Re: [Lwip] Iotdir early review of draft-ietf-lwig-curve-representations-08

[Rene Struik <[e-mail]>]

Hi Daniel:

Thanks very much for your constructive review.

I provided brief feedback on some of your comments - see below (RS>> 
<<RS). Where I did not provide a comment yet, I will reflect on these 
later (and this may benefit from looking at the results from the pending 
SecDir review, once ready, at the same time).

Best regards, Rene

On 10/25/2019 2:38 PM, Daniel Migault via Datatracker wrote:
> Reviewer: Daniel Migault
> Review result: Almost Ready
>
> Hi,
>
> I have reviewed this document as part of the IoT directorate's
> ongoing effort to review all IETF documents being processed by the
> IESG.  These comments were written primarily for the benefit of the
> internet area directors.  Document editors and WG chairs should treat
> these comments just like any other last call comments.
>
> The summary of the review is Almost Ready
>
> Overall I believe the document is well written with a lot of useful
> information. Though I have not carefully reviewed the annexes, I believe the
> document could be re-organized to  provide more implementation details of
> Wei25519 and its potentially the implementation of the isogeny between
> Wei25519.-3 and Wei25519. Note that the latest point may depend on the
> implementation status of NIST curves.
>
> Please find my review, which I hope will help to move the document to be moved
> forward.
>
> Yours,
> Daniel
>
> Abstract
>
>     This document specifies how to represent Montgomery curves and
>     (twisted) Edwards curves as curves in short-Weierstrass form and
>     illustrates how this can be used to carry out elliptic curve
>     computations using existing implementations of, e.g., ECDSA and ECDH
>     using NIST prime curves.
>
> <mglt>
> Overall I have the impression the document's intent is to define Wei25519 for
> COSE. The current document is very well documented and nicely written on the
> generic methodology used, that is using the Weierstrass models of curves using
> other models that is in our case twisted-Edward/Montgomery curves. My reading
> of the document is that it might benefit by being re-focused on Wei25519 and
> provide the necessary details in the main body - that is not the annex to
> implement: * Wei25519 - the domains parameters * the isogeny between
> Wei25519.-3 and Wei25519 - as this is necessary for reusing NIST curve
> implementation when a hard coded. That said, this depends on the implementation
> status of NIST curves and may be left in the annex.
>
> Specification is sufficient to assign code points which is sufficient with an
> Informational status.
>
> I would even have Wei25519 in the title. In my opinion the title is too generic
> and the scope should be narrow down a bit. </mglt>
>
> <mglt>
> The document introduces some notations, I believe these notations should be
> specified, and maybe use the same notation as RFC7748, if possible to avoid
> that we have one notation per document. </mglt>

RS>> Elliptic-curve and Finite Field-related notation is introduced in 
Annex B, 
seehttps://tools.ietf.org/id/draft-ietf-lwig-curve-representations-08.html#rfc.appendix.B

This notation is well-aligned with conventions in ANSI, NIST, SECG, and 
BSI specifications. It is also in line with RFC 6090.

<<RS

> 1.  Fostering Code Reuse with New Elliptic Curves
>
>     It is well-known that elliptic curves can be represented using
>     different curve models.
>
> <mglt>
> nits: It might be preferred to remain factual and simply say "Elliptic curves
> can be represented using different models." </mglt>
>
>     Recently, IETF standardized elliptic curves
>     that are claimed to have better performance and improved robustness
>     against "real world" attacks than curves represented in the
>     traditional "short" Weierstrass model.
>
> <mglt>
> Not being a native english speaker, the sentence above may lead the reader to
> think that Weierstrass representation is one reason for less robustness and
> performance. If that were the case, the reader may wonder why do we want to
> move to that representation.
>
> I believe that before Montgomery or Edwards curves have been introduced curves
> with Weierstrass model were widely deployed and implemented. </mglt>

RS>>  The reason to use the word "claimed" is that, from my perspective, 
it is unclear that the claim actually holds. {My opinion on the matter 
is irrelevant for this document, though.}

