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From: Dan Brown <danibrown@blackberry.com>
To: Neil Madden <neil.e.madden@gmail.com>, Paul Grubbs <pag225@cornell.edu>
CC: CFRG <cfrg@irtf.org>
Thread-Topic: [Cfrg] Multi-recipient public key authenticated encryption
Thread-Index: AQHWHJ3sAo0Oxh6TOE2cxrrC/lIO9KiNVcmAgAAMF4D//734oA==
Date: Mon, 27 Apr 2020 16:00:28 +0000
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Archived-At: <https://mailarchive.ietf.org/arch/msg/cfrg/3clSR2i3Zg-LDzmlzmtxFQp2sOs>
Subject: Re: [Cfrg] Multi-recipient public key authenticated encryption
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Hi Neil,

I recall that =E2=80=9Cunified model=E2=80=9D is well-known to lack some se=
curity property. Maybe, key-compromise impersonation (KCI)?

If Eve has Bob=E2=80=99s private key, can Eve impersonate Alice?

E.g. replace ECDH(alice_private, bob_public) by ECDH(bob_private, alice_pub=
lic)?

Dan

=20

From: Cfrg <cfrg-bounces@irtf.org> On Behalf Of Neil Madden
Sent: Monday, April 27, 2020 11:54 AM
To: Paul Grubbs <pag225@cornell.edu>
Cc: CFRG <cfrg@irtf.org>
Subject: Re: [Cfrg] Multi-recipient public key authenticated encryption

=20

The details of the original proposed scheme are in the linked draft or are =
in NIST SP 800-56A. To summarise, if Alice wants to encrypt a message and s=
end it to both Bob and Charlie she carries out the following steps (with so=
me minor details of syntax elided):

=20

1. Generate a random CEK and use it to encrypt the message content using so=
me symmetric AEAD scheme producing authenticated ciphertext, C.

2. kek_bob =3D KDF(ECDH(ephemeral_private, bob_public) || ECDH(alice_privat=
e, bob_public) || context_bob)

3. kek_charlie =3D KDF(ECDH(ephemeral_private, charlie_public) || ECDH(alic=
e_private, charlie_public) || context_charlie)

4. bob_box =3D AES-KW(kek_bob, CEK)

5. charlie_box =3D AES-KW(kek_charlie, CEK)

6. Send bob_box || charlie_box || ephemeral_public || C

=20

Here the context arguments are typically the public keys involved and any a=
dditional identifiers for the parties involved. The new proposal is to also=
 mix in SHA-512(C) into this KDF calculation as additional context.

=20

The threat model here is that Alice sends a message to Bob and Charlie stat=
ing that Bob is in charge while she is on holiday. Charlie uses the shared =
CEK to create a new message saying =E2=80=9COops, I meant that Charlie is i=
n charge.=E2=80=9D and sends that to Bob with the original encrypted keys (=
i.e., Charlie just replaces C). This new message from Charlie validates as =
if it came from Alice. I=E2=80=99d like to stop this kind of attack.

=20

My assertion is that if you mix SHA-512(C) into the KDF calculation then Ch=
arlie needs to find a 2nd preimage of SHA-512 to pull off this attack. (I=
=E2=80=99m using SHA-512 as an example, actually JOSE already uses SHA-256 =
in its KDF so I=E2=80=99ll probably use that).

=20

=E2=80=94 Neil





On 27 Apr 2020, at 16:10, Paul Grubbs <pag225@cornell.edu <mailto:pag225@co=
rnell.edu> > wrote:

=20

This sounds like a really interesting question, but I'm having trouble unde=
rstanding your proposed scheme - can you give a bit more detail?=20

=20

I also don't quite understand the threat model. Are you trying to prevent a=
 malicious receiver from "forging" a new payload that looks like it came fr=
om the sender?

=20

On Mon, Apr 27, 2020 at 10:12 AM Neil Madden <neil.e.madden@gmail.com <mail=
to:neil.e.madden@gmail.com> > wrote:

Hi all,

=20

I am working on an enhancement to the JOSE standards and would like feedbac=
k from members of CFRG about solutions to a particular issue if any of you =
have time.

=20

In JOSE currently if you wish to create a message that has both confidentia=
lity and sender authentication using public key cryptography then the only =
option is to both sign and then encrypt the message. This is expensive beca=
use it involves multiple passes over the message and results in a very bulk=
y nested message structure with two layers of base64-encoding.

