-----BEGIN PGP SIGNED MESSAGE----- On Sat, 29 Jun 1996, Andrew Tridgell wrote:
I've recently released a package called rsync that uses a checksum search to provide very efficient file update over a slow link. (see ftp://samba.anu.edu.au/pub/rsync if you are interested)
Now I'd like to calculate some probabilities of failure of the algorithm. The fundamental thing I need to know to do the calculation is the probability of a random piece of data of length n having the same md4 checksum as another given piece of data of the same length.
MD4 is a hashing algorithm, but it can be used for checksuming.
A first guess might be 2^-128 but I know that this sort of thing is rarely that simple. Is md4 that good?
2^-64.
Note that I am not interested in "attacks" on md4 as such as the source of the random data is just another file provided by the same user, so it won't have been specially designed to defeat md4.
If the probability is within a few orders of magnitude of 2^-128 then can I also be sure that if I only use the first b bits of a md4 checksum it will be within a few orders of magnitude of 2^-b ? There is an option in rsync to use a shorter checksum by truncating md4. This saves some bytes on the link at the risk of lowering the confidence.
The probability of failure is 2^-(b/2).
Why md4? I chose md4 because it seemed to be the fastest of the reputedly strong, publicly available checksum algorithms. Suggestions for alternative algorithms are welcome.
So far, MD4 is the fastest hashing algorithm. - -- Mark =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= markm@voicenet.com | finger -l for PGP key 0xe3bf2169 http://www.voicenet.com/~markm/ | d61734f2800486ae6f79bfeb70f95348 "Freedom is the freedom to say that two plus two make four. If that is granted, all else follows." --George Orwell, _1984_ -----BEGIN PGP SIGNATURE----- Version: 2.6.3 Charset: noconv iQCVAwUBMdVlv7Zc+sv5siulAQG0SAP9HyybTTn/ffPLhPgtooxP/abIQYZ2r6sI PW90ilTucWMNjFQ87Xl+MUUysklG4G1zx+i3ZnIP5ud3D69kh+E6s2MbvUKcOFUi TKAmB5rVSGHOvDROnY5cBGU7iSCxgiM5auq5rSu6/MvwtvSf99VtKh9UdcFp2SuH u4ukZmAE1x0= =otP1 -----END PGP SIGNATURE-----