Re: [IPsec] PAKE selection: SPSK

  Hi Dennis,

  The issue here is the meaning of a "plurality of key distribution
techniques."

  You say, "[d]ue to the group generator SKE, a pluralty of key
distribution techniques is defined - one for each possible (and secret)
value of SKE." That's not what the patent is talking about. The "plurality
of key distribution techniques" describes different techniques of key
distribution not a single technique being used with different passwords--
and therefore different SKEs.

  The descriptive portion of a patent (outside the claim) can be used to
interpret what is said in a claim. The claim describes a "plurality of
unauthenticated key distribution techniques" and looking at the patent
you can see where it says, "SPEKE can also use other unauthenticated key
distribution systems..." and goes on to describe one of them. What it
describes is another technique at key distribution, not a repetition of a
single one with different passwords (or keys). It's the other key
distribution systems that comprise the plurality, not a singular system
that's keyed using different passwords.

  The patent gives two examples, one being a straight-forward Diffie-
Hellman and another being the Modified Diffie-Hellman. There are others,
I would imagine, like El Gamal, that the patent holder would say falls
into this claim. It's reasonable to assume that the holder of the patent
doesn't want people to just use a different key distribution technique
("I'm doing Modified Diffie-Hellman not Diffie-Hellman so the patent
doesn't apply").

  The thing that D-H, Modified D-H, El Gamal, and static variants of D-H--
i.e other known techniques of unauthenticated key distribution-- is that
the key being distributed is a secret (private key) that has been
obfuscated in a form (a public key) so it cannot be recovered when
distributed. All of these things have the following in common:

   public = g^private modulo prime

(or equivalent ECC representation). That's the thing-- "public"-- that
gets distributed whether you're doing plain-jane Diffie-Hellman, whether
you're doing Modified Diffie-Hellman, whether you're doing El Gamal,
in other words, when you're doing the "plurality of key distribution
techniques". They all use the discrete logarithm problem to hide
the private key and create a public key as part of their key distribution
technique.

  Dragonfly's method of obfuscation of the private key to produce the
public key is different than the others-- it uses addition modulo the
ORDER of the group.

   public = private + mask modulo order

It is different, unique, novel, new and therefore cannot be part of any
claimed plurality of key distribution techniques. If you disagree, I defy
you to show me mention of this technique anywhere to construct and
distribute public keys out of private keys (or if you are claiming that
a patent holder can patent today things that have not yet been invented
then please make that claim).

  Down at the bottom of this email you mention that this method is
"cryptographically not sound". First of all, I will note that this means
you are, in fact, treating this technique differently than the others,
since I don't believe you are claiming that Diffie-Hellman or El Gamal
is "cryptographically not sound". That buttresses my statement above
that this technique is different. Thank you for helping to prove my
point.

  Regarding your claim, one has to know SKE to generate SKE^private
and "anyone" does not know the password, so "anyone" cannot generate
SKE^private.

  Also, you say the private key can be leaked. If you can show how a
passive attacker can determine a private key in dragonfly-- even if
you tell the passive attacker the password!-- I will show you how that
very same attacker can solve the Computational Diffie-Hellman (CDH)
problem with the same computational advantage. Since it is assumed that
the CDH problem is computationally infeasible it can safely be assumed
that the attack you suggest is also computationally infeasible.

  regards,

  Dan.

