Re: [Cfrg] J-PAKE and Schnorr NIZK for informational RFCs

Feng Hao <> Wed, 16 November 2016 15:34 UTC

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From: Feng Hao <>
To: Michel Abdalla <>
Thread-Topic: [Cfrg] J-PAKE and Schnorr NIZK for informational RFCs
Date: Wed, 16 Nov 2016 15:33:23 +0000
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Subject: Re: [Cfrg] J-PAKE and Schnorr NIZK for informational RFCs
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Dear Michel,

Thanks for the clarifications, which address the raised points pertinently. 

One small question: "M=H(0) and N=H(1), where H hashes into the appropriate group"

Can you give more details on the realization of H?


>-----Original Message-----
>From: Michel Abdalla []
>Sent: 16 November 2016 15:08
>To: Feng Hao <>
>Cc: Watson Ladd <>;
>Subject: Re: [Cfrg] J-PAKE and Schnorr NIZK for informational RFCs
>Dear Feng,
>Since you’ve raised some questions about SPAKE2, I just wanted to clarify
>some of these issues below.
>> On Nov 16, 2016, at 11:25 AM, Feng Hao <>
>> Hi Watson,
>> On your comments about comparing costs between SPAKE2 and J-PAKE
>> * It's not a fair comparison as the setup assumptions are different. SPAKE2
>requires a trusted setup, while J-PAKE doesn't. Instead, you should compare
>SPAKE2 with KOY, Jiang-Gong and GL protocols as they require the same
>trusted setup. J-PAKE should be compared with EKE, SPEKE and Dragonfly
>(which is based on SPEKE).
>> * When you say "SPAKE2 with M and N generated by hashing is secure,
>> and the proofs found in the SPAKE2 paper do work", it's best that you
>write up the full details how you do the hashing, proofs that why it's secure
>and why it doesn't affect the original proofs in the SPAKE2 paper in any way.
>Then people can check and verify your proofs instead of having to take your
>word for it. I see you are always rigorous in asking "security proofs" from
>others for everything they do (which is good), so you should consider
>applying the same rigor to yourself.
>Since the security proof only requires that M and N are two random
>elements whose discrete logs with respect to g are unknown, the proof
>would go through even if M and N were chosen as the output of a random
>oracle on some fixed inputs, say M=H(0) and N=H(1), where H hashes into
>the the appropriate group.
>> * The KOY, Jiang-Gong and GL papers are relevant as they are the same
>type of CRS-based designs as SPAKE2. These papers state that the setup
>needs to be done by a trusted party and they don't specify using a hash.
>> SPAKE2 is in the same model. It's appropriate you compare these protocols
>and definitions. This is necessary especially since you're doing something not
>specified in the original SPAKE2 paper and other related peer-reviewed
>> * You will need to convince IETF users that there is no possibility of
>> trapdoor for M and N (which may prove a bit tricky). Knowledge (or partial
>knowledge) of the relation between M and N may allow one to
>systematically break all instances of the protocol execution.
>> * Kindly note that if you can manage to convince IETF users that M and N
>are completely random, one might just plug M and N as the input of two
>random points to DUAL_EC and make it work?
>The security of SPAKE2 requires that the discrete logs of M and N with
>respect to g should remain unknown to everybody so the generation of M
>and N has to enforce this aspect.
>> * What you say about the 4 exponentiations in the subgroup is correct
>(consistent with the original paper), but this hasn't included the validation
>of the public key (which is free in EC but takes one full exponentiation in the
>finite field setting). See my further comment below.
>> I read again the original SPAKE2 paper as well as your I-D. I have the
>> following comments
>> * I think SPAKE2 is underspecified in the original paper. It doesn't state the
>requirements for M and N, but it should be clear that they must be
>completely random. Also, it doesn't state if the discrete logarithm between
>M and g (and symmetrically between M and g) must be unknown. It's not
>immediately clear to me if knowledge of the discrete logarithm for M and g
>will break anything, but all these should have been explicitly specified in the
>If one knows the discrete log of M with respect to g (let’s call this value m),
>then one can perform an offline dictionary attack on SPAKE2 as follows. The
>adversary impersonates User A and sends a random element X'=g^x' to User
>B. After receiving Y* from User B, the adversary requests the session key
>associated with this session through a reveal query. Let SK be this session
>key.  Now guess pw and compute offline Y = Y* / N^pw, K_A = Y^{x’ - pw m},
>and SK_A = H(A,B,X’,Y*,K_A).  Note that SK_A will match SK when pw is the
>correct pw.
>> * I'm a bit worried that in the actual protocol specification in the original
>paper, there is no step to perform public key validation. This could be due to
>two reasons: 1) an inadvertent omission by the authors; 2) an intentional
>design choice. In case of ambiguity like this, one normally takes it as the
>latter. The reason is simple: if public key validation is considered essential, it
>MUST be clearly specified, which is the case with most key agreement
>protocols. However, from early 2000s, some researchers called for
>abandoning the public key validation, as long as the protocol has formal
>security proofs (HMQV is one notable example, but it backfired in the end).
>Our proof implicitly assumes membership tests for all the elements being
>exchanged. Hence, the actual explanation for the under specification is an
>inadvertent omission on our part.
>> * The above observation reminds me of a paper " Multi-Factor
>Authenticated Key Exchange" by Poincheval and Zimmer in 2008 [1] where
>the protocol is specified in a similar manner as SPAKE2 without public key
>validation. We analysed the protocol and it took us a while to conclude that
>it is insecure without public key validation (despite the security proofs in the
>paper) [2]. We contacted authors of [1] and they kindly acknowledged the
>attack and also confirmed that public key validation needed to be added in
>their protocol. The attack can be traced to a subtle deficiency in their
>theoretical model which implicitly assumes that a server is trusted when it
>communicates with a client. This assumption is clearly invalid, but it is
>implicit in the model/proofs and it took 5 years for peer researchers to
>identify it!
>> * At the moment, I don't see an obvious attack due to the missing public
>key validation in the SPAKE2 specification (as in the original paper), but it's a
>potential issue that needs some attention.
>> Cheers,
>> Feng
>> [1] D. Pointcheval and S. Zimmer, "Multi-Factor Authenticated Key
>Exchange," Proceedings of Applied Cryptography and Network Security
>(ACNS¹08), pp. 277-295, LNCS 5037, 2008.
>> [2] Security Analysis of a Multi-Factor Authenticated Key Exchange
>> Protocol
>> On 15/11/2016 19:14, "Watson Ladd" <> wrote:
>>> Dear Feng,
>>> Let me make this very clear, to avoid your misunderstandings: J-PAKE
>>> is substantially less efficient than SPAKE2 over the same group.
>>> SPAKE2 with M and N generated by hashing is secure, and the proofs
>>> found in the SPAKE2 paper do work for this case. If we use a small
>>> subgroup of a finite field group, then the necessary validations for
>>> group membership double the cost of SPAKE2, but J-PAKE is still
>>> slower. J-PAKE requires an additional round, while SPAKE2 fits into
>>> the same flow as Diffie-Hellman. There is no relevance of KOY, or
>>> Jiang-Gong, or any other paper that may or may not (I didn't bother
>>> to
>>> look) present its own definitions and security model.
>>> SPAKE2 requires exactly 4 exponentations in the subgroup if we do not
>>> do anything smart about them. Two of these can be combined and
>>> replaced with a dual base exponentiation via Strauss's algorithm.
>>> Do you have anything to say to this?
>>> Sincerely,
>>> Watson
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