=20

Given that many uses of this sign-then-encrypt pattern do not require the s=
trong security properties of signatures, I have proposed [1] a public key a=
uthenticated encryption mode based on NIST=E2=80=99s one-pass unified model=
 from SP 800-56A. This avoids the nested structure and means that you don=
=E2=80=99t need multiple cryptographic primitives. The proposed algorithm u=
ses two ECDH key agreements: one between the sender=E2=80=99s ephemeral pri=
vate key and the recipient=E2=80=99s long-term public key; and a second bet=
ween the two parties=E2=80=99 long term keys. The two shared secrets are co=
ncatenated and passed through a KDF along with some context arguments. For =
a single recipient this achieves sender authentication (subject to replay),=
 and the single recipient case is what I am primarily concerned about.

=20

(If you squint this is also roughly similar to the Noise framework =E2=80=
=9CK=E2=80=9D one-way pattern, but my hands are waving quite a lot here).

=20

To support multiple recipients I copied the existing pattern used in JOSE=
=E2=80=99s ECDH-ES+A256KW algorithm family in which the message is encrypte=
d using a random Content Encryption Key (CEK) and then the CEK is encrypted=
 for each recipient using AES-KeyWrap with the ECDH-derived key. As I then =
mention in the security considerations this leads to any recipient being ab=
le to produce a forgery using that CEK and claim it came from the original =
sender:

=20

   When Key Agreement with Key Wrapping is used, with the same Content
   Encryption Key (CEK) reused for multiple recipients, any of those
   recipients can produce a new message that appears to come from the
   original sender.  The new message will be indistinguishable from a
   genuine message from the original sender to any of the other
   participants.  To avoid this attack, the content SHOULD be encrypted
   separately to each recipient with a unique CEK or a nested signature
   over the content SHOULD be used.

=20

Because I am primarily interested in single-recipient use cases, this seeme=
d like an acceptable trade-off. However, I have since been contacted by peo=
ple who would like to use this draft for multi-recipient messages and would=
 not like to fall back on a nested signature structure.

=20

An initial proposal was to solve this by simply including the MAC tag from =
the content encryption in either the per-recipient payload (encrypted using=
 AES-KeyWrap) or as an additional context field to the KDF. But the MAC is =
computed using the CEK that is known to all recipients, so for this to be s=
ecure would require second preimage resistance of the MAC with a known key,=
 which cannot be guaranteed for JOSE because it supports content encryption=
 using AES-GCM for which second preimages can be trivially computed if you =
know the key.

=20

Assuming that a per-recipient MAC is too much overhead, an alternative woul=
d be to include a collision-resistant hash of entire ciphertext (and IV and=
 associated data) in the KDF. This is unfortunate as it requires another pa=
ss over the entire message when we=E2=80=99ve already encrypted and MACed, =
but it appears to be a solution and at least is no more inefficient than th=
e original signed-then-encrypted approach which also needs to hash the enti=
re message.

=20

So two questions:

=20

1. Is including a hash (e.g., SHA-512) of the ciphertext (assuming symmetri=
c AE) in the per-recipient KDF calculation sufficient to prevent forgeries =
in the multi-recipient setting?

=20

2. Are there more efficient alternatives that don=E2=80=99t assume 2nd prei=
mage resistance of the underlying symmetric MAC?

=20

[1]: https://tools.ietf.org/html/draft-madden-jose-ecdh-1pu-03 <https://url=
defense.proofpoint.com/v2/url?u=3Dhttps-3A__tools.ietf.org_html_draft-2Dmad=
den-2Djose-2Decdh-2D1pu-2D03&d=3DDwMFaQ&c=3DyzoHOc_ZK-sxl-kfGNSEvlJYanssXN3=
q-lhj0sp26wE&r=3Dmf6j6fOClApRsArWE9wqI1rEGUVkfxZ0aXWmn35nK_c&m=3DKlOwyf9hUX=
lVGjlgt8Wi940vBk4gshSudWFblTPOqqw&s=3Dhl600UzfUwE0mwdBn12J1fBTXatCOOKthaRGK=
w9n6ZM&e=3D>=20

