/* * QR Code generator library (C) * * Copyright (c) Project Nayuki * https://www.nayuki.io/page/qr-code-generator-library * * (MIT License) * 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. */ #include #include #include #include #include "qrcodegen.h" /*---- Forward declarations for private functions ----*/ static void appendBitsToBuffer(uint16_t val, int numBits, uint8_t buffer[], int *bitLen); static int getNumDataCodewords(int version, enum qrcodegen_Ecc ecl); static bool getModule(const uint8_t qrcode[], int size, int x, int y); static void setModule(uint8_t qrcode[], int size, int x, int y, bool isBlack); static void setModuleBounded(uint8_t qrcode[], int size, int x, int y, bool isBlack); static void initializeFunctionalModules(int version, uint8_t qrcode[]); static void drawWhiteFunctionModules(uint8_t qrcode[], int version); static void drawFormatBits(enum qrcodegen_Ecc ecl, enum qrcodegen_Mask mask, uint8_t qrcode[], int size); static int getAlignmentPatternPositions(int version, uint8_t result[7]); static void appendErrorCorrection(uint8_t data[], int version, enum qrcodegen_Ecc ecl, uint8_t result[]); static int getNumRawDataModules(int version); static void drawCodewords(const uint8_t data[], int dataLen, uint8_t qrcode[], int version); static void applyMask(const uint8_t functionModules[], uint8_t qrcode[], int size, int mask); static void calcReedSolomonGenerator(int degree, uint8_t result[]); static void calcReedSolomonRemainder(const uint8_t data[], int dataLen, const uint8_t generator[], int degree, uint8_t result[]); static uint8_t finiteFieldMultiply(uint8_t x, uint8_t y); /*---- Private tables of constants ----*/ static const int16_t NUM_ERROR_CORRECTION_CODEWORDS[4][41] = { // Version: (note that index 0 is for padding, and is set to an illegal value) //0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40 Error correction level {-1, 7, 10, 15, 20, 26, 36, 40, 48, 60, 72, 80, 96, 104, 120, 132, 144, 168, 180, 196, 224, 224, 252, 270, 300, 312, 336, 360, 390, 420, 450, 480, 510, 540, 570, 570, 600, 630, 660, 720, 750}, // Low {-1, 10, 16, 26, 36, 48, 64, 72, 88, 110, 130, 150, 176, 198, 216, 240, 280, 308, 338, 364, 416, 442, 476, 504, 560, 588, 644, 700, 728, 784, 812, 868, 924, 980, 1036, 1064, 1120, 1204, 1260, 1316, 1372}, // Medium {-1, 13, 22, 36, 52, 72, 96, 108, 132, 160, 192, 224, 260, 288, 320, 360, 408, 448, 504, 546, 600, 644, 690, 750, 810, 870, 952, 1020, 1050, 1140, 1200, 1290, 1350, 1440, 1530, 1590, 1680, 1770, 1860, 1950, 2040}, // Quartile {-1, 17, 28, 44, 64, 88, 112, 130, 156, 192, 224, 264, 308, 352, 384, 432, 480, 532, 588, 650, 700, 750, 816, 900, 960, 1050, 1110, 1200, 1260, 1350, 1440, 1530, 1620, 1710, 1800, 1890, 1980, 2100, 2220, 2310, 2430}, // High }; const int8_t NUM_ERROR_CORRECTION_BLOCKS[4][41] = { // Version: (note that index 0 is for padding, and is set to an illegal value) //0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40 Error correction level {-1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 4, 4, 4, 4, 4, 6, 6, 6, 6, 7, 8, 8, 9, 9, 10, 12, 12, 12, 13, 14, 15, 16, 17, 18, 19, 19, 20, 21, 22, 24, 25}, // Low {-1, 1, 1, 1, 2, 2, 4, 4, 4, 5, 5, 5, 8, 9, 9, 10, 10, 11, 13, 14, 16, 17, 17, 18, 20, 21, 23, 25, 26, 28, 29, 31, 33, 35, 37, 38, 40, 43, 45, 47, 49}, // Medium {-1, 1, 1, 2, 2, 4, 4, 6, 6, 8, 8, 8, 10, 12, 16, 12, 17, 16, 18, 21, 20, 23, 23, 25, 27, 29, 34, 34, 35, 38, 40, 43, 45, 48, 51, 53, 56, 59, 62, 65, 68}, // Quartile {-1, 1, 1, 2, 4, 4, 4, 5, 6, 8, 8, 11, 11, 16, 16, 18, 16, 19, 