Thursday, June 11, 2015

Is HD=1 Useful?

I received an e-mail with a question as to why a HD=1 checksum would ever be useful (referred to on slide 89 of my Sept 2014 slide set on CRCs).  The point is that HD=1 means you are not guaranteeing detection of any error, not even 1-bit errors.  Here's my answer, which I am posting since it might have general interest:.

HD=1 (zero errors guaranteed to be detected) means that there is still a residual capability to randomly detect most errors (all errors except 1 in 2**k for k bits).
If you only need an error detection ratio of a few orders of magnitude this is fine if you have a large CRC.

If you are using a 256 bit cryptographic checksum (which must be assumed to have HD=1) then undetected error probability is 1 in 2**256, which is pretty good.  However, a high-HD CRC will usually get you better non-malicious error detection for less computational cost.