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Computation of the Internet Checksum via Incremental Update :: RFC1624

Network Working Group                             A. Rijsinghani, Editor
Request for Comments: 1624                 Digital Equipment Corporation
Updates: 1141                                                   May 1994
Category: Informational

                  Computation of the Internet Checksum
                         via Incremental Update

Status of this Memo

   This memo provides information for the Internet community.  This memo
   does not specify an Internet standard of any kind.  Distribution of
   this memo is unlimited.


   This memo describes an updated technique for incremental computation
   of the standard Internet checksum.  It updates the method described
   in RFC 1141.

Table of Contents

   1. Introduction ..........................................  1
   2. Notation and Equations ................................  2
   3. Discussion ............................................  2
   4. Examples ..............................................  3
   5. Checksum verification by end systems ..................  4
   6. Historical Note .......................................  4
   7. Acknowledgments .......................................  5
   8. Security Considerations ...............................  5
   9. Conclusions ...........................................  5
   10. Author's Address .....................................  5
   11. References ...........................................  6

1.  Introduction

   Incremental checksum update is useful in speeding up several
   types of operations routinely performed on IP packets, such as
   TTL update, IP fragmentation, and source route update.

   RFC 1071, on pages 4 and 5, describes a procedure to
   incrementally update the standard Internet checksum.  The
   relevant discussion, though comprehensive, was not complete.
   Therefore, RFC 1141 was published to replace this description
   on Incremental Update.  In particular, RFC 1141 provides a
   more detailed exposure to the procedure described in RFC 1071.
   However, it computes a result for certain cases that differs

Rijsinghani                                                     [Page 1]
RFC 1624             Incremental Internet Checksum              May 1994

   from the one obtained from scratch (one's complement of one's
   complement sum of the original fields).

   For the sake of completeness, this memo briefly highlights key
   points from RFCs 1071 and 1141.  Based on these discussions,
   an updated procedure to incrementally compute the standard
   Internet checksum is developed and presented.

2.  Notation and Equations

   Given the following notation:

          HC  - old checksum in header
          C   - one's complement sum of old header
          HC' - new checksum in header
          C'  - one's complement sum of new header
          m   - old value of a 16-bit field
          m'  - new value of a 16-bit field

          RFC 1071 states that C' is:

          C' = C + (-m) + m'    --    [Eqn. 1]
             = C + (m' - m)

   As RFC 1141 points out, the equation above is not useful for direct
   use in incremental updates since C and C' do not refer to the actual
   checksum stored in the header.  In addition, it is pointed out that
   RFC 1071 did not specify that all arithmetic must be performed using
   one's complement arithmetic.

   Finally, complementing the above equation to get the actual checksum,
   RFC 1141 presents the following:

          HC' = ~(C + (-m) + m')
              = HC + (m - m')
              = HC + m + ~m'    --    [Eqn. 2]

3.  Discussion

   Although this equation appears to work, there are boundary conditions
   under which it produces a result which differs from the one obtained
   by checksum computation from scratch.  This is due to the way zero is
   handled in one's complement arithmetic.

   In one's complement, there are two representations of zero: the all
   zero and the all one bit values, often referred to as +0 and -0.
   One's complement addition of non-zero inputs can produce -0 as a
   result, but never +0.  Since there is guaranteed to be at least one

Rijsinghani                                                     [Page 2]
RFC 1624             Incremental Internet Checksum              May 1994

   non-zero field in the IP header, and the checksum field in the
   protocol header is the complement of the sum, the checksum field can
   never contain ~(+0), which is -0 (0xFFFF).  It can, however, contain
   ~(-0), which is +0 (0x0000).

   RFC 1141 yields an updated header checksum of -0 when it should be
   +0.  This is because it assumed that one's complement has a
   distributive property, which does not hold when the result is 0 (see
   derivation of [Eqn. 2]).

   The problem is avoided by not assuming this property.  The correct
   equation is given below:

          HC' = ~(C + (-m) + m')    --    [Eqn. 3]
              = ~(~HC + ~m + m')

4.  Examples

   Consider an IP packet header in which a 16-bit field m = 0x5555
   changes to m' = 0x3285.  Also, the one's complement sum of all other
   header octets is 0xCD7A.

