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* CRC32 implementation.
* The basic concept of a CRC is that you treat your bit-string
* abcdefg... as a ludicrously long polynomial M=a+bx+cx^2+dx^3+...
* over Z[2]. You then take a modulus polynomial P, and compute the
* remainder of M on division by P. Thus, an erroneous message N
* will only have the same CRC if the difference E = M-N is an
* exact multiple of P. (Note that as we are working over Z[2], M-N
* = N-M = M+N; but that's not very important.)
* What makes the CRC good is choosing P to have good properties:
* - If its first and last terms are both nonzero then it cannot
* be a factor of any single term x^i. Therefore if M and N
* differ by exactly one bit their CRCs will guaranteeably
* be distinct.
* - If it has a prime (irreducible) factor with three terms then
* it cannot divide a polynomial of the form x^i(1+x^j).
* Therefore if M and N differ by exactly _two_ bits they will
* have different CRCs.
* - If it has a factor (x+1) then it cannot divide a polynomial
* with an odd number of terms. Therefore if M and N differ by
* _any odd_ number of bits they will have different CRCs.
* - If the error term E is of the form x^i*B(x) where B(x) has
* order less than P (i.e. a short _burst_ of errors) then P
* cannot divide E (since no polynomial can divide a shorter
* one), so any such error burst will be spotted.
* The CRC32 standard polynomial is
* x^32+x^26+x^23+x^22+x^16+x^12+x^11+x^10+x^8+x^7+x^5+x^4+x^2+x^1+x^0
* In fact, we don't compute M mod P; we compute M*x^32 mod P.
* The concrete implementation of the CRC is this: we maintain at
* all times a 32-bit word which is the current remainder of the
* polynomial mod P. Whenever we receive an extra bit, we multiply
* the existing remainder by x, add (XOR) the x^32 term thus
* generated to the new x^32 term caused by the incoming bit, and
* remove the resulting combined x^32 term if present by replacing
* it with (P-x^32).
* Bit 0 of the word is the x^31 term and bit 31 is the x^0 term.
* Thus, multiplying by x means shifting right. So the actual
* algorithm goes like this:
* x32term = (crcword & 1) ^ newbit;
* crcword = (crcword >> 1) ^ (x32term * 0xEDB88320);
* In practice, we pre-compute what will happen to crcword on any
* given sequence of eight incoming bits, and store that in a table
* which we then use at run-time to do the job:
* outgoingplusnew = (crcword & 0xFF) ^ newbyte;
* crcword = (crcword >> 8) ^ table[outgoingplusnew];
* where table[outgoingplusnew] is computed by setting crcword=0
* and then iterating the first code fragment eight times (taking
* the incoming byte low bit first).
* Note that all shifts are rightward and thus no assumption is
* made about exact word length! (Although word length must be at
* _least_ 32 bits, but ANSI C guarantees this for `unsigned long'
* anyway.)
#include <stdlib.h>
#include "ssh.h"
/* ----------------------------------------------------------------------
* Multi-function module. Can be compiled three ways.
* - Compile with no special #defines. Will generate a table
* that's already initialised at compile time, and one function
* crc32_compute(buf,len) that uses it. Normal usage.
* - Compile with INITFUNC defined. Will generate an uninitialised
* array as the table, and as well as crc32_compute(buf,len) it
* will also generate void crc32_init(void) which sets up the
* table at run time. Useful if binary size is important.
* - Compile with GENPROGRAM defined. Will create a standalone
* program that does the initialisation and outputs the table as
* C code.
