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Issue 778101 link

Starred by 3 users

Issue metadata

Status: Fixed
Closed: Nov 2017
EstimatedDays: ----
NextAction: ----
OS: Linux , Windows , Chrome , Mac
Pri: 2
Type: Bug-Security

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SPAKE password-scalar not multiplied by 8

Reported by, Oct 25 2017

Issue description


The M and N constants used by the BoringSSL SPAKE code (crypto/curve25519/spake25519.c) do not appear to be in the prime-order subgroup of the generator:

$ python -i 
>>> N = decodepoint('10e3df0ae37d8e7a99b5fe74b44672103dbddcbd06af680d71329a11693bc778'.decode('hex'))
>>> M = decodepoint('5ada7e4bf6ddd9adb6626d32131c6b5c51a1e347a3478f53cfcf441b88eed12e'.decode('hex'))
>>> scalarmult(N, l) == [0, 1]
>>> scalarmult(N, 2 * l) == [0, 1]
>>> scalarmult(N, 4 * l) == [0, 1]
>>> scalarmult(N, 8 * l) == [0, 1]
>>> scalarmult(M, l) == [0, 1]
>>> scalarmult(M, 2 * l) == [0, 1]

As a result, the order of the points used in protocol messages will depend on the low-order bits of SHA512(password).  An attacker could use that information to filter password candidates by a factor of 8 before conducting an online password attack.  That's not a very interesting attack, but there might be other ramifications which I'm not aware of, so I'm going through the security reporting channel for now.  At some point soon I will want to talk about replacing the M and N values in draft-ietf-kitten-krb-spake-preauth on the kitten list, which will make this issue more public.

After modifying the Python code (currently misformatted after the comment conversion, incidentally; the first few lines were converted to // comments and the rest is in a /* */ block comment) to check the point order, I get:

N = d3bfb518f44f3430f29d0c92af503865a1ed3281dc69b35dd868ba85f886c4ab
M = d048032c6ea0b6d697ddc2e86bda85a33adac920f1bf18e1b0c6d166a5cecdaf

after 7 iterations for N and 21 iterations for M.  Changing to these values is obviously an incompatible protocol change.


All Chromium versions which use the SPAKE code.




Components: Services>Chromoting
Status: Assigned (was: Unconfirmed)
I believe the only consumer of this is Chromoting. I'm not familiar with the SPAKE stuff. Adam?

Comment 3 by, Oct 26 2017

Summary: SPAKE password-scalar not multiplied by 8 (was: Security: SPAKE M/N values not in prime-order subgroup)
Thank you for this.

The issue isn't with the order of the points, it's that I missed left_shift_3 after reducing the password-scalar. It's included after reducing the ephemeral scalar, where it's less obviously needed, but then I missed it in the obvious case :(

That is quite an embarrassing screw up.

Thankfully, for Chromoting, the SPAKE messages are carried within TLS and you have to have sharing permissions in order to even be able to exchange them, I believe. So the impact is limited.

The correct fix would be to add the missing left-shift, but that would be incompatible and thus hard to deploy rapidly.

I think that I have a unilateral fix though, although I'll sit on it for a couple of days and see whether I can find a problem:

The ephemeral scalar *does* have the left-shift, so is a multiple of 8. Thus if we add $l$ (where $l$ is the order of the prime-order subgroup) to the password scalar, the other party will calculate

xB + (p+l)N + -pN = xB + lN

(where $x$ is Alice's ephemeral scalar and $p$ is her password-scalar)

Then, when Bob does the scalar-mult:

y(xB + lN) = xyB + ylN = xyB (because y is a multiple of 8 and adding 8*l of any point is a no-op)
So the resulting shared secret will be the same.

Since $l$ is prime, the LSB is 1. Thus we can add $l$ to clear the LSB of the password scalar, 2*l to clear the next bit, and 4*l to clear another bit. Thus the password scalar will be a multiple of eight, as required, without breaking anything.

As for whether the points should be in the prime-order subgroup: I didn't bother and instead decided(/failed) to clear the subgroup. Having N and M be in the prime-order subgroup slightly complicates the generation but doesn't eliminate all cofactor considerations because the peer can still send a point outside of that subgroup.

Failing to clear the subgroup would have been immediately obvious had there been any test vectors (i.e. it can't be a subtle error), but there were no other implementations to test against at the time. (Of course, I should have done a model in Python or such but hindsight is, as ever, 20/20.)

Comment 4 by, Oct 27 2017

> Having N and M be in the prime-order subgroup slightly complicates the generation but doesn't eliminate all cofactor considerations because the peer can still send a point outside of that subgroup.

I don't follow.  I'm going to calculate y(T-wM) (for Bob).  If T is outside of the subgroup, T-wM will also be outside of the subgroup, whether or not w is a multiple of 8.  However, as long as y is a multiple of 8, y(T-wM) will be in the subgroup.  So if M and N are in the subgroup, I'm missing the reason to force w to be a multiple of the cofactor, though I do see a reason to force x and y to be.

Comment 5 by, Oct 27 2017

I think you're correct in all the above:

There's nothing wrong with tweaking the point generation to put N and M in the prime-order subgroup. I didn't because:

a) it's not the case that you can ignore the co-factor in the rest of the protocol by doing that because you still need to consider the case where T is outside the subgroup. One can argue about whether x and y need to be multiples of eight but I eventually decided that SPAKE2 should follow X25519 here. So one needs the left_shift_3 function anyway so it's easy to do that with the password hash too. (Unless you copy-paste one line too few and skip it, of course.)

b) This was done during the time when the IETF was discussing what lead to which involved an exhausting debate over every tiny point of curve-picking algorithms and whether we were all secret NSA agents seeking to backdoor standards. Thus adding complexity to the point-generation function seemed likely to spur more of that.

c) this isn't a subtle error: failing to multiply the password scalar leads to interop failure. Thus, in a wider ecosystem we wouldn't expect it to be a bigger problem than, say, transcribing the N and M points incorrectly or something.

