Re: Coding Theory Question, I think


"Thinus Pollard" <thinus@xxxxxxxxxxxxx> wrote in message
news:dg6cbk$cdj$1@xxxxxxxxxxxxxxxxxxxxx
> Nope, I did some abstract algebra a few years ago where we did some coding
> theory.
>
> The system issues tickets. Each ticket contains a PIN. This PIN needs to
> be
> unique and only I should be able to issue valid PINs.
>
> The PIN contains an issue date, an expiry date, a unique serial number and
> an amount. All this data should be encoded into a 16 *digit* string.
>
> Validation should take the following form:
> 1. When entered the system should check if the entered string is valid.
> This
> is easy, use 15 digits and append a check as the 16th.
> 2. When verified the system should check if the data inside the PIN "makes
> sense".
>
> I was thinking about packing all the data into some bits and then
> encrypting
> it with a cipher (public key or symmetrical). The problem with this idea
> is
> how to map the data to a 15 digit string, without losing information? From
> the 16 digits you should be able to extract the information if you have
> the
> cypher keys.

Keep error correcting coding and cryptography concepts separate.

Error correcting coding in the communications sense would use a Reed-Solomon
or BCH code to represent your data as an expanded string of symbols. Any
book on coding theory or http://en.wikipedia.org/wiki/Error-correcting_code
will have options in the appendix which will fit your requirements.
Basically you need a MxN coding matrix H, M>>N, such that if your data
string is N-length vector X the coded output is M-length vector Y = HX; the
product done in some modulo number field. For an RS code with base 256 you
will need three decimal digits or two hex digits to print each symbol.
Decoding in the presence of errors is a bit messy but basic error detection
without correction is easy.

To encrypt this coded string, is a different matter,
http://en.wikipedia.org/wiki/Encryption and depends on the level of
protection required.

rusty


.

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