Re: [Cfrg] [TLS] Closing out tls1.3 "Limits on key usage" PRs (#765/#769)

"Paterson, Kenny" <> Wed, 15 February 2017 13:46 UTC

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From: "Paterson, Kenny" <>
To: "Dang, Quynh (Fed)" <>
Thread-Topic: [TLS] [Cfrg] Closing out tls1.3 "Limits on key usage" PRs (#765/#769)
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Date: Wed, 15 Feb 2017 13:46:28 +0000
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Cc: Atul Luykx <>, IRTF CFRG <>, "" <>
Subject: Re: [Cfrg] [TLS] Closing out tls1.3 "Limits on key usage" PRs (#765/#769)
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Hi Quynh,

I'm meant to be on vacation, but I'm finding this on-going discussion fascinating, so I'm chipping in again.

On 15 Feb 2017, at 21:12, Dang, Quynh (Fed) <<>> wrote:

Hi Atul,

I hope you had a happy Valentine!

From: Atul Luykx <<>>
Date: Tuesday, February 14, 2017 at 4:52 PM
To: Yoav Nir <<>>
Cc: 'Quynh' <<>>, IRTF CFRG <<>>, "<>" <<>>
Subject: Re: [TLS] [Cfrg] Closing out tls1.3 "Limits on key usage" PRs (#765/#769)

Why is that 2^48 input blocks rather than 2^34.5 input blocks?
Because he wants to lower the security level.

I respectfully disagree. 2^-32, 2^-33, 2^-57, 2^-60, 2^-112 are practically the same: they are practically zero.

I'm not clear what you mean by "practically" here. They're clearly not the same as real numbers. And if we are being conservative about security, then the extremes in your list are a long way apart.

And, 2^-32 is an absolute chance in this case meaning that all attackers can’t improve their chance: no matter how much computational power the attacker has.

A sufficiently powerful adversary could carry out an exhaustive key search for GCM's underlying AES key. So I'm not sure what you're claiming here when you speak of "absolute chance".

I don’t understand why the number 2^-60 is your special chosen number for this ?

This is a bit subtle, but I'll try to explain in simple terms.

We can conveniently prove a bound of about this size (actually 2^-57) for INT-CTXT for a wide range of parameters covering both TLS and DTLS (where many verification failures may be permitted). Then, since we're ultimately interested in AE security, we would like to (roughly) match this for IND-CPA security, to get as good a bound as we can for AE security (the security bounds for the two notions sum to give an AE security bound - see page 2 of the "AE bounds" note).

In view of the INT-CTXT bound there's no point pushing the IND-CPA bound much lower than 2^-60 if the ultimate target is AE security. It just hurts the data limits more without significantly improving AE security.

Finally, 2^-60 is not *our* special chosen number. We wrote a note that contained a table of values, and it's worth noting that we did not make a specific recommendation in our note for which row of the table to select.

(Naturally, though, we'd like security to be as high as possible without making rekeying a frequent event. It's a continuing surprise to me that you are pushing for an option that actually reduces security when achieving higher security does not seem to cause any problems for implementors.)

In your “theory”, 2^-112 would be in “higher” security than 2^-60.

It certainly would, if it were achievable (which it is not for GCM without putting some quite extreme limits on data per key).




The original text
recommends switching at 2^{34.5} input blocks, corresponding to a
success probability of 2^{-60}, whereas his text recommends switching at
2^{48} blocks, corresponding to a success probability of 2^{-32}.


On 2017-02-14 11:45, Yoav Nir wrote:
Hi, Quynh
On 14 Feb 2017, at 20:45, Dang, Quynh (Fed) <<>>
Hi Sean and all,
Beside my suggestion at [1],
I have a second suggestion below.
Just replacing this sentence: "
For AES-GCM, up to 2^24.5 full-size records (about 24 million) may
encrypted on a given connection while keeping a safety margin of
approximately 2^-57 for Authenticated Encryption (AE) security.
" in Section 5.5 by this sentence: " For AES-GCM, up to 2^48
(partial or full) input blocks may be encrypted with one key. For
other suggestions and analysis, see the referred paper above."
I like the suggestion, but I’m probably missing something pretty
basic about it.
2^24.5 full-size records is 2^24.5 records of 2^14 bytes each, or
(since an AES block is 16 bytes or 2^4 bytes) 2^24.5 records of 2^10
Why is that 2^48 input blocks rather than 2^34.5 input blocks?
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