Network Working Group J. Stone
Request for Comments: 3309 Stanford
Updates: 2960 R. Stewart
Category: Standards Cisco Systems
D. Otis
SANlight
September 2002
Stream Control Transmission Protocol (SCTP) Checksum Change
Status of this Memo
This document specifies an Internet standards track protocol for the
Internet community, and requests discussion and suggestions for
improvements. Please refer to the current edition of the "Internet
Official Protocol Standards" (STD 1) for the standardization state
and status of this protocol. Distribution of this memo is unlimited.
Copyright Notice
Copyright (C) The Internet Society (2002). All Rights Reserved.
Abstract
Stream Control Transmission Protocol (SCTP) currently uses an Adler-
32 checksum. For small packets Adler-32 provides weak detection of
errors. This document changes that checksum and updates SCTP to use
a 32 bit CRC checksum.
Table of Contents
1 IntrodUCtion ................................................... 2
2 Checksum Procedures ............................................ 3
3 Security Considerations......................................... 6
4 IANA Considerations............................................. 6
5 Acknowledgments ................................................ 6
6 References ..................................................... 7
Appendix ......................................................... 9
Authors' Addresses ............................................... 16
Full Copyright Statement ......................................... 17
1 Introduction
A fundamental weakness has been detected in SCTP's current Adler-32
checksum algorithm [STONE]. This document updates and replaces the
Adler-32 checksum definition in [RFC2960]. Note that there is no
graceful transition mechanism for migrating to the new checksum.
Implementations are eXPected to immediately switch to the new
algorithm; use of the old algorithm is deprecated.
One requirement of an effective checksum is that it evenly and
smoothly spreads its input packets over the available check bits.
From an email from Jonathan Stone, who analyzed the Adler-32 as part
of his doctoral thesis:
"Briefly, the problem is that, for very short packets, Adler32 is
guaranteed to give poor coverage of the available bits. Don't take
my Word for it, ask Mark Adler. :-)
Adler-32 uses two 16-bit counters, s1 and s2. s1 is the sum of the
input, taken as 8-bit bytes. s2 is a running sum of each value of
s1. Both s1 and s2 are computed mod-65521 (the largest prime less
than 2^16). Consider a packet of 128 bytes. The *most* that each
byte can be is 255. There are only 128 bytes of input, so the
greatest value which the s1 accumulator can have is 255 * 128 =
32640. So, for 128-byte packets, s1 never wraps. That is critical.
Why?
The key is to consider the distribution of the s1 values, over some
distribution of the values of the individual input bytes in each
packet. Because s1 never wraps, s1 is simply the sum of the
individual input bytes. (Even Doug's trick of adding 0x5555 doesn't
help here, and an even larger value doesn't really help: we can get
at most one mod-65521 reduction.)
Given the further assumption that the input bytes are drawn
independently from some distribution (they probably aren't: for file
system data, it's even worse than that!), the Central Limit Theorem
tells us that that s1 will tend to have a normal distribution.
That's bad: it tells us that the value of s1 will have hot-spots at
around 128 times the mean of the input distribution: around 16k,
assuming a uniform distribution. That's bad. We want the
accumulator to wrap as many times as possible, so that the resulting
sum has as close to a uniform distribution as possible. (I call this
"fairness".)
So, for short packets, the Adler-32 s1 sum is guaranteed to be
unfair. Why is that bad? It's bad because the space of valid
packets -- input data, plus checksum values -- is also small. If all
packets have checksum values very close to 32640, then the likelihood
of even a 'small' error leaving a damaged packet with a valid
checksum is higher than if all checksum values are equally likely."
Due to this inherent weakness, exacerbated by the fact that SCTP will
first be used as a signaling transport protocol where signaling
messages are usually less than 128 bytes, a new checksum algorithm is
specified by this document, replacing the current Adler-32 algorithm
with CRC-32c.
