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.
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.
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.
1. Fostering Code Reuse with New Elliptic Curves
It is well-known that elliptic curves can be represented using
different curve models.
nits: It might be preferred to remain factual and simply say "Elliptic curves can be represented using different models."
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.
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.
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.
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.
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).
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.
2. Specification of Wei25519
For the specification of Wei25519 and its relationship to Curve25519
and Edwards25519, see Appendix E.
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.
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.)
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.
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.)
This is just a comment that ascii does not help reading 1=47... but there is no much we can do.
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.
I believe we should specify somewhere that changing the representation does not ease the ECDLP for a given prime/curve
4. Examples
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...
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).
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.
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.