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List:       cfrg
Subject:    Re: [Cfrg] =?iso-8859-1?q?=A1=B0password-based_key_exchange=A1=B1revi?= =?iso-8859-1?q?sited?=
From:       "Dan Harkins" <dharkins () lounge ! org>
Date:       2012-05-28 4:35:40
Message-ID: a43e20169b5eb6135fbb4e8a5418ae00.squirrel () www ! trepanning ! net
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  Hello,

  Thank you very much for your analysis of my protocol.

On Thu, May 24, 2012 6:39 pm, zhou.sujing@zte.com.cn wrote:
> As in the calculation of "K = PE^(peer_rand*local_rand) mod p"
> K can be reduced to PE^(peer_scalar*local_scalar+local_mask*peer_mask)
> *(peer_element)^(local_scalar)*(local_element)^(peer_scalar) mod p
>
> K = PE^(peer_rand*local_rand) mod p
>    =PE^[( peer_scalar-peer_mask)*(local_scalar-local_mask)] mod p
>
> =PE^(peer_scalar*local_scalar-peer_mask*local_scalar-local_mask*peer_scalar+local_mask*peer_mask)
> mod p
>    =PE^(peer_scalar*local_scalar+local_mask*peer_mask)
> *(peer_element)^(local_scalar)*(local_element)^(peer_scalar) mod p
>
> Because  (peer_element)^(local_scalar)*(local_element)^(peer_scalar) can
> be calculated directly from the key exchange message,
> the effective part of K is
> PE^(peer_scalar*local_scalar+local_mask*peer_mask), has nothing to do with
>  local_rand and peer_rand,
> so the password based key exchange is essentially equal with the following
> "exchange"£º

  The problem with this is that peer_mask is unknown so it is not possible
to reduce computation of K in this manner.

> 2'. generate 2 random numbers between 0 and the order of the group, q:
>
>    0 < local_mask,local_scalar < q
>
> 3'. compute an element:
>    local_element = 1/(PE^local_mask) mod p
>
>    where p is the prime and q is the order. Send local_scalar and
>    local_element to other side
>
> 4'. receive peer_scalar and peer_element from other side
>
> 5'. compute shared key, K
>
>    K =PE^(peer_scalar*local_scalar)* (peer_element)^(-local_mask) mod p
>      =PE^(peer_scalar*local_scalar+local_mask*peer_mask) mod p
>
> It is simpler and less computation invloved, and hopefully easier to
> analysis the security.

  PE^(peer_scalar*local_scalar) is completely extraneous. This is just
a standard diffie-hellman with peer_mask and local_mask as the private
contributions using, presumably, a password-derived generator (you
don't actually say). The exchange above has received quite a bit of
analysis already: it's the SPEKE protocol.

  regards,

  Dan.

> From: "Dan Harkins" <dharkins at lounge.org>
> Date: Tue, 20 Dec 2011 13:38:09 -0800 (PST)
>   Hello,
>
>   I proposed a new TLS ciphersuite using a zero knowledge proof at
> IETF 82 in Taipei. The draft is here:
>
>        http://tools.ietf.org/html/draft-harkins-tls-pwd-01
>
> At the TLS WG meeting I was requested to ask people on the CFRG list
> with expertise in this field to take a look at it. So here I am, asking.
> If someone has some spare cycles this holiday season, if you just gotta
> get away from the relatives, or you are just feeling in the giving mood,
> please take a look and comment. Any analysis on this would be greatly
> appreciated. (I tried to do a formal proof but I cannot, and that's
> what's prompting this).
>
>   I can describe the key exchange broadly here. There are subtle
> differences in the draft-- like one side keeps a salted version of the
> password and communicates the salt during a HELLO message-- that don't
> affect the exchange. It is symmetric so I can describe it from one side's
> perspective. The side being described is "local" and the other side is
> "peer", it goes like this:
>
> Given: local ID, peer ID, password, an agreed-upon set of domain
> parameters defining a finite field group (it works will elliptic
> curve crypto too) and using two function:
>
>   - E = HashToElement(d) which takes some data, d, and hashes into
>     the finite field to return an element, E.
>   - x = H(y) returns a random stream, x, given some input, y.
>
> The key exchange works like this:
>
> 1. PE = HashToElement(local_ID | peer_ID | password)
>    gets a "password element"
>
>    There is an ordering defined in the draft to ensure that the IDs
>    are put in the same order on each side.
>
> 2. generate 2 random numbers between 0 and the order of the group, q:
>
>    0 < local_rand, local_mask < q
>
> 3. compute a scalar and an element:
>    local_scalar = (local_rand + local_mask) mod q
>    local_element = 1/(PE^local_mask) mod p
>
>    where p is the prime and q is the order. Send local_scalar and
>    local_element to other side
>
> 4. receive peer_scalar and peer_element from other side
>
> 5. compute shared key, K
>
>    K = (PE^peer_scalar * peer_element)^local_rand mod p =
>        (PE^(peer_rand + peer_mask) * PE^(-peer_mask))^local_rand mod p =
>        PE^(peer_rand*local_rand) mod p
>
> 6. compute a confirmation
>
>    local_confirm = H(K, local_scalar | local_element |
>                      peer_scalar | peer_element)
>
>    send confirmation to peer
>
> 7. receive peer's confirmation, calculate verifier
>
>    verifier = H(K, peer_scalar | peer_element | local_scalar |
>                 local_element)
>
>    if verifier equals peer's confirmation the peer is authenticated.
>
> The peer does the same thing but from its perspective it is "local"
> and the side described above is "peer".
>
>   Thank you in advance for any analysis that can be provided on this
> exchange.
>
>   regards,
>
>
>
>
>
>
>
>
>
>
> Regards~~~
>
> -Sujing Zhou
>



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