=20

Kind regards,

=20

Neil Madden

_______________________________________________
Cfrg mailing list
Cfrg@irtf.org <mailto:Cfrg@irtf.org>=20
https://www.irtf.org/mailman/listinfo/cfrg <https://urldefense.proofpoint.c=
om/v2/url?u=3Dhttps-3A__www.irtf.org_mailman_listinfo_cfrg&d=3DDwMFaQ&c=3Dy=
zoHOc_ZK-sxl-kfGNSEvlJYanssXN3q-lhj0sp26wE&r=3Dmf6j6fOClApRsArWE9wqI1rEGUVk=
fxZ0aXWmn35nK_c&m=3DKlOwyf9hUXlVGjlgt8Wi940vBk4gshSudWFblTPOqqw&s=3DZsd48TB=
tVxnczibcn8zmbWpsdpRyprK6NbobiMEqaec&e=3D>=20

=20

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</o:shapelayout></xml><![endif]--></head><body lang=3DEN-US link=3Dblue vli=
nk=3Dpurple><div class=3DWordSection1><p class=3DMsoNormal>Hi Neil,<o:p></o=
:p></p><p class=3DMsoNormal>I recall that =E2=80=9Cunified model=E2=80=9D i=
s well-known to lack some security property. Maybe, key-compromise imperson=
ation (KCI)?<o:p></o:p></p><p class=3DMsoNormal>If Eve has Bob=E2=80=99s pr=
ivate key, can Eve impersonate Alice?<o:p></o:p></p><p class=3DMsoNormal>E.=
g. replace ECDH(alice_private, bob_public) by ECDH(bob_private, alice_publi=
c)?<o:p></o:p></p><div><p class=3DMsoNormal><span lang=3DEN-CA>Dan<o:p></o:=
p></span></p></div><p class=3DMsoNormal><o:p>&nbsp;</o:p></p><div style=3D'=
border:none;border-left:solid blue 1.5pt;padding:0in 0in 0in 4.0pt'><div><d=
iv style=3D'border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0i=
n 0in'><p class=3DMsoNormal><b>From:</b> Cfrg &lt;cfrg-bounces@irtf.org&gt;=
 <b>On Behalf Of </b>Neil Madden<br><b>Sent:</b> Monday, April 27, 2020 11:=
54 AM<br><b>To:</b> Paul Grubbs &lt;pag225@cornell.edu&gt;<br><b>Cc:</b> CF=
RG &lt;cfrg@irtf.org&gt;<br><b>Subject:</b> Re: [Cfrg] Multi-recipient publ=
ic key authenticated encryption<o:p></o:p></p></div></div><p class=3DMsoNor=
mal><o:p>&nbsp;</o:p></p><div><p class=3DMsoNormal>The details of the origi=
nal proposed scheme are in the linked draft or are in NIST SP 800-56A. To s=
ummarise, if Alice wants to encrypt a message and send it to both Bob and C=
harlie she carries out the following steps (with some minor details of synt=
ax elided):<o:p></o:p></p></div><div><p class=3DMsoNormal><o:p>&nbsp;</o:p>=
</p></div><div><p class=3DMsoNormal>1. Generate a random CEK and use it to =
encrypt the message content using some symmetric AEAD scheme producing auth=
enticated ciphertext, C.<o:p></o:p></p></div><div><p class=3DMsoNormal>2. k=
ek_bob =3D KDF(ECDH(ephemeral_private, bob_public) || ECDH(alice_private, b=
ob_public) || context_bob)<o:p></o:p></p></div><div><p class=3DMsoNormal>3.=
 kek_charlie =3D KDF(ECDH(ephemeral_private, charlie_public) || ECDH(alice_=
private, charlie_public) || context_charlie)<o:p></o:p></p></div><div><p cl=
ass=3DMsoNormal>4. bob_box =3D AES-KW(kek_bob, CEK)<o:p></o:p></p></div><di=
v><p class=3DMsoNormal>5. charlie_box =3D AES-KW(kek_charlie, CEK)<o:p></o:=
p></p></div><div><p class=3DMsoNormal>6. Send bob_box || charlie_box || eph=
emeral_public || C<o:p></o:p></p></div><div><p class=3DMsoNormal><o:p>&nbsp=
;</o:p></p></div><div><p class=3DMsoNormal>Here the context arguments are t=
ypically the public keys involved and any additional identifiers for the pa=
rties involved. The new proposal is to also mix in SHA-512(C) into this KDF=
 calculation as additional context.<o:p></o:p></p></div><div><p class=3DMso=
Normal><o:p>&nbsp;</o:p></p></div><div><p class=3DMsoNormal>The threat mode=
l here is that Alice sends a message to Bob and Charlie stating that Bob is=
 in charge while she is on holiday. Charlie uses the shared CEK to create a=
 new message saying =E2=80=9COops, I meant that Charlie is in charge.=E2=80=
=9D and sends that to Bob with the original encrypted keys (i.e., Charlie j=
ust replaces C). This new message from Charlie validates as if it came from=
