Re: [Cfrg] SPM2 -> was Re: SPAKE2+mbDH a PAKE+PKA

"Stanislav V. Smyshlyaev" <smyshsv@gmail.com> Wed, 05 October 2016 05:55 UTC

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References: <D41831C3.A2964%paul@marvell.com> <CAMr0u6k4U0fsXV2jHxam6Lk0OmmDS1NkV9Z43QF3sjJinW7fPQ@mail.gmail.com> <CAMr0u6ngTf+_eW_qhVz0G_jUNHUqPEMyQO+4A3xrqCh2tRe6FQ@mail.gmail.com> <D418A094.A29E7%paul@marvell.com> <CAMr0u6mUWxjqZbFBriMv8wDnmsWU6g2SBm3vnvOhX=B2rRF3aQ@mail.gmail.com> <c5853319-cfa5-1180-38ce-3fb438df8151@lounge.org>
From: "Stanislav V. Smyshlyaev" <smyshsv@gmail.com>
Date: Wed, 5 Oct 2016 08:55:32 +0300
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To: Dan Harkins <dharkins@lounge.org>
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Subject: Re: [Cfrg] SPM2 -> was Re: SPAKE2+mbDH a PAKE+PKA
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Hello, Dan!

mbDH (without modifications to SPM2) allows mutual authentication by
private keys s_A and s_B in case the parties obtain trusted (i.e. obtained
by a well-authenticated channel before the mbDH itself, of course) P_A and
P_B – as well as ordinary authenticated DH.

The thing I am talking about is that SPM2 seems not to provide it – Alice,
who has a valid Bob's P_B, can be tricked by an adversary who doesn't have
a correct s_B and has only the password.


Regards,
Stanislav



2016-10-05 8:45 GMT+03:00 Dan Harkins <dharkins@lounge.org>rg>:

>
>   Privyet Stanislav,
>
> On 10/4/16 9:56 PM, Stanislav V. Smyshlyaev wrote:
>
> Dear Paul!
>
>
> Thank you very much for the corrections.
>
>
> I. In the sense of PAKE everything seems to be OK now: now the proposed
> protocol is at least as strong as SPAKE2 itself – since  SPAKE2 + mbDH for
> certain values of parameters is reduced to SPAKE2. Since the first part
> of SPAKE2 (key agreement itself) is proven to be secure, we may say that
> SPM2 should be a secure PAKE. Nevertheless a separate accurate proof would
> be interesting anyway – but I think this is not the thing we should care
> now about SPM2, there seems to be a lot more important problem.
>
>
>
> II. The problem is SPM2 in the case of known password seems to be less
> secure than mbDH (it seems to be unsecure at all in this case).
>
>
>   What security properties do you believe mbDH has beyond simple DH-- i.e.
> unauthenticated key agreement?
>
>   Dan.
>
>
> Consider the following attack (thanks to my colleague Liliya Ahmetzyanova for
> the description)
>
> Let the adversary who tries to impersonate himself as B, knows password w,
> but doesn't possess private key s_B and wants to make honest party A
> believe that he does it for some fixed value of P_B.
>
>
>
> 1.       A sends the values R_A, Y_A, where
>
> R_A = x_A * G + w * M_A;  (according to the protocol description)
>
> Y_A = y_A * P_A = y_A * s_A * G; (according to the protocol description)
>
> 2.       The adversary calculates for random x_B and y_B the values
>
> Y_B = y_B * P_B;
>
> R_B = x_B * G + w * M_B *– Y_B*;
>
> K = x_B * (R_A – w * M_A) + x_B * Y_A       (     =     x_B * (x_A * G) +
> x_B * (y_A * s_A * G));
>
> Then all actions are made according to the protocol.
>
> 3.       A calculates K according to the protocol:
>
> K = (x_A + y_A * s_A)(R_B – w * M_B + Y_B)    (    =    (x_A + y_A *
> s_A)(x_B * G)  );
>
> The key K is equal to the key of adversary = > decryption will be correct
> => the check
>
> assert Y_B == y_B * P_B will be successful;
>
>
> Thus SPM2 is not secure in the same case as mbDH is – it loses all
> private-key-related security when the password is known.
>
> Again, Paul, please correct me if I missed something.
>
>
>
> Best regards,
> Stanislav Smyshlyaev
>
>
> 2016-10-04 10:44 GMT+03:00 Paul Lambert <paul@marvell.com>om>:
>
>>
>>
>>
>> Dear Stanislav,
>>
>>
>> Just a small remark: I'm sure that in the second message you wanted to
>> send "encrypt( key=sk_BA, ((y_B, P_B), ...) )", not "encrypt( key=sk_BA,
>> ((x_B, P_B), ...) )" (and "y_A, P_A" correspondigly). Otherwise you would
>> obtain exactly the same problem as before.
>>
>>
>> Thanks! I missed making this variable change … appreciate your catching
>> this error.
>>
>> This update also made the shared key calculation more exactly match the
>> SPAKE2 RFC and I missed changing the terms in this hash in a couple places.
>>
>> These are now fixed in: https://mentor.ieee.org/80
>> 2.11/dcn/16/11-16-1329-01-00ai-pkex-alternatives.ppt
>>
>> Best Regards,
>>
>> Paul
>>
>
>
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