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

Dan Harkins <dharkins@lounge.org> Wed, 05 October 2016 05:45 UTC

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To: "Stanislav V. Smyshlyaev" <smyshsv@gmail.com>, Paul Lambert <paul@marvell.com>
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>
From: Dan Harkins <dharkins@lounge.org>
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Date: Tue, 4 Oct 2016 22:45:16 -0700
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Subject: Re: [Cfrg] SPM2 -> was Re: SPAKE2+mbDH a PAKE+PKA
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   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 toSPAKE2. 
> 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 valuesR_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 andy_Bthe 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 Kaccording 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 Kis equal to the key of adversary = > decryption will be 
> correct => the check
>
> assertY_B == y_B * P_Bwill 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 
> <mailto:paul@marvell.com>>:
>
>
>
>
>     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/802.11/dcn/16/11-16-1329-01-00ai-pkex-alternatives.ppt
>     <https://mentor.ieee.org/802.11/dcn/16/11-16-1329-01-00ai-pkex-alternatives.ppt>
>
>
>     Best Regards,
>
>     Paul
>
>
>
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