1.1 Conventions
The keywords MUST, MUST NOT, REQUIRED, SHALL, SHALL NOT,
SHOULD,SHOULD NOT, RECOMMENDED, NOT RECOMMENDED, MAY, and OPTIONAL,
when they appear in this document, are to be interpreted as described
in [RFC2119].
Bit number order is defined in [RFC1700].
2 Checksum Procedures
The procedures described in section 2.1 of this document MUST be
followed, replacing the current checksum defined in [RFC2960].
Furthermore any references within [RFC2960] to Adler-32 MUST be
treated as a reference to CRC-32c. Section 2.1 of this document
describes the new calculation and verification procedures that MUST
be followed.
2.1 Checksum Calculation
When sending an SCTP packet, the endpoint MUST strengthen the data
integrity of the transmission by including the CRC-32c checksum value
calculated on the packet, as described below.
After the packet is constructed (containing the SCTP common header
and one or more control or DATA chunks), the transmitter shall:
1) Fill in the proper Verification Tag in the SCTP common header and
initialize the Checksum field to 0's.
2) Calculate the CRC-32c of the whole packet, including the SCTP
common header and all the chunks.
3) Put the resulting value into the Checksum field in the common
header, and leave the rest of the bits unchanged.
When an SCTP packet is received, the receiver MUST first check the
CRC-32c checksum:
1) Store the received CRC-32c value,
2) Replace the 32 bits of the Checksum field in the received SCTP
packet with all '0's and calculate a CRC-32c value of the whole
received packet. And,
3) Verify that the calculated CRC-32c value is the same as the
received CRC-32c value. If not, the receiver MUST treat the
packet as an invalid SCTP packet.
The default procedure for handling invalid SCTP packets is to
silently discard them.
Any hardware implementation SHOULD be done in a way that is
verifiable by the software.
We define a 'reflected value' as one that is the opposite of the
normal bit order of the machine. The 32 bit CRC is calculated as
described for CRC-32c and uses the polynomial code 0x11EDC6F41
(Castagnoli93) or x^32+x^28+x^27+x^26+x^25
+x^23+x^22+x^20+x^19+x^18+x^14+x^13+x^11+x^10+x^9+x^8+x^6+x^0. The
CRC is computed using a procedure similar to ETHERNET CRC [ITU32],
modified to reflect transport level usage.
CRC computation uses polynomial division. A message bit-string M is
transformed to a polynomial, M(X), and the CRC is calculated from
M(X) using polynomial arithmetic [Peterson 72].
When CRCs are used at the link layer, the polynomial is derived from
on-the-wire bit ordering: the first bit 'on the wire' is the high-
order coefficient. Since SCTP is a transport-level protocol, it
cannot know the actual serial-media bit ordering. Moreover,
different links in the path between SCTP endpoints may use different
link-level bit orders.
A convention must therefore be established for mapping SCTP transport
messages to polynomials for purposes of CRC computation. The bit-
ordering for mapping SCTP messages to polynomials is that bytes are
taken most-significant first; but within each byte, bits are taken
least-significant first. The first byte of the message provides the
eight highest coefficients. Within each byte, the least-significant
SCTP bit gives the most significant polynomial coefficient within
that byte, and the most-significant SCTP bit is the least significant
polynomial coefficient in that byte. (This bit ordering is sometimes
called 'mirrored' or 'reflected' [Williams93].) CRC polynomials are
to be transformed back into SCTP transport-level byte values, using a
consistent mapping.
The SCTP transport-level CRC value should be calculated as follows:
- CRC input data are assigned to a byte stream, numbered from 0
to N-1.
- the transport-level byte-stream is mapped to a polynomial
value. An N-byte PDU with j bytes numbered 0 to N-1, is
considered as coefficients of a polynomial M(x) of order 8N-1,
with bit 0 of byte j being coefficient x^(8(N-j)-8), bit 7 of
byte j being coefficient x^(8(N-j)-1).
- the CRC remainder register is initialized with all 1s and the
CRC is computed with an algorithm that simultaneously
multiplies by x^32 and divides by the CRC polynomial.
