CRC32C - appending 0s/CRC to message - c

Question

I am trying to get a better understanding of CRC, however I am stuck a bit.
There are few sample vectors here 1 which I can calculate correctly, however I am stuck with verifying that the calculated CRC is correct.
For example, given a message of 32 bytes:
000102030405060708090a0b0c0d0e0f101112131415161718191a1b1c1d1e1f
my understanding is that you first append 32 bits of 0's to get a payload:
000102030405060708090a0b0c0d0e0f101112131415161718191a1b1c1d1e1f00000000
and calculate CRC on that message to obtain 0x73c2a486
To verify that CRC is correct you should then append CRC value to the original value, in this case:
000102030405060708090a0b0c0d0e0f101112131415161718191a1b1c1d1e1f73c2a486
And this should return 0, however I don't get that.
Would greatly appreciate if anyone could point out where I am going wrong.
Edit:
Sample code that I am using:
static uint32_t crc32c_table_small[256] =
{
0x00000000, 0xF26B8303, 0xE13B70F7, 0x1350F3F4, 0xC79A971F, 0x35F1141C, 0x26A1E7E8, 0xD4CA64EB,
0x8AD958CF, 0x78B2DBCC, 0x6BE22838, 0x9989AB3B, 0x4D43CFD0, 0xBF284CD3, 0xAC78BF27, 0x5E133C24,
0x105EC76F, 0xE235446C, 0xF165B798, 0x030E349B, 0xD7C45070, 0x25AFD373, 0x36FF2087, 0xC494A384,
0x9A879FA0, 0x68EC1CA3, 0x7BBCEF57, 0x89D76C54, 0x5D1D08BF, 0xAF768BBC, 0xBC267848, 0x4E4DFB4B,
0x20BD8EDE, 0xD2D60DDD, 0xC186FE29, 0x33ED7D2A, 0xE72719C1, 0x154C9AC2, 0x061C6936, 0xF477EA35,
0xAA64D611, 0x580F5512, 0x4B5FA6E6, 0xB93425E5, 0x6DFE410E, 0x9F95C20D, 0x8CC531F9, 0x7EAEB2FA,
0x30E349B1, 0xC288CAB2, 0xD1D83946, 0x23B3BA45, 0xF779DEAE, 0x05125DAD, 0x1642AE59, 0xE4292D5A,
0xBA3A117E, 0x4851927D, 0x5B016189, 0xA96AE28A, 0x7DA08661, 0x8FCB0562, 0x9C9BF696, 0x6EF07595,
0x417B1DBC, 0xB3109EBF, 0xA0406D4B, 0x522BEE48, 0x86E18AA3, 0x748A09A0, 0x67DAFA54, 0x95B17957,
0xCBA24573, 0x39C9C670, 0x2A993584, 0xD8F2B687, 0x0C38D26C, 0xFE53516F, 0xED03A29B, 0x1F682198,
0x5125DAD3, 0xA34E59D0, 0xB01EAA24, 0x42752927, 0x96BF4DCC, 0x64D4CECF, 0x77843D3B, 0x85EFBE38,
0xDBFC821C, 0x2997011F, 0x3AC7F2EB, 0xC8AC71E8, 0x1C661503, 0xEE0D9600, 0xFD5D65F4, 0x0F36E6F7,
0x61C69362, 0x93AD1061, 0x80FDE395, 0x72966096, 0xA65C047D, 0x5437877E, 0x4767748A, 0xB50CF789,
0xEB1FCBAD, 0x197448AE, 0x0A24BB5A, 0xF84F3859, 0x2C855CB2, 0xDEEEDFB1, 0xCDBE2C45, 0x3FD5AF46,
0x7198540D, 0x83F3D70E, 0x90A324FA, 0x62C8A7F9, 0xB602C312, 0x44694011, 0x5739B3E5, 0xA55230E6,
0xFB410CC2, 0x092A8FC1, 0x1A7A7C35, 0xE811FF36, 0x3CDB9BDD, 0xCEB018DE, 0xDDE0EB2A, 0x2F8B6829,
0x82F63B78, 0x709DB87B, 0x63CD4B8F, 0x91A6C88C, 0x456CAC67, 0xB7072F64, 0xA457DC90, 0x563C5F93,
0x082F63B7, 0xFA44E0B4, 0xE9141340, 0x1B7F9043, 0xCFB5F4A8, 0x3DDE77AB, 0x2E8E845F, 0xDCE5075C,
0x92A8FC17, 0x60C37F14, 0x73938CE0, 0x81F80FE3, 0x55326B08, 0xA759E80B, 0xB4091BFF, 0x466298FC,
0x1871A4D8, 0xEA1A27DB, 0xF94AD42F, 0x0B21572C, 0xDFEB33C7, 0x2D80B0C4, 0x3ED04330, 0xCCBBC033,
0xA24BB5A6, 0x502036A5, 0x4370C551, 0xB11B4652, 0x65D122B9, 0x97BAA1BA, 0x84EA524E, 0x7681D14D,
0x2892ED69, 0xDAF96E6A, 0xC9A99D9E, 0x3BC21E9D, 0xEF087A76, 0x1D63F975, 0x0E330A81, 0xFC588982,
0xB21572C9, 0x407EF1CA, 0x532E023E, 0xA145813D, 0x758FE5D6, 0x87E466D5, 0x94B49521, 0x66DF1622,
0x38CC2A06, 0xCAA7A905, 0xD9F75AF1, 0x2B9CD9F2, 0xFF56BD19, 0x0D3D3E1A, 0x1E6DCDEE, 0xEC064EED,
0xC38D26C4, 0x31E6A5C7, 0x22B65633, 0xD0DDD530, 0x0417B1DB, 0xF67C32D8, 0xE52CC12C, 0x1747422F,
0x49547E0B, 0xBB3FFD08, 0xA86F0EFC, 0x5A048DFF, 0x8ECEE914, 0x7CA56A17, 0x6FF599E3, 0x9D9E1AE0,
0xD3D3E1AB, 0x21B862A8, 0x32E8915C, 0xC083125F, 0x144976B4, 0xE622F5B7, 0xF5720643, 0x07198540,
0x590AB964, 0xAB613A67, 0xB831C993, 0x4A5A4A90, 0x9E902E7B, 0x6CFBAD78, 0x7FAB5E8C, 0x8DC0DD8F,
0xE330A81A, 0x115B2B19, 0x020BD8ED, 0xF0605BEE, 0x24AA3F05, 0xD6C1BC06, 0xC5914FF2, 0x37FACCF1,
0x69E9F0D5, 0x9B8273D6, 0x88D28022, 0x7AB90321, 0xAE7367CA, 0x5C18E4C9, 0x4F48173D, 0xBD23943E,
0xF36E6F75, 0x0105EC76, 0x12551F82, 0xE03E9C81, 0x34F4F86A, 0xC69F7B69, 0xD5CF889D, 0x27A40B9E,
0x79B737BA, 0x8BDCB4B9, 0x988C474D, 0x6AE7C44E, 0xBE2DA0A5, 0x4C4623A6, 0x5F16D052, 0xAD7D5351
};
static inline uint32_t crc32c_software_simple(uint32_t crc, const uint8_t * data, size_t num_bytes)
{
while (num_bytes--)
{
crc = (crc >> 8) ^ crc32c_table_small[(crc & 0xFF) ^ *data++];
}
return crc;
}
uint32_t num_bytes = 32;
uint32_t num_bytes_padded = num_bytes + sizeof(uint32_t);
uint8_t * test_data = (uint8_t*) malloc(num_bytes_padded);
for(uint32_t i = num_bytes; i < num_bytes_padded; i++) test_data[i] = 0;
for(uint32_t i = 0; i < num_bytes; i++)
{
test_data[i] = i;
}
binary(num_bytes_padded, test_data);
hex(num_bytes_padded, test_data);
uint32_t crc = 0xFFFFFFFF;
crc = ~crc32c_software_simple(crc, test_data, num_bytes_padded);
for(uint32_t i = 0; i < sizeof(uint32_t); i++) test_data[num_bytes + i] = ((uint8_t*)&crc)[i];
crc = 0xFFFFFFFF;
crc = ~crc32c_software_simple(crc, test_data, num_bytes_padded);

