At this moment I'm using a simple checksum scheme, that just adds the words in a buffer. Firstly, my question is what is the probability of a false negative, that is, the receiving system calculating the same checksum as the sending system even when the data is different (corrupted).
Secondly, how can I reduce the probability of false negatives? What is the best checksuming scheme for that. Note that each word in the buffer is of size 64 bits or 8 bytes, that is a long variable in a 64 bit system.
Assuming a sane checksum implementation, then the probability of a randomly-chosen input string colliding with a reference input string is 1 in 2n, where n is the checksum length in bits.
However, if you're talking about input that differs from the original by a low number of bits, then the probability of collision is generally much, much lower.