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Date: Thu, 11 Sep 2014 11:26:28 -0700
From: Alex Elsayed <eternaleye@...il.com>
To: discussions@...sword-hashing.net
Subject: Re: Re: Re: Re: Re: Re: Second factor (was A review per day - Schvrch)

Alex Elsayed wrote:

> Mm, with the parallel PAKE we've latched P as a necessary part of the
> protocol, so _here_ your original idea of passing H(P) to the token, which
> it uses to encrypt its (internal) value, would not weaken the scheme in
> the case of a malicious token.
> 
> Given token T holding secret X, user U holding password P, and server S:
> 
> U -> T: H(P)
> T -> U: Y = E(k=X, H(P))
> T -> S: R_t = PAKE(X)
> U -> S: R_u = PAKE(Y)
> T -> U: R_t
> U: K = R_t ^ R_u

After I posted the correction to this yesterday, I realized that there's an 
even more optimal approach combining this with my original scheme. It 
satisfies all of the properties you brought up, _and_ the property I'd like 
that the server doesn't even need to know that a token is in use at all 
(permitting a user to add a token to any account they want to) - without 
requiring any local storage on the user's machine.

Let E( K, M ) be an encryption function with key K and message M
Let H( M ) be a hash of a message M
Let sizeof( H( A ) ) == sizeof( K in E( K, B ) ) for all A and B

Given:
    Token T holding secret X
    User U holding password P and pin N
    Server S

1.) U and T establish a channel C by executing a PAKE over N
2.) U sends H(P) to T over C
3.) T computes Y = E( H(P), X ) and sends it to U over C
4.) U computes Z = E( Y, P )
5.) U and S execute a PAKE over Z

I believe this is secure for arbitrary E, H, and augmented PAKE.

Step 1 ensures that without knowing N, the token is useless - it also 
protects against someone eavesdropping the bus the token is on.

In addition, it provides for the option of the "token" being no such thing, 
and instead being some kind of server itself, or the token protocol being 
relayed by a system daemon of some sort.

Step 2 and 3 ensure that without knowing P, the token must be queried for 
each attempt

Step 4 latches P (as opposed to H(P)) as necessary for the protocol, 
limiting the damage that a malicious token can do

Because Z depends on X, which should be strong randomness, the server can't 
attempt dictionary attacks against the verifier it holds.

Finally, the number of round-trips over the network is exactly the same as a 
single execution of the PAKE, and a user who knows P can cache Y in order to 
save on queries to the token.

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