Understanding crc32

Question

I try to understand the computation of crc32. It's new to me, so the question is a basic one. With the following code I have two different ways of computing the CRC32 sum. They should (in theory) be the same, but they differ. What am I doing wrong?

The Go stdlib implementation (what a surprise) seems to be correct, but I can't find the error in my implementation.

https://play.golang.org/p/QJH2K3IQEj

package main

import (
    "fmt"
    "hash/crc32"
)

func main() {
    message := []byte("hello")
    // Is this the correct polynomial table? This is the table from
    // http://gnuradio.org/redmine/projects/gnuradio/repository/revisions/1cb52da49230c64c3719b4ab944ba1cf5a9abb92/entry/gr-digital/lib/digital_crc32.cc
    tbl := [256]uint32{0x00000000, 0x04C11DB7, 0x09823B6E, 0x0D4326D9,
        0x130476DC, 0x17C56B6B, 0x1A864DB2, 0x1E475005,
        0x2608EDB8, 0x22C9F00F, 0x2F8AD6D6, 0x2B4BCB61,
        0x350C9B64, 0x31CD86D3, 0x3C8EA00A, 0x384FBDBD,
        0x4C11DB70, 0x48D0C6C7, 0x4593E01E, 0x4152FDA9,
        0x5F15ADAC, 0x5BD4B01B, 0x569796C2, 0x52568B75,
        0x6A1936C8, 0x6ED82B7F, 0x639B0DA6, 0x675A1011,
        0x791D4014, 0x7DDC5DA3, 0x709F7B7A, 0x745E66CD,
        0x9823B6E0, 0x9CE2AB57, 0x91A18D8E, 0x95609039,
        0x8B27C03C, 0x8FE6DD8B, 0x82A5FB52, 0x8664E6E5,
        0xBE2B5B58, 0xBAEA46EF, 0xB7A96036, 0xB3687D81,
        0xAD2F2D84, 0xA9EE3033, 0xA4AD16EA, 0xA06C0B5D,
        0xD4326D90, 0xD0F37027, 0xDDB056FE, 0xD9714B49,
        0xC7361B4C, 0xC3F706FB, 0xCEB42022, 0xCA753D95,
        0xF23A8028, 0xF6FB9D9F, 0xFBB8BB46, 0xFF79A6F1,
        0xE13EF6F4, 0xE5FFEB43, 0xE8BCCD9A, 0xEC7DD02D,
        0x34867077, 0x30476DC0, 0x3D044B19, 0x39C556AE,
        0x278206AB, 0x23431B1C, 0x2E003DC5, 0x2AC12072,
        0x128E9DCF, 0x164F8078, 0x1B0CA6A1, 0x1FCDBB16,
        0x018AEB13, 0x054BF6A4, 0x0808D07D, 0x0CC9CDCA,
        0x7897AB07, 0x7C56B6B0, 0x71159069, 0x75D48DDE,
        0x6B93DDDB, 0x6F52C06C, 0x6211E6B5, 0x66D0FB02,
        0x5E9F46BF, 0x5A5E5B08, 0x571D7DD1, 0x53DC6066,
        0x4D9B3063, 0x495A2DD4, 0x44190B0D, 0x40D816BA,
        0xACA5C697, 0xA864DB20, 0xA527FDF9, 0xA1E6E04E,
        0xBFA1B04B, 0xBB60ADFC, 0xB6238B25, 0xB2E29692,
        0x8AAD2B2F, 0x8E6C3698, 0x832F1041, 0x87EE0DF6,
        0x99A95DF3, 0x9D684044, 0x902B669D, 0x94EA7B2A,
        0xE0B41DE7, 0xE4750050, 0xE9362689, 0xEDF73B3E,
        0xF3B06B3B, 0xF771768C, 0xFA325055, 0xFEF34DE2,
        0xC6BCF05F, 0xC27DEDE8, 0xCF3ECB31, 0xCBFFD686,
        0xD5B88683, 0xD1799B34, 0xDC3ABDED, 0xD8FBA05A,
        0x690CE0EE, 0x6DCDFD59, 0x608EDB80, 0x644FC637,
        0x7A089632, 0x7EC98B85, 0x738AAD5C, 0x774BB0EB,
        0x4F040D56, 0x4BC510E1, 0x46863638, 0x42472B8F,
        0x5C007B8A, 0x58C1663D, 0x558240E4, 0x51435D53,
        0x251D3B9E, 0x21DC2629, 0x2C9F00F0, 0x285E1D47,
        0x36194D42, 0x32D850F5, 0x3F9B762C, 0x3B5A6B9B,
        0x0315D626, 0x07D4CB91, 0x0A97ED48, 0x0E56F0FF,
        0x1011A0FA, 0x14D0BD4D, 0x19939B94, 0x1D528623,
        0xF12F560E, 0xF5EE4BB9, 0xF8AD6D60, 0xFC6C70D7,
        0xE22B20D2, 0xE6EA3D65, 0xEBA91BBC, 0xEF68060B,
        0xD727BBB6, 0xD3E6A601, 0xDEA580D8, 0xDA649D6F,
        0xC423CD6A, 0xC0E2D0DD, 0xCDA1F604, 0xC960EBB3,
        0xBD3E8D7E, 0xB9FF90C9, 0xB4BCB610, 0xB07DABA7,
        0xAE3AFBA2, 0xAAFBE615, 0xA7B8C0CC, 0xA379DD7B,
        0x9B3660C6, 0x9FF77D71, 0x92B45BA8, 0x9675461F,
        0x8832161A, 0x8CF30BAD, 0x81B02D74, 0x857130C3,
        0x5D8A9099, 0x594B8D2E, 0x5408ABF7, 0x50C9B640,
        0x4E8EE645, 0x4A4FFBF2, 0x470CDD2B, 0x43CDC09C,
        0x7B827D21, 0x7F436096, 0x7200464F, 0x76C15BF8,
        0x68860BFD, 0x6C47164A, 0x61043093, 0x65C52D24,
        0x119B4BE9, 0x155A565E, 0x18197087, 0x1CD86D30,
        0x029F3D35, 0x065E2082, 0x0B1D065B, 0x0FDC1BEC,
        0x3793A651, 0x3352BBE6, 0x3E119D3F, 0x3AD08088,
        0x2497D08D, 0x2056CD3A, 0x2D15EBE3, 0x29D4F654,
        0xC5A92679, 0xC1683BCE, 0xCC2B1D17, 0xC8EA00A0,
        0xD6AD50A5, 0xD26C4D12, 0xDF2F6BCB, 0xDBEE767C,
        0xE3A1CBC1, 0xE760D676, 0xEA23F0AF, 0xEEE2ED18,
        0xF0A5BD1D, 0xF464A0AA, 0xF9278673, 0xFDE69BC4,
        0x89B8FD09, 0x8D79E0BE, 0x803AC667, 0x84FBDBD0,
        0x9ABC8BD5, 0x9E7D9662, 0x933EB0BB, 0x97FFAD0C,
        0xAFB010B1, 0xAB710D06, 0xA6322BDF, 0xA2F33668,
        0xBCB4666D, 0xB8757BDA, 0xB5365D03, 0xB1F740B4}

