Re: The Elevator Problem

[Tim Dierks <timd@consensus.com>]

At 7:50 PM 6/2/96, Deranged Mutant wrote:
>Alice and Bob are in a crowded place and want to confirm they share a
>secret.
>
>Each picks a couple of random numbers, b and i.  The secret P is
>hashed i times, something like:
>
>  H_0(P) = H(P,0)               [H can be something like SHA-1...]
>  H_i(P) = H(H_i-1(P), i)
>
>They then tell each other bit b of H_i(P).
>
>This is repeated a number of times to make random guessing very
>unlikely.
>
>If all bits match, they agree that they share the secret (we assume
>neither wants to lie but discover if the other knows the secret).

It doesn't seem to me like it needs to be this complex. Here's a couple of
protocols I can think of:

For a secret S:

Alice and Bob generate and exchange random nonces. Then they calculate the
HMAC of S using the other's nonce as the MAC secret. They exchange HMACs
and each verify that their peer has correctly calculated the HMAC given the
secret and the nonce.

 - or -

Each of Alice and Bob hash S and use the result as a symmetric encryption
key; they then attempt to exchange messages. If they can exchange messages,
they must have arrived at the same key, and thus be using the same S. To
avoid replay attacks, exchange nonces and use them as a part of the key
calculation.

Note that neither of these reveals that you know S unless your peer knows
S; noone who doesn't know S can determine if Alice or Bob actually know S
or if they're using some other faked value (except for analysis of the
repercussions of the exchange).

 - Tim

Tim Dierks  --  timd@consensus.com  --  www.consensus.com
Head of Thing-u-ma-jig Engineering, Consensus Development