On Tue, June 1, 2010 6:17 am, Dennis Kügler wrote:
> Hi Dan,
>
> Let's have a closer look at the patent.
>
>>   You don't mention any specific claim from the SPEKE patent so let me
>> address the first independent claim (there are many claims dependent on
>> that one). The patent I'm referring to is US 6,792,533 dated Sept 14,
>> 2004.
>> The claim says:
>>
>>   "A cryptographic method for providing authentication, comprising:
>
> What's claimed is a method comprising four parts. All of them are
> contained in
> SPSK.
>
>
>>      providing a password-based value to a first party and a second
>> party;
>
> A value derived from the password is given to (calculated by) both
> parties.
> This is clearly the case in SPSK as psk is derived from the password.
>
>
>>      selecting a parameter based on said password-based value, said
>>         parameter defining one of a plurality of unauthenticated key
>>         distribution techniques;
>
> SPSK selects a parameter, SKE, from the password-based value psk. SKE is
> then
> used as the generator for a (masked) Diffie-Hellman key agreement. Due to
> the
> group generator SKE, a pluralty of key distribution techniques is defined
> -
> one for each possible (and secret) value of SKE.
>
>
>>      generating by said first party, in cooperation with said second
>> party,
>>         a cryptographic key based on said one of the plurality of
>>         unauthenticated key distribution techniques, wherein said second
>>         party cooperates in generating said cryptographic key by using
>>         said one of the plurality of unauthenticated key distribution
>>         techniques defined by said first value; and
>
> The derived shared secret ss is a cryptographic key derived from a masked
> Diffie-Hellman key agreement based on the secret group generator SKE.
>
>>      providing authentication of said first party to said second party
>>         based on said cryptographic key."
>
> This is the calculation of the Tag using the cryptographic key ss.
>
>>
>>   Now first of all, that is very broadly worded. Every password-based
>> protocol provides a password to the first party and second party. But
>> there's more to this claim so SPEKE doesn't cover every single protocol
>> that distributes and uses passwords.
>
> Actually, in contrast to other patents this one is rather clear. It
> describes
> exactly a key distribution mechanism based on a parameter derived from a
> password. This is what SPSK does similarly.
>
>>
>>   The next part talks about selecting a parameter based on the password
>> value and dragonfly certainly does that but the important part of this
>> portion of the claim, and the following part of the claim, is the
>> "plurality of unauthenticated key distribution techniques". What is
>> that?
>
> See above. By selecting an alternative group generator (SKE instead of g)
> and
> using an anonymous (and masked) Diffie-Hellman key exchange a plurality of
> unauthenticated key distribution techniques is defined.
>
>>
>>   There are different kinds of public key distribution systems where
>> there
>> is a "private key" and a "public key" which is based on the "private
>> key". Earlier in the descriptive portion of the patent (which is not
>> part of a claim but can be used to interpret a claim) it says "SPEKE can
>> also use other unauthenticated public-key distribution systems, such as
>> the Modified Diffie-Hellman" and goes on to show an example of that. I
>> don't believe that the Modified D-H alone comprises a "plurality of
>> unauthenticated key distribution techniques." I would also imagine that
>> a static-ephemeral D-H or a static-static D-H that used a
>> password-derived
>> parameter to perform that particular type of unauthenticated key
>> distribution technique would probably be covered.
>
> I don't get your point. This is probably to make clear that e.g. a masked
> Diffie-Hellman is also covered by the patent???
>
>>
>>   What is common on all these unauthenticated key distribution
>> techniques is how a public key based on the private key is distributed
>> to the other party. The private key is communicated in an obfuscated
>> form based on the discrete logarithm problem-- e.g. pub = g^priv mod p.
>> That is not done in dragonfly.
>
> There are two general approaches: The first approach is to "scramble" the
> public key (EKE) and to keep the private key unaltered and the other
> approach
> is to send the public key in clear but to indirectly alter the private by
> modifying the parameters.
>
>>
>>   In dragonfly the private key is obfuscated by adding it to a random
>> number modulus the order of the group. The random number is unmasked
>> in a fashion that gives the private key to the second party in a form
>> that does not let it know the private key. Such a technique is new and
>> novel and not part of any known "plurality of unauthenticated key
>> distribution techniques".
>
> The obfuscation is cryptographically not sound. As you transmit both
> Scalar =
> (private + mask) and Element = SKE^(-mask) simultaneously anyone can
> compute
> the public key SKE^private = Element*SKE^Scalar (in which case we're back
> to
> SPEKE). This construction however unnecessarily risks to leak the private
> key, as any bias in the random number generation will reveal information
> on
> the private key. Especially when computing random numbers modulo a prime
> preventing a bias is not trivial.
>
>
>>
>>   So it is my contention that for this claim to apply then both a
>> password-based parameter must be used AND that password-based parameter
>> must be used with a known technique of unauthenticated key distribution.
>> It is not and this claim does not apply to dragonfly.
>
> I disagree. It does very well apply to SPSK/dragonfly.
>
>>
>>   If it was not claim 1 that you were referring to above then please
>> say exactly what claim in the SPEKE patent you are talking about.
>>
>> > - "Dragonfly is secure and has received cryptographic review". Please
>> > provide
>> > a reference to the cryptographically reviewed document.
>>
>>   Both the IEEE 802.11 TGs Draft and the EAP-pwd variant have been
>> reviewed.
>
> So nothing has been published and has been reviewed by the cryptographic
> community?
>
>>
>> > - The construction used for computing the group generator is
>> susceptible
>> > to
>> > side channel (timing) attacks and may leak the shared password. I'd
>> > therefore
>> > recommend to replace the randomized search algorithm by a deterministc
>> > algorithm.
>>
>>   I had a discussion about that. The IEEE 802.11 TGs Draft had a
>> password
>> element created based on the password before the exchange started
>> (it was computed a configuration time when a particular group was
>> selected). Then, when the exchange started the identities of the two
>> parties were run through the random function and used in the "scalar-op"
>> to derive a pair-wise unique element with which to do dragonfly. This
>> would foil the side channel attack. But I was convinced that this was
>> not
>> so important and eliminated the extra step to provide ease of analysis.
>> If you think this is important the SPSK draft could certainly introduce
>> this technique to get around a side channel attack.
>
> I think that should be addressed.
>
>>
>>   I'm not so sure how important that is though (basically I was
>> convinced
>> it's not so important). If you know I can find a solution to the curve
>> the
>> first time you can eliminate some passwords from the pool of potential
>> passwords but you don't know which ones unless you have run them all
>> through the algorithm beforehand. And even if you have run all possible
>> password through the algorithm it certainly doesn't leak the shared
>> password, it just allows the attacker to eliminate some passwords from
>> the pool of potential passwords. And to do so this attack has to be
>> mounted and that is not a trivial attack.
>
> If the attacker can eleminate only a few passwords every time you execute
> the
> protocol he's done with the attack quickly.
>
> Best regards,
>
> Dennis
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