Crypto suggestion - re: Fatal Flaws in Credit Cards

[Bill Stewart <stewarts@ix.netcom.com>]

Nathaniel's written about the "fatal flaw" in any system that
involves typing credit card numbers into your computer being that
they're easy for a keyboard-sniffer or similar cracker to recognize.
An obvious work-around for this (and for many of the problems with
Social Security / Taxpayer ID numbers) is to use some sort of smartcard
that generates one-shot numbers that the credit card company (or tax thugs)
can map back to the "real" owner's ID.  The downside of this approach
is that you need a lot of bits to support it, since you have to accomodate
the expected number of users * the average uses/user + overhead,
and that may (for credit cards) be annoyingly long to type in
(though fine for electrical-interface cards, or cards that display
their numbers as barcodes for a wand reader, or whatever.)

Some potential algorithms:
1) public-key - 512 bits isn't really enough (cracking it doesn't necessarily
        let you charge to everybody's Visa number, but it does let you
        figure out what everybody's is), and that's already too long.

2) data-base of randomly generated numbers - the would do ok for SSNs;
        give everybody a dozen or two, and let them get more if
        they want.  That wouldn't even require a smartcard, but it
        would tend to require a SSN card that you don't lose,
        since you probably won't remember the dozen long numbers on the back.
        This would of course require redesigning all those databases
        that know an SSN is 9 digits long - I view this as a Good Thing,
        especially since it may get people to stop using them as database keys.

        Is it practical for credit cards?  Ten billion customers times
        a million uses each is 16 digits; I suppose that's not much longer
        than current card numbers, though each card company would need to
        keep track of more numbers.  You'd probably cache a hundred or a
thousand
        in the card, and update the card every couple of years?

3) Some kind of hash or secret-key encryption of a constant (your "real"
card number)
        and a random number?  This would still be susceptible to brute-force
        search (10**20 not being an exceptionally large number), and you'd
        need an algorithm with either zero or a very low probability of
        collisions.  A secret-key version would require a tamper-proof card
        to reduce probability of theft, and I'm not sure I believe in
        tamper-proof cards, even if you have a lot of keys and a salt
        that tells the credit-card company which key to use.

Any other suggestions?
        
#--
#				Thanks;  Bill
# Bill Stewart, stewarts@ix.netcom.com, Pager/Voicemail 1-408-787-1281
# http://www.idiom.com/~wcs