I can see a counter argument that it's worth publishing point-picking algorithms that integrate the cofactor directly because people might use them on other curves and having an input called "cofactor" will make them think whilst they might otherwise just duplicate the "multiply by 8" in the code. I don't have strong feelings about it and was mostly worried about (b) at the time.

Comment 6 by, Oct 27 2017

(p.s. looks like picked up putting M and N in the prime-order subgroup along the way. Although that draft seems to have languished, unifying with it still seems like a decent idea for other protocols.)
Labels: Security_Severity-Low Security_Impact-Stable reward-topanel OS-Chrome OS-Linux OS-Mac OS-Windows
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Comment 8 by, Oct 31 2017

Labels: Pri-2
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Comment 9 by, Oct 31 2017

The following revision refers to this bug:

commit 696c13bd6ab78011adfe7b775519c8b7cc82b604
Author: Adam Langley <>
Date: Tue Oct 31 20:58:29 2017

Clear bottom three bits of password scalar in SPAKE2.

Due to a copy-paste error, the call to |left_shift_3| is missing after
reducing the password scalar in SPAKE2. This means that three bits of
the password leak in Alice's message. (Two in Bob's message as the point
N happens to have order 4l, not 8l.)

The “correct” fix is to put in the missing call to |left_shift_3|, but
that would be a breaking change. In order to fix this in a unilateral
way, we add points of small order to the masking point to bring it into
prime-order subgroup.

BUG= chromium:778101 

Change-Id: I440931a3df7f009b324d2a3e3af2d893a101804f
Reviewed-by: Adam Langley <>
Reviewed-by: David Benjamin <>
Commit-Queue: Adam Langley <>
CQ-Verified: CQ bot account: <>


Comment 10 by, Oct 31 2017

(Will let this fix proof in the tree for about a week before starting merges.)

Comment 11 by, Oct 31 2017

(And the timer doesn't start until another change rolls BoringSSL into Chromium.)
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Comment 12 by, Nov 3 2017

The following revision refers to this bug:

commit a263d1cf62a9c75be6aaafdec88aacfcef1e8fd2
Author: Adam Langley <>
Date: Fri Nov 03 15:08:25 2017

Roll src/third_party/boringssl/src 664e99a64..696c13bd6

BUG= 778101 

Change-Id: I8dda4f3db952597148e3c7937319584698d00e1c
Reviewed-by: Avi Drissman <>
Reviewed-by: David Benjamin <>
Commit-Queue: Steven Valdez <>
Cr-Commit-Position: refs/heads/master@{#513774}

Comment 13 by, Nov 10 2017

Labels: Merge-Request-63
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Comment 14 by, Nov 10 2017

Labels: -Merge-Request-63 Merge-Review-63 Hotlist-Merge-Review
This bug requires manual review: DEPS changes referenced in bugdroid comments.
Please contact the milestone owner if you have questions.
Owners: cmasso@(Android), cmasso@(iOS), gkihumba@(ChromeOS), govind@(Desktop)

For more details visit - Your friendly Sheriffbot
+awhalley@ for M63 merge revivew
Labels: M-63
Also pls apply appropriate milestone labels. Adding M63 per comment #13 for now.
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Comment 17 by, Nov 11 2017

Status: Fixed (was: Assigned)
Please mark security bugs as fixed as soon as the fix lands, and before requesting merges. This update is based on the merge- labels applied to this issue. Please reopen if this update was incorrect.

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govind@ - good for 63 (for a cherrypick of the SPAKE2 changes in #9, rather than the full roll in #12)
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Comment 19 by, Nov 12 2017

Labels: -Restrict-View-SecurityTeam Restrict-View-SecurityNotify
Labels: -Merge-Review-63 Merge-Approved-63
Approving merge for cl listed at #9 to M63 branch 3239 based on comment #18.

Cl listed at #12 is not approved for merge per comment #18.
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Comment 21 by, Nov 16 2017

This issue has been approved for a merge. Please merge the fix to any appropriate branches as soon as possible!

If all merges have been completed, please remove any remaining Merge-Approved labels from this issue.

Thanks for your time! To disable nags, add the Disable-Nags label.

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Comment 22 by, Nov 16 2017

The following revision refers to this bug:

commit cab9ce4c11edf393672dfed492deed665dca9015
Author: Adam Langley <>
Date: Thu Nov 16 18:20:46 2017

Please merge your change to M63 branch 3239 by 4:00 PM PT, tomorrow (Friday) so we can pick it up for next week Beta release. Thank you.
Labels: -Hotlist-Merge-Review -Merge-Approved-63 merge-merged-3239
Labels: -reward-topanel reward-unpaid reward-500
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Thanks for the report, ghudson@! The Chrome VRP panel decided to award $500 for this. A member of our finance team will be in touch to arrange for payment.
Labels: -reward-unpaid reward-inprocess
Labels: Release-0-M63
Labels: CVE-2017-15423
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Comment 30 by, Feb 17 2018

Labels: -Restrict-View-SecurityNotify allpublic
This bug has been closed for more than 14 weeks. Removing security view restrictions.

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Comment 31 by, Mar 27 2018

Labels: -M-63 M-65
Labels: CVE_description-missing
Labels: -CVE_description-missing CVE_description-submitted

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