NAME
cksum — write file
checksums and sizes 2
SYNOPSIS
cksum |
[file ...] |
DESCRIPTION
The cksum utility shall calculate and
write to standard output a cyclic redundancy check ( CRC )
for each input file, and also write to standard output the number of octets
in each file. The CRC used is based on the polynomial used
for CRC error checking in the networking standard
ISO 8802-3
B7. The
CRC checksum shall be obtained in the following way: The
encoding is defined by the generating polynomial: G(x) = x32 + x26 + x23 +
x22 + x16 + x12 + x11 + x10 + x8 + x7 + x5 + x4 + x2 + x + Mathematically,
the CRC value corresponding to a given file shall be
defined by the following procedure:
- The n bits to be evaluated are considered to be the coefficients of a mod 2 polynomial M(x) of degree n−1. These n bits are the bits from the file, with the most significant bit being the most significant bit of the first octet of the file and the last bit being the least significant bit of the last octet, padded with zero bits (if necessary) to achieve an integral number of octets, followed by one or more octets representing the length of the file as a binary value, least significant octet first. The smallest number of octets capable of representing this integer shall be used. 32
- M(x) is multiplied by x (i.e., shifted left 32 bits) and divided by G(x) using mod 2 division, producing a remainder R(x) of degree ≤ 31.
- The coefficients of R(x) are considered to be a 32-bit sequence.
- The bit sequence is complemented and the result is the CRC.
OPTIONS
None.
OPERANDS
The following operand shall be supported by the implementation:
- file
-
A pathname of a file to be checked. If no file operands are specified, the standard input is used.
STANDARD INPUT
The standard input is used only if no file operands are specified. See Input Files.
INPUT FILES
The input files can be any file type.
ENVIRONMENT VARIABLES
The following environment variables shall affect the execution of
cksum:
LANG-
This variable shall determine the locale to use for the locale categories when both LC_ALL and the corresponding environment variable (beginning with LC_ ) do not specify a locale. See 2.6.
LC_ALL-
This variable shall determine the locale to be used to override any values for locale categories specified by the settings of LANG or any environment variables beginning with LC_.
LC_CTYPE-
This variable shall determine the locale for the interpretation of sequences of bytes of text data as characters (e.g., single- versus multibyte characters in arguments).
LC_MESSAGES-
This variable shall determine the language in which messages should be written.
ASYNCHRONOUS EVENTS
Default.
STANDARD OUTPUT
For each file processed successfully, the
cksum utility shall write in the following format:
"%u %d %s\n", <checksum>, <# of octets>,
<pathname>
If no file operand was specified, the pathname and its leading space shall be omitted.
STANDARD ERROR
Used only for diagnostic messages.
OUTPUT FILES
None.
EXTENDED DESCRIPTION
None.
EXIT STATUS
The cksum utility shall exit with one of
the following values:
CONSEQUENCES OF ERRORS
Default.
RATIONALE
EXAMPLES
The cksum utility is typically used to
quickly compare a suspect file against a trusted version of the same.
However, no claims are made by POSIX. 2 that this
comparison is cryptographically secure; the historical sum utility from
which cksum was inspired has traditionally been used
mainly to ensure that files transmitted over noisy media arrive intact. The
chances of a damaged file producing the same CRC as the
original are astronomically small; deliberate deception is difficult, but
probably not impossible. Although input files to
cksum can be any type, the results need not be what
would be expected on character special device files or on file types not
described by POSIX. 1 {8}. Since POSIX.
2 does not specify the block size used when doing input, checksums of
character special files need not process all of the data in those files. The
algorithm is expressed in terms of a bitstream divided into octets. If a
file is transmitted between two systems and undergoes any data
transformation (such as moving 8-bit characters into 9-bit bytes or changing
‘‘little Endian’’ byte ordering to
‘‘big Endian’’), identical CRC
values cannot be expected. Implementations performing such transformations
may extend cksum to handle such situations.