   Then the header checksum would be:

          HC = ~(0xCD7A + 0x5555)
             = ~0x22D0
             =  0xDD2F

   The new checksum via recomputation is:

          HC' = ~(0xCD7A + 0x3285)
              = ~0xFFFF
              =  0x0000

   Using [Eqn. 2], as specified in RFC 1141, the new checksum is
   computed as:

          HC' = HC + m + ~m'
              =  0xDD2F + 0x5555 + ~0x3285
              =  0xFFFF

   which does not match that computed from scratch, and moreover can
   never obtain for an IP header.

Rijsinghani                                                     [Page 3]
RFC 1624             Incremental Internet Checksum              May 1994

   Applying [Eqn. 3] to the example above, we get the correct result:

          HC' = ~(C + (-m) + m')
              = ~(0x22D0 + ~0x5555 + 0x3285)
              = ~0xFFFF
              =  0x0000

5.  Checksum verification by end systems

   If an end system verifies the checksum by including the checksum
   field itself in the one's complement sum and then comparing the
   result against -0, as recommended by RFC 1071, it does not matter if
   an intermediate system generated a -0 instead of +0 due to the RFC
   1141 property described here.  In the example above:

          0xCD7A + 0x3285 + 0xFFFF = 0xFFFF
          0xCD7A + 0x3285 + 0x0000 = 0xFFFF

   However, implementations exist which verify the checksum by computing
   it and comparing against the header checksum field.

   It is recommended that intermediate systems compute incremental
   checksum using the method described in this document, and end systems
   verify checksum as per the method described in RFC 1071.

   The method in [Eqn. 3] is slightly more expensive than the one in RFC
   1141.  If this is a concern, the two additional instructions can be
   eliminated by subtracting complements with borrow [see Sec. 7].  This
   would result in the following equation:

          HC' = HC - ~m - m'    --    [Eqn. 4]

          In the example shown above,

          HC' = HC - ~m - m'
              =  0xDD2F - ~0x5555 - 0x3285
              =  0x0000

6.  Historical Note

   A historical aside: the fact that standard one's complement
   arithmetic produces negative zero results is one of its main
   drawbacks; it makes for difficulty in interpretation.  In the CDC
   6000 series computers [4], this problem was avoided by using
   subtraction as the primitive in one's complement arithmetic (i.e.,
   addition is subtraction of the complement).

Rijsinghani                                                     [Page 4]
RFC 1624             Incremental Internet Checksum              May 1994

7.  Acknowledgments

   The contribution of the following individuals to the work that led to
   this document is acknowledged:

          Manu Kaycee - Ascom Timeplex, Incorporated
          Paul Koning - Digital Equipment Corporation
          Tracy Mallory - 3Com Corporation
          Krishna Narayanaswamy - Digital Equipment Corporation
          Atul Pandya - Digital Equipment Corporation

   The failure condition was uncovered as a result of IP testing on a
   product which implemented the RFC 1141 algorithm.  It was analyzed,
   and the updated algorithm devised.  This algorithm was also verified
   using simulation.  It was also shown that the failure condition
   disappears if the checksum verification is done as per RFC 1071.

8.  Security Considerations

   Security issues are not discussed in this memo.

9.  Conclusions

   It is recommended that either [Eqn. 3] or [Eqn. 4] be the
   implementation technique used for incremental update of the standard
   Internet checksum.

10.  Author's Address

   Anil Rijsinghani
   Digital Equipment Corporation
   550 King St
   Littleton, MA 01460

   Phone: (508) 486-6786
   EMail: anil@levers.enet.dec.com

Rijsinghani                                                     [Page 5]
RFC 1624             Incremental Internet Checksum              May 1994

11.  References

   [1] Postel, J., "Internet Protocol - DARPA Internet Program Protocol
       Specification", STD 5, RFC 791, DARPA, September 1981.

   [2] Braden, R., Borman, D., and C. Partridge, "Computing the Internet
       Checksum", RFC 1071, ISI, Cray Research, BBN Laboratories,
       September 1988.

   [3] Mallory, T., and A. Kullberg, "Incremental Updating of the
       Internet Checksum", RFC 1141, BBN Communications, January 1990.

   [4] Thornton, J., "Design of a Computer -- the Control
       Data 6600", Scott, Foresman and Company, 1970.

Rijsinghani                                                     [Page 6]