 Alice. I=E2=80=99d like to stop this kind of attack.<o:p></o:p></p></div><=
div><p class=3DMsoNormal><o:p>&nbsp;</o:p></p></div><div><p class=3DMsoNorm=
al>My assertion is that if you mix SHA-512(C) into the KDF calculation then=
 Charlie needs to find a 2nd preimage of SHA-512 to pull off this attack. (=
I=E2=80=99m using SHA-512 as an example, actually JOSE already uses SHA-256=
 in its KDF so I=E2=80=99ll probably use that).<o:p></o:p></p></div><div><p=
 class=3DMsoNormal><o:p>&nbsp;</o:p></p></div><div><p class=3DMsoNormal>=E2=
=80=94 Neil<o:p></o:p></p><div><p class=3DMsoNormal><br><br><o:p></o:p></p>=
<blockquote style=3D'margin-top:5.0pt;margin-bottom:5.0pt'><div><p class=3D=
MsoNormal>On 27 Apr 2020, at 16:10, Paul Grubbs &lt;<a href=3D"mailto:pag22=
5@cornell.edu">pag225@cornell.edu</a>&gt; wrote:<o:p></o:p></p></div><p cla=
ss=3DMsoNormal><o:p>&nbsp;</o:p></p><div><div><p class=3DMsoNormal>This sou=
nds like a really interesting question, but I'm having trouble understandin=
g your proposed scheme - can you give a bit more detail?&nbsp;<o:p></o:p></=
p><div><p class=3DMsoNormal><o:p>&nbsp;</o:p></p></div><div><p class=3DMsoN=
ormal>I also don't quite understand the threat model. Are you trying to pre=
vent a malicious receiver from &quot;forging&quot; a new payload that looks=
 like it came from the sender?<o:p></o:p></p></div></div><p class=3DMsoNorm=
al><o:p>&nbsp;</o:p></p><div><div><p class=3DMsoNormal>On Mon, Apr 27, 2020=
 at 10:12 AM Neil Madden &lt;<a href=3D"mailto:neil.e.madden@gmail.com">nei=
l.e.madden@gmail.com</a>&gt; wrote:<o:p></o:p></p></div><blockquote style=
=3D'border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;m=
argin-left:4.8pt;margin-right:0in'><div><p class=3DMsoNormal>Hi all,<o:p></=
o:p></p><div><p class=3DMsoNormal><o:p>&nbsp;</o:p></p></div><div><p class=
=3DMsoNormal>I am working on an enhancement to the JOSE standards and would=
 like feedback from members of CFRG about solutions to a particular issue i=
f any of you have time.<o:p></o:p></p></div><div><p class=3DMsoNormal><o:p>=
&nbsp;</o:p></p></div><div><p class=3DMsoNormal>In JOSE currently if you wi=
sh to create a message that has both confidentiality and sender authenticat=
ion using public key cryptography then the only option is to both sign and =
then encrypt the message. This is expensive because it involves multiple pa=
sses over the message and results in a very bulky nested message structure =
with two layers of base64-encoding.<o:p></o:p></p></div><div><p class=3DMso=
Normal><o:p>&nbsp;</o:p></p></div><div><p class=3DMsoNormal>Given that many=
 uses of this sign-then-encrypt pattern do not require the strong security =
properties of signatures, I have proposed [1] a public key authenticated en=
cryption mode based on NIST=E2=80=99s one-pass unified model from SP 800-56=
A. This avoids the nested structure and means that you don=E2=80=99t need m=
ultiple cryptographic primitives. The proposed algorithm uses two ECDH key =
agreements: one between the sender=E2=80=99s ephemeral private key and the =
recipient=E2=80=99s long-term public key; and a second between the two part=
ies=E2=80=99 long term keys. The two shared secrets are concatenated and pa=
ssed through a KDF along with some context arguments. For a single recipien=
t this achieves sender authentication (subject to replay), and the single r=
ecipient case is what I am primarily concerned about.<o:p></o:p></p></div><=
div><p class=3DMsoNormal><o:p>&nbsp;</o:p></p></div><div><p class=3DMsoNorm=
al>(If you squint this is also roughly similar to the Noise framework =E2=
=80=9CK=E2=80=9D one-way pattern, but my hands are waving quite a lot here)=
.<o:p></o:p></p></div><div><p class=3DMsoNormal><o:p>&nbsp;</o:p></p></div>=
<div><p class=3DMsoNormal>To support multiple recipients I copied the exist=