#define POLY (0xEDB88320L)
#define INITFUNC /* the gen program needs the init func :-) */
* This variant of the code generates the table at run-time from an
* init function.
static unsigned long crc32_table[256];
void crc32_init(void)
unsigned long crcword;
int i;
for (i = 0; i < 256; i++) {
unsigned long newbyte, x32term;
int j;
crcword = 0;
newbyte = i;
for (j = 0; j < 8; j++) {
x32term = (crcword ^ newbyte) & 1;
crcword = (crcword >> 1) ^ (x32term * POLY);
newbyte >>= 1;
crc32_table[i] = crcword;
* This variant of the code has the data already prepared.
static const unsigned long crc32_table[256] = {
0x00000000L, 0x77073096L, 0xEE0E612CL, 0x990951BAL,
0x076DC419L, 0x706AF48FL, 0xE963A535L, 0x9E6495A3L,
0x0EDB8832L, 0x79DCB8A4L, 0xE0D5E91EL, 0x97D2D988L,
0x09B64C2BL, 0x7EB17CBDL, 0xE7B82D07L, 0x90BF1D91L,
0x1DB71064L, 0x6AB020F2L, 0xF3B97148L, 0x84BE41DEL,
0x1ADAD47DL, 0x6DDDE4EBL, 0xF4D4B551L, 0x83D385C7L,
0x136C9856L, 0x646BA8C0L, 0xFD62F97AL, 0x8A65C9ECL,
0x14015C4FL, 0x63066CD9L, 0xFA0F3D63L, 0x8D080DF5L,
0x3B6E20C8L, 0x4C69105EL, 0xD56041E4L, 0xA2677172L,
0x3C03E4D1L, 0x4B04D447L, 0xD20D85FDL, 0xA50AB56BL,
0x35B5A8FAL, 0x42B2986CL, 0xDBBBC9D6L, 0xACBCF940L,
0x32D86CE3L, 0x45DF5C75L, 0xDCD60DCFL, 0xABD13D59L,
0x26D930ACL, 0x51DE003AL, 0xC8D75180L, 0xBFD06116L,
0x21B4F4B5L, 0x56B3C423L, 0xCFBA9599L, 0xB8BDA50FL,
0x2802B89EL, 0x5F058808L, 0xC60CD9B2L, 0xB10BE924L,
0x2F6F7C87L, 0x58684C11L, 0xC1611DABL, 0xB6662D3DL,
0x76DC4190L, 0x01DB7106L, 0x98D220BCL, 0xEFD5102AL,
0x71B18589L, 0x06B6B51FL, 0x9FBFE4A5L, 0xE8B8D433L,
0x7807C9A2L, 0x0F00F934L, 0x9609A88EL, 0xE10E9818L,
0x7F6A0DBBL, 0x086D3D2DL, 0x91646C97L, 0xE6635C01L,
0x6B6B51F4L, 0x1C6C6162L, 0x856530D8L, 0xF262004EL,
0x6C0695EDL, 0x1B01A57BL, 0x8208F4C1L, 0xF50FC457L,
0x65B0D9C6L, 0x12B7E950L, 0x8BBEB8EAL, 0xFCB9887CL,
0x62DD1DDFL, 0x15DA2D49L, 0x8CD37CF3L, 0xFBD44C65L,
0x4DB26158L, 0x3AB551CEL, 0xA3BC0074L, 0xD4BB30E2L,
0x4ADFA541L, 0x3DD895D7L, 0xA4D1C46DL, 0xD3D6F4FBL,
0x4369E96AL, 0x346ED9FCL, 0xAD678846L, 0xDA60B8D0L,
0x44042D73L, 0x33031DE5L, 0xAA0A4C5FL, 0xDD0D7CC9L,
0x5005713CL, 0x270241AAL, 0xBE0B1010L, 0xC90C2086L,
0x5768B525L, 0x206F85B3L, 0xB966D409L, 0xCE61E49FL,
0x5EDEF90EL, 0x29D9C998L, 0xB0D09822L, 0xC7D7A8B4L,
0x59B33D17L, 0x2EB40D81L, 0xB7BD5C3BL, 0xC0BA6CADL,
