Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions

[Philip L <[e-mail]>]

Please excuse the spam. I thought for just a moment somehow that the
function was verifiably random... like one of those hard problems (for
decidability?).

Just a random thought...

On Thu, Jul 27, 2017 at 4:51 AM, Thomas Garcia <[e-mail]>
wrote:

>
> Thanks for helping me clear those things up!
>
> Thomas G.
>
> On Wed, Jul 26, 2017 at 12:42 PM, Sharon Goldberg <[e-mail]
> > wrote:
>
>> Hi Thomas,
>>
>> 1. It seems that one of the properties that you are interested that the
>>> VRF will have is determinism. On the other hand, the EC-VRF value is
>>> dependent on the choice of some random number k. How are these two facts
>>> compatible? Am I missing something?
>>>
>>
>> We require determinism from the VRF hash output, which is obtained from
>> the VRF proof via the "proof2hash" function.
>>
>> The EC-VRF proof has 3 values: gamma, c, s
>> Values c and s depends on the choice of random number k
>> But value gamma does not depend on k.
>>
>> We get determinism because the VRF hash output (derived using
>> "proof2hash") depends only on gamma, but not on c and s.
>>
>> Slide 28 from my CFRG presentations gives a pictorial explanation of this:
>> http://www.cs.bu.edu/~goldbe/papers/VRF_ietf99_print.pdf
>>
>> 2. The value c calculated in EC-VRF is only 128 bits long for Ed25519. In
>>> normal usage of Ed25519 the signature uses the full length of the hash
>>> output. Doesn't this expose the signature to collision attacks?
>>>
>>> No. We worked this out in our proofs of security.  Section B.2.1 of this
>> paper explains why this works.
>>
>> https://eprint.iacr.org/2017/099.pdf
>>
>> Thanks,
>> Sharon
>>
>>
>>
>>> Thank you for your comments. Indeed, VRFs have been around since 1999.
>>>> They are really "verifiable PRFs" but the name is by now standard in the
>>>> crypto literature, and changing it will cause more confusion than keeping
>>>> it.
>>>>
>>>> In terms of the VRF's security properties, there are three:
>>>>  uniqueness, collision resistance, and pseudorandomness. These are defined
>>>> in our draft (https://tools.ietf.org/html/draft-goldbe-vrf-01#section-3
>>>> ).
>>>>
>>>> How VRFs prevent dictionary attacks: a public hash is subject to a
>>>> dictionary attack because, given the output, an adversary can evaluate the
>>>> hash on different inputs and see what hits the outputs. In a VRF, the
>>>> adversary can't evaluate the hash on different inputs.
>>>>
>>>> You say it's not surprising that "random oracle model proof can prove
>>>> the output of a hash to be random". But actually, the output of a hash is
>>>> NOT random if the input and the hash function are known. This is because
>>>> the output of a hash is deterministic (every input maps to a unique
>>>> output). That's exactly what enables dictionary attacks. This is in
>>>> contrast to a VRF, where the output is (pseudo)random even given knowledge
>>>> of the input. Only once the VRF proof is given, does the VRF output stop
>>>> looking random. Note that random oracles are not essential for VRFs, and
>>>> non-random-oracles constructions exist (but are less efficient than what we
>>>> propose to standardize).
>>>>
>>>> As far as use cases, here are a few:
>>>>
>>>> In the NSEC5 use case for DNSSEC, you have sensitive data (domain
>>>> names) and you sign consecutive pairs of hashes of domain names in order to
>>>> be able to prove absence of a name. If you just use standard hashing,
>>>> whenever signed hash values are disclosed, your sensitive data is subject
>>>> to dictionary attacks. VRFs solve that problem, and sensitive names don't
>>>> have to be disclosed at all. More details are in
