Comments on: Jam Resistant Communication Without a Shared Key

By: William L. Bahn

William L. Bahn — Thu, 20 May 2010 04:56:17 +0000

As already noted, the probability of a hallucination making it thorugh the decoding process can be made arbitrarily small. For a packet with a 33% mark density and an encoding that specifies 32 checksum bits, the likelihood of a hallucination that exists at the end of the message bits is (1/3)^32 or 5.4e-16 (1 in 1853 trillion).

What is not as obvious is that the chance of a message that survives the checksum bits containing any errors at all is even less, so the receiver can safely assume that all received messages are error free. In other words, messages are either received correctly, or not received at all. As a result, there is no point in adding any form of error detector or correction within a message, but for traffic consisting of multiple messages (as would almost always be the case) you can add additional messages that enable you to recover from some specified minimum number of lost messages.

By: anonymous

anonymous — Wed, 03 Feb 2010 23:46:29 +0000

All communications have some probability of error. Both through wires and wireless. You can never be 100% sure your message got through, no matter what algorithms you use. But with checksums etc., you can make the probability of undetected errors to be exponentially small. BBC avoids errors in exactly the same way.

And all crypto has that same kind of probabilistic security (except the OTP). If you encrypt a message with AES-256, an attacker could randomly guess your key in a single try. But the probability of that happening is 2^-256. That’s astronomically low (for comparison, there are only 2^266 atoms in the visible universe). So it’s practically impossible to break AES-256 using that attack, for all practical purposes. BBC is the same.

By: Hysun

Hysun — Tue, 15 Dec 2009 01:08:37 +0000

This is brilliant! I’m slowly making my way through Schneier’s _Applied Cryptography_, so it’s cool to see what’s new in the crypto world.

One thing that bothers me, though, is the problem of the “hallucinations,” which are basically false-positives. Even though a reasonably sized checksum would make it highly unlikely, it will always be possible that a hallucination is decoded and mistaken for the intended message. Still, the chances are so low that I’m sure it is an acceptable margin of error for 99% of the applications out there.

Very cool.