0xEDB88320L, 0x9ABFB3B6L, 0x03B6E20CL, 0x74B1D29AL,
0xEAD54739L, 0x9DD277AFL, 0x04DB2615L, 0x73DC1683L,
0xE3630B12L, 0x94643B84L, 0x0D6D6A3EL, 0x7A6A5AA8L,
0xE40ECF0BL, 0x9309FF9DL, 0x0A00AE27L, 0x7D079EB1L,
0xF00F9344L, 0x8708A3D2L, 0x1E01F268L, 0x6906C2FEL,
0xF762575DL, 0x806567CBL, 0x196C3671L, 0x6E6B06E7L,
0xFED41B76L, 0x89D32BE0L, 0x10DA7A5AL, 0x67DD4ACCL,
0xF9B9DF6FL, 0x8EBEEFF9L, 0x17B7BE43L, 0x60B08ED5L,
0xD6D6A3E8L, 0xA1D1937EL, 0x38D8C2C4L, 0x4FDFF252L,
0xD1BB67F1L, 0xA6BC5767L, 0x3FB506DDL, 0x48B2364BL,
0xD80D2BDAL, 0xAF0A1B4CL, 0x36034AF6L, 0x41047A60L,
0xDF60EFC3L, 0xA867DF55L, 0x316E8EEFL, 0x4669BE79L,
0xCB61B38CL, 0xBC66831AL, 0x256FD2A0L, 0x5268E236L,
0xCC0C7795L, 0xBB0B4703L, 0x220216B9L, 0x5505262FL,
0xC5BA3BBEL, 0xB2BD0B28L, 0x2BB45A92L, 0x5CB36A04L,
0xC2D7FFA7L, 0xB5D0CF31L, 0x2CD99E8BL, 0x5BDEAE1DL,
0x9B64C2B0L, 0xEC63F226L, 0x756AA39CL, 0x026D930AL,
0x9C0906A9L, 0xEB0E363FL, 0x72076785L, 0x05005713L,
0x95BF4A82L, 0xE2B87A14L, 0x7BB12BAEL, 0x0CB61B38L,
0x92D28E9BL, 0xE5D5BE0DL, 0x7CDCEFB7L, 0x0BDBDF21L,
0x86D3D2D4L, 0xF1D4E242L, 0x68DDB3F8L, 0x1FDA836EL,
0x81BE16CDL, 0xF6B9265BL, 0x6FB077E1L, 0x18B74777L,
0x88085AE6L, 0xFF0F6A70L, 0x66063BCAL, 0x11010B5CL,
0x8F659EFFL, 0xF862AE69L, 0x616BFFD3L, 0x166CCF45L,
0xA00AE278L, 0xD70DD2EEL, 0x4E048354L, 0x3903B3C2L,
0xA7672661L, 0xD06016F7L, 0x4969474DL, 0x3E6E77DBL,
0xAED16A4AL, 0xD9D65ADCL, 0x40DF0B66L, 0x37D83BF0L,
0xA9BCAE53L, 0xDEBB9EC5L, 0x47B2CF7FL, 0x30B5FFE9L,
0xBDBDF21CL, 0xCABAC28AL, 0x53B39330L, 0x24B4A3A6L,
0xBAD03605L, 0xCDD70693L, 0x54DE5729L, 0x23D967BFL,
0xB3667A2EL, 0xC4614AB8L, 0x5D681B02L, 0x2A6F2B94L,
0xB40BBE37L, 0xC30C8EA1L, 0x5A05DF1BL, 0x2D02EF8DL
int main(void)
unsigned long crcword;
int i;
for (i = 0; i < 256; i++) {
(i % 4 == 0 ? " " : " "),
(i % 4 == 3 ? (i == 255 ? "\n" : ",\n") : ","));
return 0;
unsigned long crc32_update(unsigned long crcword, const void *buf, size_t len)
const unsigned char *p = (const unsigned char *) buf;
while (len--) {
unsigned long newbyte = *p++;
newbyte ^= crcword & 0xFFL;
crcword = (crcword >> 8) ^ crc32_table[newbyte];
return crcword;
unsigned long crc32_compute(const void *buf, size_t len)
return crc32_update(0L, buf, len);
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