The following C-language program can be used as a model to describe the algorithm. It assumes that a char is one octet. It also assumes that the entire file is
available for one pass through the function. This was done for simplicity in demonstrating the algorithm, rather than as an implementation model.
static unsigned long crctab[] = { 0x0, 0x77073096, 0xee0e612c, 0x990951ba, 0x076dc419, 0x706af48f, 0xe963a535, 0x9e6495a3, 0x0edb8832, 0x79dcb8a4, 0xe0d5e91e, 0x97d2d988, 0x09b64c2b, 0x7eb17cbd, 0xe7b82d07, 0x90bf1d91, 0x1db71064, 0x6ab020f2, 0xf3b97148, 0x84be41de, 0x1adad47d, 0x6ddde4eb, 0xf4d4b551, 0x83d385c7, 0x136c9856, 0x646ba8c0, 0xfd62f97a, 0x8a65c9ec, 0x14015c4f, 0x63066cd9, 0xfa0f3d63, 0x8d080df5, 0x3b6e20c8, 0x4c69105e, 0xd56041e4, 0xa2677172, 0x3c03e4d1, 0x4b04d447, 0xd20d85fd, 0xa50ab56b, 0x35b5a8fa, 0x42b2986c, 0xdbbbc9d6, 0xacbcf940, 0x32d86ce3, 0x45df5c75, 0xdcd60dcf, 0xabd13d59, 0x26d930ac, 0x51de003a, 0xc8d75180, 0xbfd06116, 0x21b4f4b5, 0x56b3c423, 0xcfba9599, 0xb8bda50f, 0x2802b89e, 0x5f058808, 0xc60cd9b2, 0xb10be924, 0x2f6f7c87, 0x58684c11, 0xc1611dab, 0xb6662d3d, 0x76dc4190, 0x01db7106, 0x98d220bc, 0xefd5102a, 0x71b18589, 0x06b6b51f, 0x9fbfe4a5, 0xe8b8d433, 0x7807c9a2, 0x0f00f934, 0x9609a88e, 0xe10e9818, 0x7f6a0dbb, 0x086d3d2d, 0x91646c97, 0xe6635c01, 0x6b6b51f4, 0x1c6c6162, 0x856530d8, 0xf262004e, 0x6c0695ed, 0x1b01a57b, 0x8208f4c1, 0xf50fc457, 0x65b0d9c6, 0x12b7e950, 0x8bbeb8ea, 0xfcb9887c, 0x62dd1ddf, 0x15da2d49, 0x8cd37cf3, 0xfbd44c65, 0x4db26158, 0x3ab551ce, 0xa3bc0074, 0xd4bb30e2, 0x4adfa541, 0x3dd895d7, 0xa4d1c46d, 0xd3d6f4fb, 0x4369e96a, 0x346ed9fc, 0xad678846, 0xda60b8d0, 0x44042d73, 0x33031de5, 0xaa0a4c5f, 0xdd0d7cc9, 0x5005713c, 0x270241aa, 0xbe0b1010, 0xc90c2086, 0x5768b525, 0x206f85b3, 0xb966d409, 0xce61e49f, 0x5edef90e, 0x29d9c998, 0xb0d09822, 0xc7d7a8b4, 0x59b33d17, 0x2eb40d81, 0xb7bd5c3b, 0xc0ba6cad, 0xedb88320, 0x9abfb3b6, 0x03b6e20c, 0x74b1d29a, 0xead54739, 0x9dd277af, 0x04db2615, 0x73dc1683, 0xe3630b12, 0x94643b84, 0x0d6d6a3e, 0x7a6a5aa8, 0xe40ecf0b, 0x9309ff9d, 0x0a00ae27, 0x7d079eb1, 0xf00f9344, 0x8708a3d2, 0x1e01f268, 0x6906c2fe, 0xf762575d, 0x806567cb, 0x196c3671, 0x6e6b06e7, 0xfed41b76, 0x89d32be0, 0x10da7a5a, 0x67dd4acc, 0xf9b9df6f, 0x8ebeeff9, 0x17b7be43, 0x60b08ed5, 0xd6d6a3e8, 0xa1d1937e, 0x38d8c2c4, 0x4fdff252, 0xd1bb67f1, 0xa6bc5767, 0x3fb506dd, 0x48b2364b, 0xd80d2bda, 0xaf0a1b4c, 0x36034af6, 0x41047a60, 0xdf60efc3, 0xa867df55, 0x316e8eef, 0x4669be79, 0xcb61b38c, 0xbc66831a, 0x256fd2a0, 0x5268e236, 0xcc0c7795, 0xbb0b4703, 0x220216b9, 0x5505262f, 0xc5ba3bbe, 0xb2bd0b28, 0x2bb45a92, 0x5cb36a04, 0xc2d7ffa7, 0xb5d0cf31, 0x2cd99e8b, 0x5bdeae1d, 0x9b64c2b0, 0xec63f226, 0x756aa39c, 0x026d930a, 0x9c0906a9, 0xeb0e363f, 0x72076785, 0x05005713, 0x95bf4a82, 0xe2b87a14, 0x7bb12bae, 0x0cb61b38, 0x92d28e9b, 0xe5d5be0d, 0x7cdcefb7, 0x0bdbdf21, 0x86d3d2d4, 0xf1d4e242, 0x68ddb3f8, 0x1fda836e, 0x81be16cd, 0xf6b9265b, 0x6fb077e1, 0x18b74777, 0x88085ae6, 0xff0f6a70, 0x66063bca, 0x11010b5c, 0x8f659eff, 0xf862ae69, 0x616bffd3, 0x166ccf45, 0xa00ae278, 0xd70dd2ee, 0x4e048354, 0x3903b3c2, 0xa7672661, 0xd06016f7, 0x4969474d, 0x3e6e77db, 0xaed16a4a, 0xd9d65adc, 0x40df0b66, 0x37d83bf0,
0xa9bcae53, 0xdebb9ec5, 0x47b2cf7f, 0x30b5ffe9, 0xbdbdf21c, 0xcabac28a, 0x53b39330, 0x24b4a3a6, 0xbad03605, 0xcdd70693, 0x54de5729, 0x23d967bf, 0xb3667a2e, 0xc4614ab8, 0x5d681b02, 0x2a6f2b94, 0xb40bbe37, 0xc30c8ea1, 0x5a05df1b, 0x2d02ef8d };
unsigned long memcrc(const unsigned char ∗b, size_t n) { /∗ Input arguments: ∗ const char∗ b == byte sequence to checksum ∗ size_t n == length of sequence ∗/