- the polynomial is multiplied by x^32 and divided by G(x), the
generator polynomial, producing a remainder R(x) of degree less
than or equal to 31.
- the coefficients of R(x) are considered a 32 bit sequence.
- the bit sequence is complemented. The result is the CRC
polynomial.
- The CRC polynomial is mapped back into SCTP transport-level
bytes. Coefficient of x^31 gives the value of bit 7 of SCTP
byte 0, the coefficient of x^24 gives the value of bit 0 of
byte 0. The coefficient of x^7 gives bit 7 of byte 3 and the
coefficient of x^0 gives bit 0 of byte 3. The resulting four-
byte transport-level sequence is the 32-bit SCTP checksum
value.
IMPLEMENTATION NOTE: Standards documents, textbooks, and vendor
literature on CRCs often follow an alternative formulation, in which
the register used to hold the remainder of the long-division
algorithm is initialized to zero rather than all-1s, and instead the
first 32 bits of the message are complemented. The long-division
algorithm used in our formulation is specified, such that the the
initial multiplication by 2^32 and the long-division are combined
into one simultaneous operation. For such algorithms, and for
messages longer than 64 bits, the two specifications are precisely
equivalent. That equivalence is the intent of this document.
Implementors of SCTP are warned that both specifications are to be
found in the literature, sometimes with no restriction on the long-
division algorithm. The choice of formulation in this document is to
permit non-SCTP usage, where the same CRC algorithm may be used to
protect messages shorter than 64 bits.
If SCTP could follow link level CRC use, the CRC would be computed
over the link-level bit-stream. The first bit on the link mapping to
the highest-order coefficient, and so on, down to the last link-level
bit as the lowest-order coefficient. The CRC value would be
transmitted immediately after the input message as a link-level
'trailer'. The resulting link-level bit-stream would be (M(X)x) *
x^32) + (M(X)*x^32))/ G(x), which is divisible by G(X). There would
thus be a constant CRC remainder for 'good' packets. However, given
that implementations of RFC2960 have already proliferated, the IETF
discussions considered that the benefit of a 'trailer' CRC did not
outweigh the cost of making a very large change in the protocol
processing. Further, packets accepted by the SCTP 'header' CRC are
in one-to-one correspondence with packets accepted by a modified
procedure using a 'trailer' CRC value, and where the SCTP common
checksum header is set to zero on transmission and is received as
zero.
There may be a computational advantage in validating the Association
against the Verification Tag, prior to performing a checksum, as
invalid tags will result in the same action as a bad checksum in most
cases. The exceptions for this technique would be INIT and some
SHUTDOWN-COMPLETE exchanges, as well as a stale COOKIE-ECHO. These
special case exchanges must represent small packets and will minimize
the effect of the checksum calculation.
3 Security Considerations
In general, the security considerations of RFC2960 apply to the
protocol with the new checksum as well.
4 IANA Considerations
There are no IANA considerations required in this document.
5 Acknowledgments
The authors would like to thank the following people that have
provided comments and input on the checksum issue:
Mark Adler, Ran Atkinson, Stephen Bailey, David Black, Scott Bradner,
Mikael Degermark, Laurent Glaude, Klaus Gradischnig, Alf Heidermark,
Jacob Heitz, Gareth Kiely, David Lehmann, Allision Mankin, Lyndon
Ong, Craig Partridge, Vern Paxson, Kacheong Poon, Michael Ramalho,
David Reed, Ian Rytina, Hanns Juergen Schwarzbauer, Chip Sharp, Bill
Sommerfeld, Michael Tuexen, Jim Williams, Jim Wendt, Michael Welzl,
Jonathan Wood, Lloyd Wood, Qiaobing Xie, La Monte Yarroll.
Special thanks to Dafna Scheinwald, Julian Satran, Pat Thaler, Matt
Wakeley, and Vince Cavanna, for selection criteria of polynomials and
examination of CRC polynomials, particularly CRC-32c [Castagnoli93].