As to performance, this depends on implementation details, see, e.g., 
remarks on existing hardware implementations (see the forelast para of 
https://tools.ietf.org/id/draft-ietf-lwig-curve-representations-08.html#rfc.section.6). 
As to robustness, see the second para of 
https://tools.ietf.org/id/draft-ietf-lwig-curve-representations-08.html#rfc.section.8). 
As to different perspectives on performance vs. robustness, see also 
Item 1.3b of p. 77 of 
https://csrc.nist.gov/CSRC/media/Publications/fips/186/4/final/documents/comments-received-fips186-4-december-2015.pdf. 
<https://csrc.nist.gov/CSRC/media/Publications/fips/186/4/final/documents/comments-received-fips186-4-december-2015.pdf>

To my knowledge, Weierstrass curves, such as the NIST prime curves are 
still very much prevalent to-date (so "were widely deployed" is probably 
something that actually still is).

<<RS

>
>     This document specifies an
>     alternative representation of points of Curve25519, a so-called
>     Montgomery curve, and of points of Edwards25519, a so-called twisted
>     Edwards curve, which are both specified in [RFC7748], as points of a
>     specific so-called "short" Weierstrass curve, called Wei25519.  We
>     also define how to efficiently switch between these different
>     representations.
>
> <mglt>
> I understand the switch can be performed in two ways, it might help the reader
> to distinguish two scenario one with a being a parameter and one with a being
> hard coded.
>
> We may also briefly expose why Curve25519 cannot be "proxied" by Ed-to-Wei
> followed by Wei25519. In which case Wei25519 would be an implementation detail.
> This would justify the need to add code points for Wei25519. </mglt>
>
>     Use of Wei25519 allows easy definition of new signature schemes and
>     key agreement schemes already specified for traditional NIST prime
>     curves, thereby allowing easy integration with existing
>     specifications, such as NIST SP 800-56a [SP-800-56a], FIPS Pub 186-4
>     [FIPS-186-4], and ANSI X9.62-2005 [ANSI-X9.62], and fostering code
>     reuse on platforms that already implement some of these schemes using
>     elliptic curve arithmetic for curves in "short" Weierstrass form (see
>     Appendix C.1).
>
> <mglt>
> Not being a cryptographer at all. I am wondering if the definition of "new"
> signature scheme is correct. At least it sounds a dangerous slope. I think the
> text wants to say it allows to re-use signature scheme defines for the NIST
> curves using another curves Wei25519, namely ECDSA in our case. </mglt>
RS>> New refers to a new instantiation, e.g., ECDSA with the Wei25519 
curve simply defines a new curve to be used with an existing generically 
specified ECDSA specification. <<RS
> 2.  Specification of Wei25519
>
>     For the specification of Wei25519 and its relationship to Curve25519
>     and Edwards25519, see Appendix E.
>
> <mglt>
> If we are defining Wei25519, it seems that at least the definition of Wei25519
> needs to be part of the main draft. A deep explanation as well as other
> information may be left in the annexe. I would thus probably recommend to add
> the necessary domain parameters that are needed to instantiate Wei25519. </mglt>
>
>     For further details and background
>     information on elliptic curves, we refer to the other appendices.
>
>     The use of Wei25519 allows reuse of existing generic code that
>     implements short-Weierstrass curves, such as the NIST curve P-256, to
>     also implement the CFRG curves Curve25519 and Edwards25519.  We also
>     cater to reusing of existing code where some domain parameters may
>     have been hardcoded, thereby widening the scope of applicability.  To
>     this end, we specify the short-Weierstrass curves Wei25519.2 and
>     Wei25519.-3, with hardcoded domain parameter a=2 and a=-3 (mod p),
>     respectively; see Appendix G.  (Here, p is the characteristic of the
>     field over which these curves are defined.)
>
> <mglt>
> The text needs here a bit more more explanations. As I understood, we are not
> simply changing the representation but also considering the constraint of the
> NIST curves implementations. My understanding is that NIST curves have hard
> coded a=-3, so we need to work around this with the isogeny. The construction
> is, in my opinion, a bit different from what simple isomorphism. It might also
> be good to have that overview stated in the introduction section.
>
> Annexes are good, but the necessary information for an implementation may be
> moved up to the main body.
>
> </mglt>
>
> 3.  Use of Representation Switches
>
>     The curve Wei25519.-3 (which has hardcoded domain parameter a=-3 (mod
>     p)) is not isomorphic to the curve Wei25519, but is related in a
>     slightly weaker sense: the curve Wei25519 is isogenous to the curve
>     Wei25519.-3, where the mapping of Appendix G.2 is an isogeny of
>     degree l=47 that maps the specified base point G of Wei25519 to the
>     specified base point G' of Wei25519.-3 and where the so-called dual
>     isogeny (which maps Wei25519.-3 to Wei25519) has the same degree
>     l=47, but does not map G' to G, but to a fixed multiple hereof, where
>     this multiple is l=47.  Consequently, a public-private key pair
>     (k,R:=k*G) for Wei25519 corresponds to the public-private key pair
>     (k, R':= k*G') for Wei25519.-3 (via the l-isogeny), whereas the
>     public-private key pair (k, R':=k*G') corresponds to the public-
>     private key pair (l*k, l*R=l*k*G) of Wei25519 (via the dual isogeny).
>     (Note the extra scalar l=47 here.)
>
> <mglt>
> This is just a comment that ascii does not help reading 1=47... but there is no
> much we can do. </mglt>
>
>     Alternative curve representations can, therefore, be used in any
>     cryptographic scheme that involves computations on public-private key
>     pairs, where implementations may carry out computations on the
>     corresponding object for the isomorphic or isogenous curve and
>     convert the results back to the original curve (where, in case this
>     involves an l-isogeny, one has to take into account the factor l).
>     This includes use with elliptic-curve based signature schemes and key
>     agreement and key transport schemes.
>
> <mglt>I believe we should specify somewhere that changing the representation
> does not ease the ECDLP for a given prime/curve</mglt>

