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Re: Size of a CRC (or similar) code for a given length of message

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On 25/09/15 13:07, Julio Di Egidio wrote:
> On Friday, September 25, 2015 at 10:59:47 AM UTC+1, James Harris
> wrote:
>> I see from
>> 
>> https://en.wikipedia.org/wiki/Cyclic_redundancy_check
>> 
>> that, typically, an n-bit CRC applied to a data block of arbitrary
>>  length will detect a single error burst up to n bits long.
>> 
>> That's fine - or as fine as the complex mathematics of CRCs gets! -
>> but if looking to select a CRC calculation (or some other data
>> integrity check) are there any guidelines on how wide the CRC code
>> should be for given levels of assurance against random corruption
>> for a given size of message?
>> 
>> At the moment I am looking to protect a very short header of about
>> 12 bytes, give or take, and wonder what levels of confidence a
>> certain number of CRC bits would give against data corruption.
>> 
>> For example, if I used a 3-bit CRC to protect a 12-byte header how
>>  'good' would that be compared to a 5-bit CRC? And if the header
>> became 24 bytes, say, what effect would that have on the
>> effectiveness of 3-bit and 5-bit CRCs? (Always assuming that other
>> aspects of the CRC calculation are chosen well.)
>> 
>> If I later wanted to protect a message of a thousand or a 
>> hundred-thousand bytes how wide would the CRC need to be to
>> maintain a similar level of confidence?
>> 
>> Any ideas?
> 
> If you want 100% confidence, send the whole message twice.  CRC is
> like hashing, a trade-off.  Unless the message is short enough...
> 

These things are always a trade-off, but sending the message twice is
certainly not any kind of a guarantee.  Generally speaking, sending a
message twice is less useful than sending a CRC - if there are any
systematic causes for corruption, you'll get the same incorrect message
each time.  There are times when you might want to send the message
twice - but the best thing to do there would be to have a CRC as well,
preferably a different CRC (such as a different seed, or some added
salt) on each copy.

The most appropriate choice for error detection and possibly error
correction mechanism will depend entirely on the circumstances.

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Size of a CRC (or similar) code for a given length of message James Harris <james.harris.1@gmail.com> - 2015-09-25 10:59 +0100
  Re: Size of a CRC (or similar) code for a given length of message David Brown <david.brown@hesbynett.no> - 2015-09-25 13:05 +0200
    Re: Size of a CRC (or similar) code for a given length of message James Harris <james.harris.1@gmail.com> - 2015-09-25 13:42 +0100
      Re: Size of a CRC (or similar) code for a given length of message David Brown <david.brown@hesbynett.no> - 2015-09-25 15:15 +0200
  Re: Size of a CRC (or similar) code for a given length of message Julio Di Egidio <julio@diegidio.name> - 2015-09-25 04:07 -0700
    Re: Size of a CRC (or similar) code for a given length of message David Brown <david.brown@hesbynett.no> - 2015-09-25 14:32 +0200
      Re: Size of a CRC (or similar) code for a given length of message Julio Di Egidio <julio@diegidio.name> - 2015-09-25 05:40 -0700
    Re: Size of a CRC (or similar) code for a given length of message James Harris <james.harris.1@gmail.com> - 2015-09-25 13:45 +0100
  Re: Size of a CRC (or similar) code for a given length of message Öö Tiib <ootiib@hot.ee> - 2015-09-25 04:17 -0700
    Re: Size of a CRC (or similar) code for a given length of message David Brown <david.brown@hesbynett.no> - 2015-09-25 14:36 +0200
      Re: Size of a CRC (or similar) code for a given length of message James Harris <james.harris.1@gmail.com> - 2015-09-25 13:49 +0100

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