Special thanks to Mr. Ross Williams and his document [Williams93].
This non-formal perspective on software ASPects of CRCs furthered
understanding of authors previously unfamiliar with CRC computation.
More formal treatments of [Blahut 94] or [Peterson 72], was also
essential.
6 References
[Castagnoli93] G. Castagnoli, S. Braeuer and M. Herrman,
"Optimization of Cyclic Redundancy-Check Codes with
24 and 32 Parity Bits", IEEE Transactions on
Communications, Vol. 41, No. 6, June 1993
[McKee75] H. McKee, "Improved {CRC} techniques detects
erroneous leading and trailing 0's in transmitted
data blocks", Computer Design Volume 14 Number 10
Pages 102-4,106, October 1975
[RFC1700] Reynolds, J. and J. Postel, "ASSIGNED NUMBERS", RFC
1700, October 1994.
[RFC2026] Bradner, S., "The Internet Standards Process --
Revision 3", BCP 9, RFC2026, October 1996.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC2119, March 1997.
[RFC2960] Stewart, R., Xie, Q., Morneault, K., Sharp, C.,
Schwarzbauer, H., Taylor, T., Rytina, I., Kalla, M.,
Zhang, L. and V. Paxson, "Stream Control Transmission
Protocol," RFC2960, October 2000.
[ITU32] ITU-T Recommendation V.42, "Error-correcting
procedures for DCEs using asynchronous-to-synchronous
conversion", section 8.1.1.6.2, October 1996.
7.1 Informative References
[STONE] Stone, J., "Checksums in the Internet", Doctoral
dissertation - August 2001.
[Williams93] Williams, R., "A PAINLESS GUIDE TO CRC ERROR
DETECTION ALGORITHMS" - Internet publication, August
1993,
http://www.geocities.com/SiliconValley/Pines/
8659/crc.htm.
[Blahut 1994] R.E. Blahut, Theory and Practice of Error Control
Codes, Addison-Wesley, 1994.
[Easics 2001] http://www.easics.be/weBTools/crctool. Online tools
for synthesis of CRC Verilog and VHDL.
[Feldmeier 95] David C. Feldmeier, Fast software implementation of
error detection codes, IEEE Transactions on
Networking, vol 3 no 6, pp 640-651, December, 1995.
[Glaise 1997] R. J. Glaise, A two-step computation of cyclic
redundancy code CRC-32 for ATM networks, IBM Journal
of Research and Development} vol 41 no 6, 1997.
http://www.research.ibm.com/journal/rd/416/
glaise.Html.
[Prange 1957] E. Prange, Cyclic Error-Correcting codes in two
symbols, Technical report AFCRC-TN-57-103, Air Force
Cambridge Research Center, Cambridge, Mass. 1957.
[Peterson 1972] W. W. Peterson and E.J Weldon, Error Correcting
Codes, 2nd. edition, MIT Press, Cambridge,
Massachusetts.
[Shie2001] Ming-Der Shieh et. al, A Systematic Approach for
Parallel CRC Computations. Journal of Information
Science and Engineering, Vol.17 No.3, pp.445-461
[Sprachman2001] Michael Sprachman, Automatic Generation of Parallel
CRC Circuits, IEEE Design & Test May-June 2001
Appendix
This appendix is for information only and is NOT part of the
standard.
The anticipated deployment of SCTP ranges over several orders of
magnitude of link speed: from cellular-power telephony devices at
tens of kilobits, to local links at tens of gigabits. Implementors
of SCTP should consider their link speed and choose, from the wide
range of CRC implementations, one which matches their own design
point for size, cost, and throughput. Many techniques for computing
CRCs are known. This Appendix surveys just a few, to give a feel for
the range of techniques available.
CRCs are derived from early work by Prange in the 1950s [Prange 57].
The theory underlying CRCs and choice of generator polynomial can be
introduced by either the theory of Galois fields [Blahut 94] or as
ideals of an algebra over cyclic codes [cite Peterson 72].
