Playing Cards - Caution!

[ph@netcom.com (Peter Hendrickson)]

A few days ago I suggested that playing cards are a good source
of entropy.  This was based on claim by Persi Diaconis which
was quoted in The Economist.

I've researched the claim and I now believe it would be wise not to
use playing cards as a source of entropy for cryptographic
applications.

A fully random deck of 52 cards has about 225 bits of entropy.  That
means that each riffle shuffle introduces about 32 bits of entropy.
Intuitively, that seems like a lot of entropy for one riffle shuffle.
I've tried a few riffle shuffles with a sorted deck.  While hardly
scientific, the level of randomness does not look like 32 bits.  Most
of the time the cards alternate.

The claim that 7 riffle shuffles of a deck of 52 cards will bring
the deck to a state of near randomness appears in this book:

Diaconis, Persi "Group Representations in Probability and Statistics"
Hayward, California: Institute of Mathematical Statistics, 1988.
ISBN 0-940600-14-5

The section "An Analysis of Real Riffle Shuffles" begins on page 77.

A model is presented which Diaconis believes is similar to how people
shuffle in real life.  What is troubling from a cryptographic point of
view is that there is little empirical evidence to back this up.  What
is more, Diaconis mentions that there is some variation in shufflers.
A neat shuffler will be less random.  (Side note: The Economist claims
Diaconis can execute 8 perfect shuffles in less than a minute.  This
means the deck is returned to its original order!)

>From the point of view of cryptography, neatness is not a very precise
term and should not be relied upon.

The book says that in the late 1960s, tournament bridge players
started using computers (!) to shuffle the cards as hand shuffling was
considered suspect.  This is less than reassuring.

Nothing I have written here is intended to reflect poorly on Dr.
Diaconis.  We were not solving the same problem, nor have I fully
understood his work.

In my first article I said this:

"Playing cards are a nice source of randomness because they are widely
available and their behavior has been under study for a long time by
people with strong financial reasons for finding flaws.  I slightly
prefer cards to dice because dice may be slightly predictable or even
loaded."

The study of randomness in cards looks much harder to me now.  Also,
flaws which may be exploitable for financial reasons when real money
is on the table may have to be substantially more dramatic than the
flaws required to exploit, for instance, an alleged one-time pad.

Here's why I now prefer dice: Dice are simple.  Each die throw can be
made to be quite independent of all other die throws.  Even loaded dice
may be used by throwing them repeatedly and adding the results mod the
number of sides to the die.  Dice which are suspect may be studied by
repeated throwing.  Non-independence can be more easily studied as
it can be assumed that a throw of the die is, at most, related only
to the previous throw and none before.

Peter Hendrickson
ph@netcom.com