On Fri, Nov 18, 2016 at 7:40 AM, Paul Koning <paulkon...@comcast.net> wrote:
> I don't know enough math to do the work, but a little rubbed off from > listening to those who do. > > CRC polynomials have special properties, they aren't arbitrary > polynomials. That reduces the number of possible choices dramatically. In > fact, I remember that finding a good one is hard work; > Finding only "good" polynomials and then testing those against the data is far more work than doing the brute-force search of all order-n polynomials that have a relatively small number of terms including x^0. However, National might not have restricted their search to a small number of terms, which had been done in the early days to minimize hardware (number of XOR gates, and resulting depth of XOR tree). By the mid-1980s that was less of a concern. There is some evidence that using an order n polynomial with roughly n/2 terms may typically be stronger than order n polynomials with few terms, in which case a brute force search for a 56 bit polynomial becomes almost completely intractable, short of a distributed search on a large number of machines with GPUs. > I would assume this means you can deduce the CRC polynomial by > straightforward math from a few well chosen test data blocks. > If I had the hardware that wrote the disk in question, there are a lot of things I could do, including that. I may have to tell the owner of the disk drive that I can give him the uncorrected data only.