One of the simplest techniques is direct bit-serial hardware
implementations, using the generator polynomial as the taps of a
linear feedback shift register (LSFR). LSFR computation follows
directly from the mathematics, and is generally attributed to Prange.
Tools exist which, a CRC generator polynomial, will produce
synthesizable Verilog code for CRC hardware [Easics 2001].
Since LSFRs do not scale well in speed, a variety of other techniques
have been explored. One technique exploits the fact that the divisor
of the polynomial long-division, G, is known in advance. It is thus
possible to pre-compute lookup tables giving the polynomial remainder
of multiple input bits --- typically 2, 4, or 8 bits of input at a
time. This technique can be used either in software or in hardware.
Software to compute lookup tables yielding 2, 4, or 8 bits of result
is freely available. [Williams93]
For multi-gigabit links, the above techniques may still not be fast
enough. One technique for computing CRCS at OC-48 rates is 'two-
stage' CRC computation [Glaise 1997]. Here, some multiple of G(x),
G(x)H(x), is chosen so as to minimize the number of nonzero
coefficients, or weight, of the product G(x)H(x). The low weight of
the product polynomial makes it susceptible to efficient hardware
divide-by-constant implementations. This first stage gives M(x)/
(G(x)H(x)), as its result. The second stage then divides the result
of the first stage by H(x), yielding (M(x)/(G(x)H(x)))/H(x). If H(x)
is also relatively prime to G(x), this gives M(x)/G(x). Further
developments on this approach can be found in [Shie2001] and
[Sprachman2001].
The literature also includes a variety of software CRC
implementations. One approach is to use a carefully-tuned assembly
code for direct polynomial division. [Feldmeier 95] reports that for
low-weight polynomials, tuned polynomial arithmetic gives higher
throughput than table-lookup algorithms. Even within table-lookup
algorithms, the size of the table can be tuned, either for total
cache footprint, or (for space-restricted environments) to minimize
total size.
Implementors should keep in mind, the bit ordering described in
Section 2: the ordering of bits within bytes for computing CRCs in
SCTP is the least significant bit of each byte is the most-
significant polynomial coefficient(and vice-versa). This 'reflected'
SCTP CRC bit ordering matches on-the-wire bit order for Ethernet and
other serial media, but is the reverse of traditional Internet bit
ordering.
One technique to accommodate this bit-reversal can be explained as
follows: sketch out a hardware implementation, assuming the bits are
in CRC bit order; then perform a left-to-right inversion (mirror
image) on the entire algorithm. (We defer, for a moment, the issue
of byte order within words.) Then compute that "mirror image" in
software. The CRC from the "mirror image" algorithm will be the
bit-reversal of a correct hardware implementation. When the link-
level media sends each byte, the byte is sent in the reverse of the
host CPU bit-order. Serialization of each byte of the "reflected"
CRC value re-reverses the bit order, so in the end, each byte will be
transmitted on-the-wire in the specified bit order.
The following non-normative sample code is taken from an open-source
CRC generator [Williams93], using the "mirroring" technique and
yielding a lookup table for SCTP CRC32-c with 256 entries, each 32
bits wide. While neither especially slow nor especially fast, as
software table-lookup CRCs go, it has the advantage of working on
both big-endian and little-endian CPUs, using the same (host-order)
lookup tables, and using only the pre-defined ntohl() and htonl()
operations. The code is somewhat modified from [Williams93], to
ensure portability between big-endian and little-endian
architectures. (Note that if the byte endian-ness of the target
architecture is known to be little-endian the final bit-reversal and
byte-reversal steps can be folded into a single operation.)