RS>> This is a good observation. I captured this generally in the 
Security Considerations section (see first para of 
https://tools.ietf.org/id/draft-ietf-lwig-curve-representations-08.html#rfc.section.8) 
and also reminded the reader of this when introducing each isomorphism 
discussed in the document. See 
https://tools.ietf.org/id/draft-ietf-lwig-curve-representations-08.html#rfc.appendix.D, 
<https://tools.ietf.org/id/draft-ietf-lwig-curve-representations-08.html#rfc.appendix.D> 
where I added this remark for the isomorphic mapping from twisted 
Edwards to Montgomey (Annex D.1, end of first para), Montgomery to 
Weierstrass (Annex D.2, end of first para). I did not repeat this for 
the twisted Edwards to Weierstrass mapping (Annex D.3) or with the 
low-degree isogenies (Annex F), but could certainly sprinkle this in 
there as well, if so desired.

<<RS

>
> 4.  Examples
>
> <mglt>
> I do not believe these are example regarding the focus of the document. Of
> course, the document could be more generic, but here we focus on 25519, so I
> would rename Example as Implementation. Or move subsection to one level, that
> is 4.1 -> 4. 4.2->5... </mglt>
>
> 8.  Security Considerations
>
>     Elliptic curves are generally used as objects in a broader
>     cryptographic scheme that may include processing steps that depend on
>     the representation conventions used (such as with, e.g., key
>     derivation following key establishment).  These schemes should
>     (obviously) unambiguously specify fixed representations of each input
>     and output (e.g., representing each elliptic curve point always in
>     short-Weierstrass form and in uncompressed tight MSB/msb format).
>
> <mglt>
> I think it might be worth mentioning here that while the scheme used in this
> document may be applied for other curves that 25519, not all modules are
> isomorphic to Weierstrass. In addition not all Weierstrass representation can
> be switched to a Montgomery representation. </mglt>

RS>> As you suggested above, not all curves can be expressed in Montgomery or twisted Edwards format (see also the 6th para of Appendix B.1:https://tools.ietf.org/id/draft-ietf-lwig-curve-representations-08.html#rfc.appendix.B.1). This being said, all [non-binary] curves *are* isomorphic to one in short-Weierstrass format, so that the short-Weierstrass format can be thought of as a "catch all" representation format.
<<RS

>
>     To prevent cross-protocol attacks, private keys SHOULD only be used
>     with one cryptographic scheme.  Private keys MUST NOT be reused
>     between Ed25519 (as specified in [RFC8032]) and ECDSA25519 (as
>     specified in Section 4.3).
>
>     To prevent intra-protocol cross-instantiation attacks, ephemeral
>     private keys MUST NOT be reused between instantiations of ECDSA25519.
>
>

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