21, 25, 25, 25, 34, 30, 32, 35, 37, 40, 42, 45, 48, 51, 54, 57, 60, 63, 66, 70, 74, 77, 81}, // High }; /*---- Function implementations ----*/ // Public function - see documentation comment in header file. bool qrcodegen_isAlphanumeric(const char *text) { for (; *text != '\0'; text++) { char c = *text; if (('0' <= c && c <= '9') || ('A' <= c && c <= 'Z')) continue; else switch (c) { case ' ': case '$': case '%': case '*': case '+': case '-': case '.': case '/': case ':': continue; default: return false; } return false; } return true; } // Public function - see documentation comment in header file. bool qrcodegen_isNumeric(const char *text) { for (; *text != '\0'; text++) { char c = *text; if (c < '0' || c > '9') return false; } return true; } // Public function - see documentation comment in header file. int qrcodegen_encodeBinary(uint8_t dataAndTemp[], size_t dataLen, uint8_t qrcode[], enum qrcodegen_Ecc ecl, int minVersion, int maxVersion, enum qrcodegen_Mask mask) { assert(1 <= minVersion && minVersion <= maxVersion && maxVersion <= 40); assert(0 <= (int)ecl && (int)ecl <= 3 && -1 <= (int)mask && (int)mask <= 7); int version; int dataUsedBits = -1; int dataCapacityBits = -1; for (version = minVersion; ; version++) { if ((version <= 9 && dataLen < (1U << 8)) || dataLen < (1U << 16)) { dataCapacityBits = getNumDataCodewords(version, ecl) * 8; // Number of data bits available dataUsedBits = 4 + (version <= 9 ? 8 : 16); if (dataLen > (unsigned int)INT_MAX / 8 || (unsigned int)(INT_MAX - dataUsedBits) < dataLen * 8) continue; dataUsedBits += dataLen * 8; if (dataUsedBits <= dataCapacityBits) break; // This version number is found to be suitable } if (version >= maxVersion) // All versions in the range could not fit the given data return 0; } assert(dataUsedBits >= 0 && dataCapacityBits >= 0); memset(qrcode, 0, qrcodegen_BUFFER_LEN_FOR_VERSION(version) * sizeof(qrcode[0])); int bitLen = 0; appendBitsToBuffer(4, 4, qrcode, &bitLen); appendBitsToBuffer((uint16_t)dataLen, (version <= 9 ? 8 : 16), qrcode, &bitLen); for (size_t i = 0; i < dataLen; i++) appendBitsToBuffer(dataAndTemp[i], 8, qrcode, &bitLen); int terminatorBits = dataCapacityBits - bitLen; if (terminatorBits > 4) terminatorBits = 4; appendBitsToBuffer(0, terminatorBits, qrcode, &bitLen); appendBitsToBuffer(0, (8 - bitLen % 8) % 8, qrcode, &bitLen); for (uint8_t padByte = 0xEC; bitLen < dataCapacityBits; padByte ^= 0xEC ^ 0x11) appendBitsToBuffer(padByte, 8, qrcode, &bitLen); assert(bitLen % 8 == 0); appendErrorCorrection(qrcode, version, ecl, dataAndTemp); initializeFunctionalModules(version, qrcode); drawCodewords(dataAndTemp, getNumRawDataModules(version) / 8, qrcode, version); drawWhiteFunctionModules(qrcode, version); initializeFunctionalModules(version, dataAndTemp); mask = qrcodegen_Mask_0; applyMask(dataAndTemp, qrcode, qrcodegen_getSize(version), (int)mask); drawFormatBits(ecl, (int)mask, qrcode, qrcodegen_getSize(version)); return version; } // Appends the given sequence of bits to the given byte-based bit buffer, increasing the bit length. static void appendBitsToBuffer(uint16_t val, int numBits, uint8_t buffer[], int *bitLen) { assert(0 <= numBits && numBits <= 16 && (long)val >> numBits == 0); for (int i = numBits - 1; i >= 0; i--, (*bitLen)++) buffer[*bitLen >> 3] |= ((val >> i) & 1) << (7 - (*bitLen & 7)); } // Returns the number of 8-bit codewords that can be used for storing data (not ECC), // for the given version number and error correction level. The result is in the range [9, 2956]. static int