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Date: Thu, 11 Sep 2014 11:31:46 -0700
From: Andy Lutomirski <luto@...capital.net>
To: discussions <discussions@...sword-hashing.net>
Subject: Re: [PHC] Re: Re: Re: Re: Re: Re: Second factor (was A review per day
 - Schvrch)

On Thu, Sep 11, 2014 at 11:26 AM, Alex Elsayed <eternaleye@...il.com> wrote:
> 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

This step loses the property that a malicious token doesn't weaken
security over no token at all -- a malicious token can do an offline
dictionary attack on the password.

I'll try to write up a formal statement of my personal desiderata for
token-assisted PAKE next week :)

--Andy

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