>>>> https://eprint.iacr.org/2017/099.pdf
>>>>
>>>> In CONIKS (also Google Key Transparency, Signal secure messaging,
>>>> Yahoo! Coname) you also have some sensitive data (user names) that are put
>>>> into a Merkle-like authenticated data structure. If you just use standard
>>>> hashing, whenever hash values are disclosed, sensitive data is subject to
>>>> dictionary attacks. If you use VRFs, sensitive data again can be disclosed
>>>> only on an as-needed basis. More details are in
>>>> https://eprint.iacr.org/2014/1004.pdf.
>>>>
>>>> In a cryptocurrency use case, you wish perform a coin flip that is
>>>> deterministic and provably correct, but cannot be done by just anyone.
>>>> More details are in https://people.csail.mit.ed
>>>> u/nickolai/papers/gilad-algorand-eprint.pdf and possibly other
>>>> cryptocurrency papers.
>>>>
>>>> Bryan Ford mentioned an additional usecase at the mic on Tuesday:
>>>> distributed password protection protocols
>>>>
>>>> Many of these use case are already putting VRFs into production use
>>>> (esp. the CONIKS one).  You can see a list of the various implementations
>>>> we have found in the "implementation status" section of our draft.  One of
>>>> the reasons we think this spec is so important is that we found flaws in
>>>> several of the implementations that can be used to trivially break
>>>> uniqueness.  (See eg: https://github.com/google/
>>>> keytransparency/issues/567)
>>>>
>>>> Thanks,
>>>> Sharon
>>>>
>>>> On Fri, Jul 21, 2017 at 7:32 PM, Dan Brown <[e-mail]>
>>>> wrote:
>>>>
>>>>> Answering myself below: VRFs have been around since 1999, so are not
>>>>> so new.  ‎Still don't like the name, and still have trouble seeing the
>>>>> value.
>>>>>
>>>>> *From: *Dan Brown
>>>>> *Sent: *Tuesday, July 18, 2017 2:29 PM
>>>>> *To: *Sharon Goldberg; [e-mail]
>>>>> *Cc: *[e-mail]; Leonid Reyzin; Dimitrios Papadopoulos
>>>>> *Subject: *Re: [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
>>>>>
>>>>> Hi Sharon and CFRG,
>>>>>
>>>>>
>>>>>
>>>>> On VRFs, my uncertain comments to consider at your leisure:
>>>>>
>>>>>
>>>>>
>>>>> Is it fair to say VRFs are relatively new?  If so, then maybe a little
>>>>> more caution is needed about their use.  It seems a tad hasty that it is
>>>>> being used already.
>>>>>
>>>>>
>>>>>
>>>>> To me, it seems that VRFs are basically signatures, with an extra
>>>>> feature.  My concern is that this extra feature might get overused, before
>>>>> it is thoroughly reviewed.
>>>>>
>>>>>
>>>>>
>>>>> It is unsurprising to me that random oracle model proof can prove the
>>>>> output of a hash to be random.  My intuitive concern is that at least
>>>>> informally, this is kind of circular.  Hashes often have some
>>>>> non-random-ish properties that might affect the extra security (over
>>>>> signatures) that VRFs are aiming for.  I guess I would much prefer a proof
>>>>> saying if the hash has (well-studied) properties XYZ, then your
>>>>> construction are VRFs.  (Maybe you have this already?  If so, then tell me
>>>>> so.)
>>>>>
>>>>>
>>>>>
>>>>> Since, VRFs require sending the “proofs” on the wire, I find it hard
>>>>> to see how it could be used to prevent dictionary attacks.  I assume that
>>>>> you are saying the proofs must be encrypted when one needs to avoid
>>>>> dictionary models?  I suppose all the details are there in I-D and papers,
>>>>> but for now, I am confused about the threat model (which parties have keys,
>>>>> etc., if they require a secure channel and mutual trust, why just use plain
>>>>> old hash,…). To resist dictionary attacks, were already have PAKEs and
>>>>> PBHashing.  Now this?
>>>>>
>>>>>
>>>>>
>>>>> Finally, on a bikeshed-coloring note, I object to the name “verifiable