getNumDataCodewords(int version, enum qrcodegen_Ecc ecl) { assert(0 <= (int)ecl && (int)ecl < 4 && 1 <= version && version <= 40); return getNumRawDataModules(version) / 8 - NUM_ERROR_CORRECTION_CODEWORDS[(int)ecl][version]; } // Public function - see documentation comment in header file. int qrcodegen_getSize(int version) { assert(1 <= version && version <= 40); return version * 4 + 17; } // Public function - see documentation comment in header file. bool qrcodegen_getModule(const uint8_t qrcode[], int version, int x, int y) { int size = qrcodegen_getSize(version); return (0 <= x && x < size && 0 <= y && y < size) && getModule(qrcode, size, x, y); } // Gets the module at the given coordinates, which must be in bounds. static bool getModule(const uint8_t qrcode[], int size, int x, int y) { assert(21 <= size && size <= 177 && 0 <= x && x < size && 0 <= y && y < size); int index = y * size + x; int bitIndex = index & 7; int byteIndex = index >> 3; return ((qrcode[byteIndex] >> bitIndex) & 1) != 0; } // Sets the module at the given coordinates, which must be in bounds. static void setModule(uint8_t qrcode[], int size, int x, int y, bool isBlack) { assert(21 <= size && size <= 177 && 0 <= x && x < size && 0 <= y && y < size); int index = y * size + x; int bitIndex = index & 7; int byteIndex = index >> 3; if (isBlack) qrcode[byteIndex] |= 1 << bitIndex; else qrcode[byteIndex] &= (1 << bitIndex) ^ 0xFF; } // Sets the module at the given coordinates, doing nothing if out of bounds. static void setModuleBounded(uint8_t qrcode[], int size, int x, int y, bool isBlack) { if (0 <= x && x < size && 0 <= y && y < size) setModule(qrcode, size, x, y, isBlack); } // Fills the given QR Code grid with white modules for the given version's size, // then marks every function module in the QR Code as black. static void initializeFunctionalModules(int version, uint8_t qrcode[]) { // Initialize QR Code int size = qrcodegen_getSize(version); memset(qrcode, 0, (size * size + 7) / 8 * sizeof(qrcode[0])); // Fill horizontal and vertical timing patterns for (int i = 0; i < size; i++) { setModule(qrcode, size, 6, i, true); setModule(qrcode, size, i, 6, true); } // Fill 3 finder patterns (all corners except bottom right) for (int i = 0; i < 8; i++) { for (int j = 0; j < 8; j++) { setModule(qrcode, size, j, i, true); setModule(qrcode, size, size - 1 - j, i, true); setModule(qrcode, size, j, size - 1 - i, true); } } // Fill numerous alignment patterns uint8_t alignPatPos[7] = {0}; int numAlign = getAlignmentPatternPositions(version, alignPatPos); for (int i = 0; i < numAlign; i++) { for (int j = 0; j < numAlign; j++) { if ((i == 0 && j == 0) || (i == 0 && j == numAlign - 1) || (i == numAlign - 1 && j == 0)) continue; // Skip the three finder corners else { for (int k = -2; k <= 2; k++) { for (int l = -2; l <= 2; l++) setModule(qrcode, size, alignPatPos[i] + l, alignPatPos[j] + k, true); } } } } // Fill format bits for (int i = 0; i < 8; i++) { setModule(qrcode, size, i, 8, true); setModule(qrcode, size, 8, i, true); setModule(qrcode, size, size - 1 - i, 8, true); setModule(qrcode, size, 8, size - 1 - i, true); } setModule(qrcode, size, 8, 8, true); // Fill version if (version >= 7) { for (int i = 0; i < 6; i++) { for (int j = 0; j < 3; j++) { int k = size - 11 + j; setModule(qrcode, size, k, i, true); setModule(qrcode, size, i, k, true); } } } } // Draws white function modules and possibly some black modules onto the given QR Code, without changing // non-function modules. This does not draw the format bits. This