/*************************************************************/
/* Note Definition for Ross Williams table generator would */
/* be: TB_WIDTH=4, TB_POLLY=0x1EDC6F41, TB_REVER=TRUE */
/* For Mr. Williams direct calculation code use the settings */
/* cm_width=32, cm_poly=0x1EDC6F41, cm_init=0xFFFFFFFF, */
/* cm_refin=TRUE, cm_refot=TRUE, cm_xorort=0x00000000 */
/*************************************************************/
/* Example of the crc table file */
#ifndef __crc32cr_table_h__
#define __crc32cr_table_h__
#define CRC32C_POLY 0x1EDC6F41
#define CRC32C(c,d) (c=(c>>8)^crc_c[(c^(d))&0xFF])
unsigned long crc_c[256] =
{
0x00000000L, 0xF26B8303L, 0xE13B70F7L, 0x1350F3F4L,
0xC79A971FL, 0x35F1141CL, 0x26A1E7E8L, 0xD4CA64EBL,
0x8AD958CFL, 0x78B2DBCCL, 0x6BE22838L, 0x9989AB3BL,
0x4D43CFD0L, 0xBF284CD3L, 0xAC78BF27L, 0x5E133C24L,
0x105EC76FL, 0xE235446CL, 0xF165B798L, 0x030E349BL,
0xD7C45070L, 0x25AFD373L, 0x36FF2087L, 0xC494A384L,
0x9A879FA0L, 0x68EC1CA3L, 0x7BBCEF57L, 0x89D76C54L,
0x5D1D08BFL, 0xAF768BBCL, 0xBC267848L, 0x4E4DFB4BL,
0x20BD8EDEL, 0xD2D60DDDL, 0xC186FE29L, 0x33ED7D2AL,
0xE72719C1L, 0x154C9AC2L, 0x061C6936L, 0xF477EA35L,
0xAA64D611L, 0x580F5512L, 0x4B5FA6E6L, 0xB93425E5L,
0x6DFE410EL, 0x9F95C20DL, 0x8CC531F9L, 0x7EAEB2FAL,
0x30E349B1L, 0xC288CAB2L, 0xD1D83946L, 0x23B3BA45L,
0xF779DEAEL, 0x05125DADL, 0x1642AE59L, 0xE4292D5AL,
0xBA3A117EL, 0x4851927DL, 0x5B016189L, 0xA96AE28AL,
0x7DA08661L, 0x8FCB0562L, 0x9C9BF696L, 0x6EF07595L,
0x417B1DBCL, 0xB3109EBFL, 0xA0406D4BL, 0x522BEE48L,
0x86E18AA3L, 0x748A09A0L, 0x67DAFA54L, 0x95B17957L,
0xCBA24573L, 0x39C9C670L, 0x2A993584L, 0xD8F2B687L,
0x0C38D26CL, 0xFE53516FL, 0xED03A29BL, 0x1F682198L,
0x5125DAD3L, 0xA34E59D0L, 0xB01EAA24L, 0x42752927L,
0x96BF4DCCL, 0x64D4CECFL, 0x77843D3BL, 0x85EFBE38L,
0xDBFC821CL, 0x2997011FL, 0x3AC7F2EBL, 0xC8AC71E8L,
0x1C661503L, 0xEE0D9600L, 0xFD5D65F4L, 0x0F36E6F7L,
0x61C69362L, 0x93AD1061L, 0x80FDE395L, 0x72966096L,
0xA65C047DL, 0x5437877EL, 0x4767748AL, 0xB50CF789L,
0xEB1FCBADL, 0x197448AEL, 0x0A24BB5AL, 0xF84F3859L,
0x2C855CB2L, 0xDEEEDFB1L, 0xCDBE2C45L, 0x3FD5AF46L,
0x7198540DL, 0x83F3D70EL, 0x90A324FAL, 0x62C8A7F9L,
0xB602C312L, 0x44694011L, 0x5739B3E5L, 0xA55230E6L,
0xFB410CC2L, 0x092A8FC1L, 0x1A7A7C35L, 0xE811FF36L,
0x3CDB9BDDL, 0xCEB018DEL, 0xDDE0EB2AL, 0x2F8B6829L,
0x82F63B78L, 0x709DB87BL, 0x63CD4B8FL, 0x91A6C88CL,
0x456CAC67L, 0xB7072F64L, 0xA457DC90L, 0x563C5F93L,
0x082F63B7L, 0xFA44E0B4L, 0xE9141340L, 0x1B7F9043L,
0xCFB5F4A8L, 0x3DDE77ABL, 0x2E8E845FL, 0xDCE5075CL,