    crc := uint32(0xffffffff)

    // different result
    for _, v := range message {
        crc = tbl[v^(byte(crc>>24)&0xff)] ^ (crc << 8)
    }

    crc = ^crc
    fmt.Printf("%10d == 0x%x\n", crc, crc) //  422667581 == 0x1931653d

    // same as http://zorc.breitbandkatze.de/crc.html
    chk := crc32.ChecksumIEEE(message)
    fmt.Printf("%10d == 0x%x\n", chk, chk) //  907060870 == 0x3610a686
}

Edit (from a comment below): I understand that the source code of Go's crc32 and mine are different. But why is my implementation giving a different result? The table I am using has the same starting polynome (from the wiki page for CRC-32) as Go's implementation (0x04C11DB7), except that Go uses the reversed polynome and therfore a different algorithm is not surprising. "My" algorithm comes from various different C/C++ sources, such as the one linked in the source.

Answer 1

First, it seem that you are not using the right table (or at least the same than the golang standard library): you can check it simply by comparing your table to the one available in the crc32 package. Here is a playground example.

Then, you algorithm is also wrong. To be honest, I didn't even tried to check whether you put the right values at the right places, but simply dug out the code used by crc32.Checksum. Here is a fixed version of your algorithm:

crc := uint32(0xffffffff) for _, v := range message { crc = tbl[byte(crc)^v] ^ (crc >> 8) } return ^crc

As you see, the in-loop calculation is a bit different. you can see it in action with the crc32.IEEE polynominal table here.