>>>>> random function”, on several grounds.
>>>>>
>>>>>
>>>>>
>>>>>    1. It is not a function.  It is at least four functions, keygen,
>>>>>    sign, verify, and hashify.
>>>>>    2. If you make it into a keyed function F_sk(m), as in
>>>>>    prooftohash(sign_sk(m)), it is not verifiable.
>>>>>    3. Verification requires the intermediate proof, which is
>>>>>    certainly not even pseudorandom (it is easy to distinguish valid signatures
>>>>>    from random).
>>>>>    4. It is pseudorandom, not random.  (The keys are random, but many
>>>>>    crypto has keys, without having “random” in its name: encryption, MAC,
>>>>>    signatures, key exchange, …, they also don’t verifiable or random in their
>>>>>    names either.)
>>>>>    5. The similar phrase “verifiably random”, albeit as a misnomer,
>>>>>    has past precedents, see NIST P-256 and Brainpool, etc.  When I see VRF, I
>>>>>    think a function, that aims to VR in that sense, and great, now we can
>>>>>    improve on Brainpool, etc.
>>>>>    6. “Random function” should be reserved for the ideal random
>>>>>    mapping concept, for example, as studied by Flajolet-Odlyzko (ok they only
>>>>>    studied the case of equal size domain and range).  The random oracle model,
>>>>>    is the idea of approximating this ideal, etc.  An actual approximation
>>>>>    should not be name as the ideal (sorry, I’m kind of repeating my point 4).
>>>>>
>>>>>
>>>>>
>>>>> Please forgive the fact that my comments above are not very
>>>>> constructive (or if the tone is wrong).  This is a new topic for me, so I
>>>>> am reluctant too many suggestions.  Nonetheless, I suggest (0) waiting a
>>>>> little, (1) a non-random-oracle security proof (if you don’t have it yet),
>>>>> (2) re-naming the scheme to something like re-hashable (or digestible)
>>>>> signatures (and re-name the various parts, i.e. proof -> signature, etc.).
>>>>>
>>>>>
>>>>>
>>>>> Best regards,
>>>>>
>>>>>
>>>>>
>>>>> Dan
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> *From:* Cfrg [mailto:[e-mail]] *On Behalf Of *Sharon
>>>>> Goldberg
>>>>> *Sent:* Wednesday, July 12, 2017 5:42 AM
>>>>> *To:* [e-mail]
>>>>> *Cc:* [e-mail]; Dimitrios Papadopoulos <[e-mail]>; Leonid
>>>>> Reyzin <[e-mail]>
>>>>> *Subject:* [Cfrg] draft-goldbe-vrf: Verifiable Random Functions
>>>>>
>>>>>
>>>>>
>>>>> Dear CFRG,
>>>>>
>>>>> I'm presenting at next week's meeting on Verifiable Random Functions.
>>>>> A VRF is the public-key version of keyed cryptographic hash. Only the
>>>>> holder of the VRF secret key can compute the hash, but anyone with the
>>>>> public key can verify it.  VRFs can be used to prevent dictionary attacks
>>>>> on hash-based data structures, and have applications to key transparency
>>>>> (CONIKS), DNSSEC (NSEC5), and cryptocurrencies (Algorand).
>>>>>
>>>>> In advance of the meeting, please see:
>>>>>
>>>>> 1) Our substantially updated -01 draft:
>>>>> https://datatracker.ietf.org/doc/draft-goldbe-vrf/
>>>>>
>>>>> 2) Our project page, with links to various VRF implementations:
>>>>> https://www.cs.bu.edu/~goldbe/projects/vrf
>>>>>
>>>>> Comments welcome.  Thanks,
>>>>>
>>>>> Sharon
>>>>>
>>>>> --
>>>>> Sharon Goldberg
>>>>> Computer Science, Boston University
>>>>> http://www.cs.bu.edu/~goldbe
>>>>>
>>>>
>>>>
>>>>
>>>> --
>>>> ---
>>>> Sharon Goldberg
>>>> Computer Science, Boston University
>>>> http://www.cs.bu.edu/~goldbe
>>>>
>>>> _______________________________________________
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>>>> https://www.irtf.org/mailman/listinfo/cfrg
>>>>
>>>>
>>>
>>
>>
>> --
>> ---
>> Sharon Goldberg
>> Computer Science, Boston University
>> http://www.cs.bu.edu/~goldbe
>>
>
>
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