requires all function modules to be previously // marked black (namely by initializeFunctionalModules()), because this may skip redrawing black function modules. static void drawWhiteFunctionModules(uint8_t qrcode[], int version) { // Draw horizontal and vertical timing patterns int size = qrcodegen_getSize(version); for (int i = 7; i < size - 7; i += 2) { setModule(qrcode, size, 6, i, false); setModule(qrcode, size, i, 6, false); } // Draw 3 finder patterns for (int i = -4; i <= 4; i++) { for (int j = -4; j <= 4; j++) { int dist = abs(i); if (abs(j) > dist) dist = abs(j); if (dist == 2 || dist == 4) { setModuleBounded(qrcode, size, 3 + j, 3 + i, false); setModuleBounded(qrcode, size, size - 4 + j, 3 + i, false); setModuleBounded(qrcode, size, 3 + j, size - 4 + i, false); } } } // Draw numerous alignment patterns uint8_t alignPatPos[7] = {0}; int numAlign = getAlignmentPatternPositions(version, alignPatPos); for (int i = 0; i < numAlign; i++) { for (int j = 0; j < numAlign; j++) { if ((i == 0 && j == 0) || (i == 0 && j == numAlign - 1) || (i == numAlign - 1 && j == 0)) continue; // Skip the three finder corners else { for (int k = -1; k <= 1; k++) { for (int l = -1; l <= 1; l++) setModule(qrcode, size, alignPatPos[i] + l, alignPatPos[j] + k, k == 0 && l == 0); } } } } // Draw version block if (version >= 7) { // Calculate error correction code and pack bits int rem = version; // version is uint6, in the range [7, 40] for (int i = 0; i < 12; i++) rem = (rem << 1) ^ ((rem >> 11) * 0x1F25); long data = (long)version << 12 | rem; // uint18 assert(data >> 18 == 0); // Draw two copies for (int i = 0; i < 6; i++) { for (int j = 0; j < 3; j++) { int k = size - 11 + j; setModule(qrcode, size, k, i, (data & 1) != 0); setModule(qrcode, size, i, k, (data & 1) != 0); data >>= 1; } } } } // Based on the given ECC level and mask, this calculates the format bits // and draws their black and white modules onto the given QR Code. static void drawFormatBits(enum qrcodegen_Ecc ecl, enum qrcodegen_Mask mask, uint8_t qrcode[], int size) { // Calculate error correction code and pack bits assert(0 <= (int)mask && (int)mask <= 7); int data; switch (ecl) { case qrcodegen_Ecc_LOW : data = 1; break; case qrcodegen_Ecc_MEDIUM : data = 0; break; case qrcodegen_Ecc_QUARTILE: data = 3; break; case qrcodegen_Ecc_HIGH : data = 2; break; default: assert(false); } data = data << 3 | (int)mask; // ecl-derived value is uint2, mask is uint3 int rem = data; for (int i = 0; i < 10; i++) rem = (rem << 1) ^ ((rem >> 9) * 0x537); data = data << 10 | rem; data ^= 0x5412; // uint15 assert(data >> 15 == 0); // Draw first copy for (int i = 0; i <= 5; i++) setModule(qrcode, size, 8, i, ((data >> i) & 1) != 0); setModule(qrcode, size, 8, 7, ((data >> 6) & 1) != 0); setModule(qrcode, size, 8, 8, ((data >> 7) & 1) != 0); setModule(qrcode, size, 7, 8, ((data >> 8) & 1) != 0); for (int i = 9; i < 15; i++) setModule(qrcode, size, 14 - i, 8, ((data >> i) & 1) != 0); // Draw second copy for (int i = 0; i <= 7; i++) setModule(qrcode, size, size - 1 - i, 8, ((data >> i) & 1) != 0); for (int i = 8; i < 15; i++) setModule(qrcode, size, 8, size - 15 + i, ((data >> i) & 1) != 0); setModule(qrcode, size, 8, size - 8, true); } // Calculates the positions of alignment patterns in ascending order for the given version number, // storing them to the given array and returning an array length in the range [0, 7]. static int getAlignmentPatternPositions(int version, uint8_t result[7]) { if (version == 1) return 0; int size = qrcodegen_getSize(version); int