register unsigned int i, c, s = 0;
for (i = n; i > 0; --i) { c = (unsigned int)(∗b++); s = (s << 8) ˆ crctab[(s >> 24) ˆ c]; }
/∗ extend with the length of the string ∗/ while (n != 0) { c = n & 0377; n >>= 8; s = (s << 8) ˆ crctab[(s >> 24) ˆ c]; }
return ∼s; }
HISTORY OF DECISIONS MADE
The historical practice of writing the number of
‘‘blocks’’ has been removed in favor of writing
the number of octets since the latter is not only more useful, but
historical implementations have not been consistent in defining what a
‘‘block’’ meant. Octets are used instead of
bytes because bytes can differ in size between systems. The algorithm used
was selected to increase the robustness of the utility’s operation.
Neither the System V nor
BSD sum
algorithm was selected. Since each of these was different and each was the
default behavior on those systems, no realistic compromise was available if
either were selected—some set of historical applications would break.
Therefore, the name was changed to cksum. Although
the historical sum commands will probably continue to be provided for many
years to come, programs designed for portability across systems should use
the new name. The algorithm selected is based on that used by the Ethernet
standard for the Frame Check Sequence Field. The algorithm used does not
match the technical definition of a checksum; the term is used for
historical reasons. The length of the file is included in the
CRC calculation because this parallels Ethernet’s
inclusion of a length field in its CRC, but also because
it guards against inadvertent collisions between files that begin with
different series of zero octets. The chance that
two different files will produce identical CRCs is much greater when their lengths are not considered. Keeping the length and the checksum of the file itself separate would yield a slightly more robust algorithm, but historical usage has always been that a single number (the checksum as printed) represents the signature of the file. It was decided that historical usage was the more important consideration.
Earlier drafts contained modifications to the Ethernet algorithm that involved extracting table values whenever an intermediate result became zero. This was demonstrated to be less robust than the current method and mathematically difficult to describe or justify.
Editor’s Note: The following bibliographic
references will be cleaned up before the standard is completed. The
calculation used is identical to that given in pseudo-code on page 1011 of
Communications of the
ACM, August, 1988 in
the article ‘‘Computation of Cyclic Redundancy Checks Via
Table Lookup’’ by Dilip V. Sarwate. The pseudo-code rendition
is: X <- 0; Y <- 0; for i <- m -1 step -1 until 0 do begin T <-
X(1) ˆ A[i]; X(1) <- X(0); X(0) <- Y(1); Y(1) <- Y(0); Y(0)
<- 0; comment: f[T] and f’[T] denote the T-th words in the table f
and f’ ; X <- X ˆ f[T]; Y <- Y ˆ f’[T];
end The pseudo-code is reproduced exactly as given; however, note that in
cksum ’s case, A[i] represents a byte of the
file, the words X and Y are a treated as a single 32-bit value, and the
tables f and f’ are a single table containing 32-bit values. The
article also discusses generating the table(s). Other sources consulted
about CRC ’s: ‘‘A Tutorial on
CRC Computations,’’ Ramabadran and Gaitonde,
IEEE
Micro, p. 62, August 1988; Computer Networks, Andrew Tanenbaum,
Prentice-Hall, Inc.