; i += 1) {
w[i] = message[(BLOCK_WORDS*b) + i];
if(w[i] == 0) {
Serial.print('0');
} else {
Serial.print(w[i], HEX);
}
Serial.print(' ');
}
Serial.println();
for(unsigned short i = BLOCK_WORDS; i < ROUNDS; i += 1) {
rotR(w[i - 15], 1);
s0 = rotRBuffer;
rotR(w[i - 15], 8);
s0 ^= rotRBuffer;
s0 ^= (w[i - 15] >> 7);
rotR(w[i - 2], 19);
s1 = rotRBuffer;
rotR(w[i - 2], 61);
s1 ^= rotRBuffer;
s1 ^= (w[i - 2] >> 6);
w[i] = w[i - 16] + s0 + w[i - 7] + s1;
}
for(unsigned short i = 0; i < HASH_WORDS; i += 1) {
a[i] = h[i];
Serial.print(a[i], HEX);
Serial.print(' ');
}
Serial.println();
for(unsigned short i = 0; i < ROUNDS; i += 1) {
rotR(a[4], 14);
s1 = rotRBuffer;
rotR(a[4], 18);
s1 ^= rotRBuffer;
rotR(a[4], 41);
s1 ^= rotRBuffer;
s0 = (a[4] & a[5]) ^ ((~a[4]) & a[6]); // Used in place of ch.
t0 = a[7] + s1 + s0 + k[i] + w[i];
rotR(a[0], 28);
s0 = rotRBuffer;
rotR(a[0], 34);
s0 ^= rotRBuffer;
rotR(a[0], 39);
s0 ^= rotRBuffer;
s1 = (a[0] & a[1]) ^ (a[0] & a[2]) ^ (a[1] & a[2]); // Used in place of maj.
t1 = s0 + s1;
a[7] = a[6];
a[6] = a[5];
a[5] = a[4];
a[4] = a[3] + t0;
a[3] = a[2];
a[2] = a[1];
a[1] = a[0];
a[0] = t0 + t1;
}
Serial.print("pre-add h: ");
for(unsigned short i = 0; i < HASH_WORDS; i += 1) {
Serial.print(h[i], HEX);
Serial.print(' ');
}
Serial.println();
Serial.print("pre-add a: ");
for(unsigned short i = 0; i < HASH_WORDS; i += 1) {
Serial.print(a[i], HEX);
Serial.print(' ');
}
Serial.println();
for(unsigned short i = 0; i < HASH_WORDS; i += 1) {
h[i] += a[i];
Serial.print(h[i], HEX);
Serial.print(' ');
}
Serial.println();
}
}
void SHA512Hash::outputHash(char* hashOut) {
for(unsigned short i = 0; i < HASH_WORDS; i += 1) {
for(unsigned short j = 0; j < WORD_CONVERSION; j += 1) {
hashOut[(WORD_CONVERSION*i) + j] = h[i] >> (WORD_SHIFT - (BIT_CONVERSION*j));
}
}
}
void SHA512Hash::hashBytes(char* hashOut, char* messageIn, unsigned long long messageBytes) {
initialize(messageIn, messageBytes);
uint64_t* message = new uint64_t[wordIndex + 1];
buildMessage(message, messageIn, messageBytes);
hashProcess(message);
outputHash(hashOut);
delete[] message;
}
#endif
The .ino File:
#include "Arduino.h"
#include "HardwareSerial.h"
#include "src/include/SHA512.h"
void setup() {
Serial.begin(9600);
while(!Serial) {
delay(250);
}
SHA512Hash hash;
char cornedBeef[64];
unsigned long long messageLength = 3;
char message[messageLength] = {"abc"};
hash.hashBytes(cornedBeef, message, messageLength);
for(unsigned short i = 0; i < 64; i += 1) {
if(cornedBeef[i] > 0x0f) {
Serial.print(cornedBeef[i], HEX);
} else {
Serial.print('0');
Serial.print(cornedBeef[i], HEX);
}
}
Serial.println('\n');
messageLength = 0;
char message1[messageLength] = {""};
hash.hashBytes(cornedBeef, message1, messageLength);
for(unsigned short i = 0; i < 64; i += 1) {
if(cornedBeef[i] > 0x0f) {
Serial.print(cornedBeef[i], HEX);
} else {
Serial.print('0');
Serial.print(cornedBeef[i], HEX);
}
}
Serial.println('\n');
messageLength = 56;
char message2[messageLength] = {"abcdbcdecdefdefgefghfghighijhijkijkljklmklmnlmnomnopnopq"};
hash.hashBytes(cornedBeef, message2, messageLength);
for(unsigned short i = 0; i < 64; i += 1) {
if(cornedBeef[i] > 0x0f) {
Serial.print(cornedBeef[i], HEX);
} else {
Serial.print('0');
Serial.print(cornedBeef[i], HEX);
}
}
Serial.println('\n');
messageLength = 111;
char message3[messageLength] = {"abcdefghbcdefghicdefghijdefghijkefghijklfghijklmghijklmnhijklmnoijklmnopjklmnopqklmnopqrlmnopqrsmnopqrstnopqrst"};
hash.hashBytes(cornedBeef, message3, messageLength);
for(unsigned short i = 0; i < 64; i += 1) {
if(cornedBeef[i] > 0x0f) {
Serial.print(cornedBeef[i], HEX);
} else {
Serial.print('0');
Serial.print(cornedBeef[i], HEX);
}
}
Serial.println('\n');
messageLength = 112;
char message4[messageLength] = {"abcdefghbcdefghicdefghijdefghijkefghijklfghijklmghijklmnhijklmnoijklmnopjklmnopqklmnopqrlmnopqrsmnopqrstnopqrstu"};
hash.hashBytes(cornedBeef, message4, messageLength);
for(unsigned short i = 0; i < 64; i += 1) {
if(cornedBeef[i] > 0x0f) {
Serial.print(cornedBeef[i], HEX);
} else {
Serial.print('0');
Serial.print(cornedBeef[i], HEX);
}
}
Serial.println('\n');
/*
messageLength = 240;
char message5[messageLength] = {"apovabapouea198asa8d91f15efgpoasohidoiea89a9da8f1a32sdf4ado8ivha1a6s8e68868668asefadhajfshacasedlkjadADAIPHLKJAzzzzlakdf97165g00abcdefghbcdefghicdefghijdefghijkefghijklfghijklmghijklmnhijklmnoijklmnopjklmnopqklmnopqrlmnopqrsmnopqrstnopqrstu"};
hash.hashBytes(cornedBeef, message5, messageLength);
for(unsigned short i = 0; i < 64; i += 1) {
if(cornedBeef[i] > 0x0f) {
Serial.print(cornedBeef[i], HEX);
} else {
Serial.print('0');
Serial.print(cornedBeef[i], HEX);
}
}
Serial.println('\n');
*/
}
void loop() {}