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+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.
+
+Abstract
+
+   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
+
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+   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
+
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+Rijsinghani                                                     [Page 5]
+
+RFC 1624             Incremental Internet Checksum              May 1994
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+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.
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+Rijsinghani                                                     [Page 6]
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