Re: [Cfrg] Task looming over the CFRG

[Michael Hamburg <[e-mail]>]

Kevin,

Sorry to be ambiguous: the curve I designed has a 448-bit field and a 446-bit prime-order subgroup, so a parallel rho attack should cost just under 2^223 point operations on average.  So it sits between the 192 and 256-bit security levels.

I’m not particularly invested in getting this curve into TLS, but I’d like to know whether there’s a point in submitting it for this purpose, or if it will be rejected for having the “wrong security level".

Matching the nominal security level of the asymmetric part to that of the symmetric part sounds obvious on its face, but in fact it is not usually done above the 128-bit level.  For example, Suite B doesn’t specify a direct matching of nominal security levels: it specifies AES-256 with SHA-384 and ECDSA-NIST-p384 for TOP SECRET communications.  Likewise, almost nobody pairs AES-256 with the matching RSA-15k, and even AES-128 is usually paired with the nominally weaker RSA-2048.

This actually makes sense.  Nobody is going to do a 128-bit exhaust for many decades.  Not Google, not the NSA, not the KGB, nobody.  With today’s most efficient supercomputers, the heat output from 2^128 operations would be far more than enough to boil the oceans dry [1].  So we’re talking about defenses against sub-128-bit attacks, and defense in depth against hypothetical advances in cryptography, and quantum resistance for primitives that can resist at all.  Stronger curves, ciphers and hashes will stand or fall on their own, not all together as computer power surpasses their nominal security level.

Also, nobody uses AES-192.

So I don’t think it’s obvious that matching the AES security levels is a requirement.  If the RG thinks it is, or if there’s some obscure legal requirement that the levels match, then fine.  Just describe why.

Cheers,
— Mike

[1] Lenstra, Kleinjung, Thomé.  “Universal security: from bits and mips to pools, lakes — and beyond”.  https://eprint.iacr.org/2013/635.pdf

On May 5, 2014, at 12:49 PM, Igoe, Kevin M. <[e-mail]> wrote:

> Mike:
>  
>   Being off by a few bits isn’t a show stopper. but 32-bits is probably too
> much.  The security levels echo the AES security levels of AES-128, AES-192
> and AES-256.  Using a 224 bit curve with AES-128 only provides roughly 112-bits
> of security versus the 128 bits ostensibly provided by AES-128.  I just want to ensure
> that a user who thinks they are getting 128 bits of security gets 128 bits of 
> security.
>  
>                               Kevin
>  
> From: Michael Hamburg [mailto:[e-mail]] 
> Sent: Monday, May 05, 2014 2:25 PM
> To: Igoe, Kevin M.
> Cc: [e-mail]
> Subject: Re: [Cfrg] Task looming over the CFRG
>  
> Hi Kevin,
>  
> As the designer of an ECC system which is aimed at 224-ish-bit security, I’m curious: is it a firm requirement that the curves be set at 128, 192 and 256 bits?  Or was there consensus in the meeting that the curves should be set at these security levels?  Patrick Longa aimed his talk at these security levels, but I don’t recall this being stated as a requirement.
>  
> Cheers,
> — Mike
>  
>  
> On May 5, 2014, at 10:58 AM, Igoe, Kevin M. <[e-mail]> wrote:
> 
> 
> As most the folks who read this list have noticed, a virtual interim meeting of the CFRG
> was held on Tues 29 April to discuss the way forward for elliptic curve cryptography
> in the IETF.  This was driven by an earnest plea from the TLS WG for firm guidance from 
> the CGRG on the selection of elliptic curves for use in TLS.  They need an answer before 
> the Toronto IETF meeting in late July.  TLS needs curves for several levels of security (128, 
> 192 and 256), suitable for use in both key agreement and in digital signatures.
>  
> ·         The consensus of the attendees was that it would be best for TLS to have a single
> “mandatory to implement” curve for each of the three security levels.
>  
> ·         Though the attendees were reluctant to make a formal commitment, there
> was clearly a great deal of support for the Montgomery curve curve25519 (FYI, the 
> 25519 refers to the fact that arithmetic is done modulo the prime 2**255 – 19 ).
>  
> ·         curve25519 only fills one of the three required security levels.  We still need
> curves of size near 384 bits and 512 bits.
>  
> ·         NIST curves: I doubt TLS will be willing to revisit the question of elliptic curves once the 
> CFRG has made their recommendation.  Another option to consider is advising TLS to
> use of the NIST curves in the short term, buying time for the CFRG to do an unrushed 
> exploration of the alternatives, drawing academia and other standards bodies into the 
> discussion.
>  
> P.S.  It has been suggested that the CFRG hold a session at the Crypto conference in
> Santa Barbara in an effort to draw in more participation from the academic community.
> No guarantees we can pull this off, but it is worth the attempt. Thoughts? Volunteers?
>  
> P.P.S. We need to start lining up speakers for the CFRG session at IETF-90 (Toronto).
>  
>  
> ----------------+--------------------------------------------------
> Kevin M. Igoe   | "We can't solve problems by using the same kind
> [e-mail]  | of thinking we used when we created them."
>                 |              - Albert Einstein -
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>  
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