0x92A8FC17L, 0x60C37F14L, 0x73938CE0L, 0x81F80FE3L,
0x55326B08L, 0xA759E80BL, 0xB4091BFFL, 0x466298FCL,
0x1871A4D8L, 0xEA1A27DBL, 0xF94AD42FL, 0x0B21572CL,
0xDFEB33C7L, 0x2D80B0C4L, 0x3ED04330L, 0xCCBBC033L,
0xA24BB5A6L, 0x502036A5L, 0x4370C551L, 0xB11B4652L,
0x65D122B9L, 0x97BAA1BAL, 0x84EA524EL, 0x7681D14DL,
0x2892ED69L, 0xDAF96E6AL, 0xC9A99D9EL, 0x3BC21E9DL,
0xEF087A76L, 0x1D63F975L, 0x0E330A81L, 0xFC588982L,
0xB21572C9L, 0x407EF1CAL, 0x532E023EL, 0xA145813DL,
0x758FE5D6L, 0x87E466D5L, 0x94B49521L, 0x66DF1622L,
0x38CC2A06L, 0xCAA7A905L, 0xD9F75AF1L, 0x2B9CD9F2L,
0xFF56BD19L, 0x0D3D3E1AL, 0x1E6DCDEEL, 0xEC064EEDL,
0xC38D26C4L, 0x31E6A5C7L, 0x22B65633L, 0xD0DDD530L,
0x0417B1DBL, 0xF67C32D8L, 0xE52CC12CL, 0x1747422FL,
0x49547E0BL, 0xBB3FFD08L, 0xA86F0EFCL, 0x5A048DFFL,
0x8ECEE914L, 0x7CA56A17L, 0x6FF599E3L, 0x9D9E1AE0L,
0xD3D3E1ABL, 0x21B862A8L, 0x32E8915CL, 0xC083125FL,
0x144976B4L, 0xE622F5B7L, 0xF5720643L, 0x07198540L,
0x590AB964L, 0xAB613A67L, 0xB831C993L, 0x4A5A4A90L,
0x9E902E7BL, 0x6CFBAD78L, 0x7FAB5E8CL, 0x8DC0DD8FL,
0xE330A81AL, 0x115B2B19L, 0x020BD8EDL, 0xF0605BEEL,
0x24AA3F05L, 0xD6C1BC06L, 0xC5914FF2L, 0x37FACCF1L,
0x69E9F0D5L, 0x9B8273D6L, 0x88D28022L, 0x7AB90321L,
0xAE7367CAL, 0x5C18E4C9L, 0x4F48173DL, 0xBD23943EL,
0xF36E6F75L, 0x0105EC76L, 0x12551F82L, 0xE03E9C81L,
0x34F4F86AL, 0xC69F7B69L, 0xD5CF889DL, 0x27A40B9EL,
0x79B737BAL, 0x8BDCB4B9L, 0x988C474DL, 0x6AE7C44EL,
0xBE2DA0A5L, 0x4C4623A6L, 0x5F16D052L, 0xAD7D5351L,
};
#endif
/* Example of table build routine */
#include <stdio.h>
#include <stdlib.h>
#define OUTPUT_FILE "crc32cr.h"
#define CRC32C_POLY 0x1EDC6F41L
FILE *tf;
unsigned long
reflect_32 (unsigned long b)
{
int i;
unsigned long rw = 0L;
for (i = 0; i < 32; i++){
if (b & 1)
rw = 1 << (31 - i);
b >>= 1;
}
return (rw);
}
unsigned long
build_crc_table (int index)
{
int i;
unsigned long rb;
rb = reflect_32 (index);
for (i = 0; i < 8; i++){
if (rb & 0x80000000L)
rb = (rb << 1) ^ CRC32C_POLY;
else
rb <<= 1;
}
return (reflect_32 (rb));
}
main ()
{
int i;
printf ("\nGenerating CRC-32c table file <%s>\n", OUTPUT_FILE);
if ((tf = fopen (OUTPUT_FILE, "w")) == NULL){
printf ("Unable to open %s\n", OUTPUT_FILE);
exit (1);
}
fprintf (tf, "#ifndef __crc32cr_table_h__\n");
fprintf (tf, "#define __crc32cr_table_h__\n\n");
fprintf (tf, "#define CRC32C_POLY 0x%08lX\n", CRC32C_POLY);
fprintf (tf, "#define CRC32C(c,d) (c=(c>>8)^crc_c[(c^(d))&0xFF])\n");
fprintf (tf, "\nunsigned long crc_c[256] =\n{\n");
for (i = 0; i < 256; i++){
