RFC 1624 (rfc1624) - Page 2 of 6
Computation of the Internet Checksum via Incremental Update
Alternative Format: Original Text Document
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