Can a TCP checksum fail to detect an error? If yes, how is this dealt with?

Question

If a TCP payload gets corrupted in transit the recomputed checksum won\'t match the transmitted checksum. Great, all fine so far.

If a TCP checksum gets corrupted in

Answer 1

Assume

packet payload: 1000 byte

packet checksum: 2 byte

probability of packet with double error, one of wchich in checksum (assume P very small, less than 1/10^5):

A = 8P*(1000*8P) = 6*10^4 * P^2

probability of exact checksum:

B = 1/2^16 = 6/10^4

probability of false positive:

A * B = 40 * P^2 

The probability is low (P=1/10^6, then the probability of false positive A*B=4/10^11) but in any case with any crc algorithm it can't be zero. The probability of a random 1000 byte packet to appear as another random 1000 byte packet is P^8000, as if all bytes contain errors.

If P is high, for example from 1/10^3 to 1, the calculations above does not apply. In that case A=1 (all packets contain double errors) and the probability of false positive is just A*B = 6/10^4. It's not a very relevant case because more than 99% of received packets will contain errors in crc.