numAlign = version / 7 + 2; int step; if (version != 32) step = (version * 4 + numAlign * 2 + 1) / (2 * numAlign - 2) * 2; // ceil((size - 13) / (2*numAlign - 2)) * 2 else // C-C-C-Combo breaker! step = 26; for (int i = numAlign - 1, pos = size - 7; i >= 1; i--, pos -= step) result[i] = pos; result[0] = 6; return numAlign; } // Appends error correction bytes to each block of the given data array, then interleaves bytes // from the blocks and stores them in the result array. data[0 : rawCodewords - totalEcc] contains // the input data. data[rawCodewords - totalEcc : rawCodewords] is used as a temporary work area // and will be clobbered by this function. The final answer is stored in result[0 : rawCodewords]. static void appendErrorCorrection(uint8_t data[], int version, enum qrcodegen_Ecc ecl, uint8_t result[]) { // Calculate parameter numbers assert(0 <= (int)ecl && (int)ecl < 4 && 1 <= version && version <= 40); int numBlocks = NUM_ERROR_CORRECTION_BLOCKS[(int)ecl][version]; int totalEcc = NUM_ERROR_CORRECTION_CODEWORDS[(int)ecl][version]; assert(totalEcc % numBlocks == 0); int blockEccLen = totalEcc / numBlocks; int rawCodewords = getNumRawDataModules(version) / 8; int dataLen = rawCodewords - totalEcc; int numShortBlocks = numBlocks - rawCodewords % numBlocks; int shortBlockDataLen = rawCodewords / numBlocks - blockEccLen; // Split data into blocks and append ECC after all data uint8_t generator[30]; calcReedSolomonGenerator(blockEccLen, generator); for (int i = 0, j = dataLen, k = 0; i < numBlocks; i++) { int blockLen = shortBlockDataLen; if (i >= numShortBlocks) blockLen++; calcReedSolomonRemainder(&data[k], blockLen, generator, blockEccLen, &data[j]); j += blockEccLen; k += blockLen; } // Interleave (not concatenate) the bytes from every block into a single sequence for (int i = 0, k = 0; i < numBlocks; i++) { for (int j = 0, l = i; j < shortBlockDataLen; j++, k++, l += numBlocks) result[l] = data[k]; if (i >= numShortBlocks) k++; } for (int i = numShortBlocks, l = numBlocks * shortBlockDataLen, k = (numShortBlocks + 1) * shortBlockDataLen; i < numBlocks; i++, k += shortBlockDataLen + 1, l++) result[l] = data[k]; for (int i = 0, k = dataLen; i < numBlocks; i++) { for (int j = 0, l = dataLen + i; j < blockEccLen; j++, k++, l += numBlocks) result[l] = data[k]; } } // Returns the number of data bits that can be stored in a QR Code of the given version number, after // all function modules are excluded. This includes remainder bits, so it may not be a multiple of 8. static int getNumRawDataModules(int version) { assert(1 <= version && version <= 40); int result = (16 * version + 128) * version + 64; if (version >= 2) { int numAlign = version / 7 + 2; result -= (25 * numAlign - 10) * numAlign - 55; if (version >= 7) result -= 18 * 2; // Subtract version information } return result; } // Draws the raw codewords (including data and ECC) onto the given QR Code. This requires the initial state of // the QR Code to be black at function modules and white at codeword modules (including unused remainder bits). static void drawCodewords(const uint8_t data[], int dataLen, uint8_t qrcode[], int version) { int size = qrcodegen_getSize(version); int i = 0; // Bit index into the data // Do the funny zigzag scan for (int right = size - 1; right >= 1; right -= 2) { // Index of right column in each column pair if (right == 6) right = 5; for (int vert = 0; vert < size; vert++) { // Vertical counter for (int j = 0; j < 2; j++) { int x = right - j; // Actual x coordinate bool upwards = ((right & 2) == 0) ^ (x < 6); int y = upwards ? size - 1 - vert : vert; // Actual y coordinate if (!getModule(qrcode, size, x, y) && i < dataLen * 8) { bool black = ((data[i >> 3] >> (7 - (i & 7))) & 1) != 0; setModule(qrcode, size, x, y, black); i++; } // If there are any remainder bits (0 to 7), they are already // set to 0/false/white when the grid of modules was initialized } } } assert(i == dataLen * 8); } // XORs the data modules in this QR Code with the given mask pattern. Due to XOR's mathematical // properties, calling applyMask(m) twice with the same value is equivalent to no change at all. // This means it is possible to apply a mask, undo it, and try another mask. Note that a final // well-formed QR Code symbol needs exactly one mask applied (not zero, not two, etc.). static void applyMask(const uint8_t functionModules[], uint8_t qrcode[], int size, int mask) { assert(0 <= mask && mask <= 7); for (int y = 0; y < size; y++) { for (int x = 0; x < size; x++) { if (getModule(functionModules, size, x, y)) continue; bool invert; switch (mask) { case 0: invert = (x + y) % 2 == 0; break; case 1: invert = y % 2 == 0; break; case 2: invert = x % 3 == 0; break; case 3: invert = (x + y) % 3 == 0; break; case 4: invert = (x / 3 + y / 2) % 2 == 0; break; case 5: invert = x * y % 2 + x * y % 3 == 0; break; case 6: invert = (x * y % 2 + x * y % 3) % 2 == 0; break; case 7: invert = ((x + y) % 2 + x * y % 3) % 2 == 0; break; default: assert(false); } bool val = getModule(qrcode, size, x, y); setModule(qrcode, size, x, y, val ^ invert); } } } // Calculates the Reed-Solomon generator polynomial of the given degree, storing in result[0 : degree]. static void calcReedSolomonGenerator(int degree, uint8_t result[]) { // Start with the monomial x^0 assert(1 <= degree && degree <= 30); memset(result, 0, degree * sizeof(result[0])); result[degree - 1] = 1; // Compute the product polynomial (x - r^0) * (x - r^1) * (x - r^2) * ... * (x - r^{degree-1}), // drop the highest term, and store the rest of the coefficients in order of descending powers. // Note that r = 0x02, which is a generator element of this field GF(2^8/0x11D). int root = 1; for (int i = 0; i < degree; i++) { // Multiply the current product by (x - r^i) for (int j = 0; j < degree; j++) { result[j] = finiteFieldMultiply(result[j], (uint8_t)root); if (j + 1 < degree) result[j] ^= result[j + 1]; } root = (root << 1) ^ ((root >> 7) * 0x11D); // Multiply by 0x02 mod GF(2^8/0x11D) } } // Calculates the remainder of the polynomial data[0 : dataLen] when divided by the generator[0 : degree], where all // polynomials are in big endian and the generator has an implicit leading 1 term, storing the result in result[0 : degree]. static void calcReedSolomonRemainder(const uint8_t data[], int dataLen, const uint8_t generator[], int degree, uint8_t result[]) { // Perform polynomial division assert(1 <= degree && degree <= 30); memset(result, 0, degree * sizeof(result[0])); for (int i = 0; i < dataLen; i++) { uint8_t factor = data[i] ^ result[0]; memmove(&result[0], &result[1], (degree - 1) * sizeof(result[0])); result[degree - 1] = 0; for (int j = 0; j < degree; j++) result[j] ^= finiteFieldMultiply(generator[j], factor); } } // Returns the product of the two given field elements modulo GF(2^8/0x11D). All argument values are valid. static uint8_t finiteFieldMultiply(uint8_t x, uint8_t y) { // Russian peasant multiplication uint8_t z = 0; for (int i = 7; i >= 0; i--) { z = (z << 1) ^ ((z >> 7) * 0x11D); z ^= ((y >> i) & 1) * x; } return z; }