fprintf (tf, "0x%08lXL, ", build_crc_table (i));
if ((i & 3) == 3)
fprintf (tf, "\n");
}
fprintf (tf, "};\n\n#endif\n");
if (fclose (tf) != 0)
printf ("Unable to close <%s>." OUTPUT_FILE);
else
printf ("\nThe CRC-32c table has been written to <%s>.\n",
OUTPUT_FILE);
}
/* Example of crc insertion */
#include "crc32cr.h"
unsigned long
generate_crc32c(unsigned char *buffer, unsigned int length)
{
unsigned int i;
unsigned long crc32 = ~0L;
unsigned long result;
unsigned char byte0,byte1,byte2,byte3;
for (i = 0; i < length; i++){
CRC32C(crc32, buffer[i]);
}
result = ~crc32;
/* result now holds the negated polynomial remainder;
* since the table and algorithm is "reflected" [williams95].
* That is, result has the same value as if we mapped the message
* to a polynomial, computed the host-bit-order polynomial
* remainder, performed final negation, then did an end-for-end
* bit-reversal.
* Note that a 32-bit bit-reversal is identical to four inplace
* 8-bit reversals followed by an end-for-end byteswap.
* In other words, the bytes of each bit are in the right order,
* but the bytes have been byteswapped. So we now do an explicit
* byteswap. On a little-endian machine, this byteswap and
* the final ntohl cancel out and could be elided.
*/
byte0 = result & 0xff;
byte1 = (result>>8) & 0xff;
byte2 = (result>>16) & 0xff;
byte3 = (result>>24) & 0xff;
crc32 = ((byte0 << 24)
(byte1 << 16)
(byte2 << 8)
byte3);
return ( crc32 );
}
int
insert_crc32(unsigned char *buffer, unsigned int length)
{
SCTP_message *message;
unsigned long crc32;
message = (SCTP_message *) buffer;
message->common_header.checksum = 0L;
crc32 = generate_crc32c(buffer,length);
/* and insert it into the message */
message->common_header.checksum = htonl(crc32);
return 1;
}
int
validate_crc32(unsigned char *buffer, unsigned int length)
{
SCTP_message *message;
unsigned int i;
unsigned long original_crc32;
unsigned long crc32 = ~0L;
/* save and zero checksum */
message = (SCTP_message *) buffer;
original_crc32 = ntohl(message->common_header.checksum);
message->common_header.checksum = 0L;
crc32 = generate_crc32c(buffer,length);
return ((original_crc32 == crc32)? 1 : -1);
}
Authors' Addresses
Jonathan Stone
Room 446, Mail code 9040
Gates building 4A
Stanford, Ca 94305
EMail: jonathan@dsg.stanford.edu
Randall R. Stewart
24 Burning Bush Trail.
Crystal Lake, IL 60012
USA
EMail: rrs@cisco.com
Douglas Otis
800 E. Middlefield
Mountain View, CA 94043
USA
EMail: dotis@sanlight.net
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