Answer 1

What you have there is a complete calculation of a CRC that does not require appending zeros to the end. The way it is used is to simply compute the CRC on the message (with nothing appended), and then append the computed CRC. On the other end, compute the CRC on the just the message (not including the CRC) and compare the computed CRC with the one that followed the message in the transmission. As opposed to looking for a zero. Super simple, and the way you would do it for any hash value.
It is true however that if you compute the CRC on the message and the appended CRC, assuming that the CRC is encoded in the proper bit and byte order, then the mathematics assures that the result will be the same constant, the "residual" for that CRC, for all correct message/CRC combinations. The residual in this case is not all zeros, because the CRC is exclusive-ored with a non-zero constant. You could do it by checking for the residual if you like, but it seems like a waste of time to compute the CRC on four more bytes, as well as adding some obscurity to the code, when you could just compare.

Answer 2

The example code does a post complement of the CRC. This will cause the verify CRC to be a constant non-zero value, in this case verify CRC == 0x48674bc7 if there are no errors (regardless of message size). The calling code needed a fix on the first call to crc32c_software_simple, to use num_bytes instead of num_bytes_padded, as noted in the comment below.
If there was no post complement of the CRC, then the verify would produce a zero CRC.
The code also does a pre-complement of the CRC, but this will not affect the verify.
int main()
{
uint32_t num_bytes = 32;
uint32_t num_bytes_padded = num_bytes + sizeof(uint32_t);
uint8_t * test_data = (uint8_t*) malloc(num_bytes_padded);
for(uint32_t i = num_bytes; i < num_bytes_padded; i++) test_data[i] = 0;
for(uint32_t i = 0; i < num_bytes; i++)
{
test_data[i] = i;
}
uint32_t crc = 0xFFFFFFFF;
crc = ~crc32c_software_simple(crc, test_data, num_bytes); // num_bytes fix
for(uint32_t i = 0; i < sizeof(uint32_t); i++) test_data[num_bytes + i] = ((uint8_t*)&crc)[i];
crc = 0xFFFFFFFF;
crc = ~crc32c_software_simple(crc, test_data, num_bytes_padded);
// if no errors, crc == 0x48674bc7
return 0;
}