ing pattern used in JOSE=E2=80=99s ECDH-ES+A256KW algorithm family in which=
 the message is encrypted using a random Content Encryption Key (CEK) and t=
hen the CEK is encrypted for each recipient using AES-KeyWrap with the ECDH=
-derived key. As I then mention in the security considerations this leads t=
o any recipient being able to produce a forgery using that CEK and claim it=
 came from the original sender:<o:p></o:p></p></div><div><p class=3DMsoNorm=
al><o:p>&nbsp;</o:p></p></div><div><pre style=3D'break-before:page'>=C2=A0=
=C2=A0 When Key Agreement with Key Wrapping is used, with the same Content<=
o:p></o:p></pre><pre>=C2=A0=C2=A0 Encryption Key (CEK) reused for multiple =
recipients, any of those<o:p></o:p></pre><pre>=C2=A0=C2=A0 recipients can p=
roduce a new message that appears to come from the<o:p></o:p></pre><pre>=C2=
=A0=C2=A0 original sender.=C2=A0 The new message will be indistinguishable =
from a<o:p></o:p></pre><pre>=C2=A0=C2=A0 genuine message from the original =
sender to any of the other<o:p></o:p></pre><pre>=C2=A0=C2=A0 participants.=
=C2=A0 To avoid this attack, the content SHOULD be encrypted<o:p></o:p></pr=
e><pre>=C2=A0=C2=A0 separately to each recipient with a unique CEK or a nes=
ted signature<o:p></o:p></pre><pre>=C2=A0=C2=A0 over the content SHOULD be =
used.<o:p></o:p></pre></div><div><p class=3DMsoNormal><o:p>&nbsp;</o:p></p>=
</div><div><p class=3DMsoNormal>Because I am primarily interested in single=
-recipient use cases, this seemed like an acceptable trade-off. However, I =
have since been contacted by people who would like to use this draft for mu=
lti-recipient messages and would not like to fall back on a nested signatur=
e structure.<o:p></o:p></p></div><div><p class=3DMsoNormal><o:p>&nbsp;</o:p=
></p></div><div><p class=3DMsoNormal>An initial proposal was to solve this =
by simply including the MAC tag from the content encryption in either the p=
er-recipient payload (encrypted using AES-KeyWrap) or as an additional cont=
ext field to the KDF. But the MAC is computed using the CEK that is known t=
o all recipients, so for this to be secure would require second preimage re=
sistance of the MAC with a known key, which cannot be guaranteed for JOSE b=
ecause it supports content encryption using AES-GCM for which second preima=
ges can be trivially computed if you know the key.<o:p></o:p></p></div><div=
><p class=3DMsoNormal><o:p>&nbsp;</o:p></p></div><div><p class=3DMsoNormal>=
Assuming that a per-recipient MAC is too much overhead, an alternative woul=
d be to include a collision-resistant hash of entire ciphertext (and IV and=
 associated data) in the KDF. This is unfortunate as it requires another pa=
ss over the entire message when we=E2=80=99ve already encrypted and MACed, =
but it appears to be a solution and at least is no more inefficient than th=
e original signed-then-encrypted approach which also needs to hash the enti=
re message.<o:p></o:p></p></div><div><p class=3DMsoNormal><o:p>&nbsp;</o:p>=
</p></div><div><p class=3DMsoNormal>So two questions:<o:p></o:p></p></div><=
div><p class=3DMsoNormal><o:p>&nbsp;</o:p></p></div><div><p class=3DMsoNorm=
al>1. Is including a hash (e.g., SHA-512) of the ciphertext (assuming symme=
tric AE) in the per-recipient KDF calculation sufficient to prevent forgeri=
es in the multi-recipient setting?<o:p></o:p></p></div><div><p class=3DMsoN=
ormal><o:p>&nbsp;</o:p></p></div><div><p class=3DMsoNormal>2. Are there mor=
e efficient alternatives that don=E2=80=99t assume 2nd preimage resistance =
of the underlying symmetric MAC?<o:p></o:p></p></div><div><p class=3DMsoNor=
mal><o:p>&nbsp;</o:p></p></div><div><p class=3DMsoNormal>[1]:&nbsp;<a href=
=3D"https://urldefense.proofpoint.com/v2/url?u=3Dhttps-3A__tools.ietf.org_h=
tml_draft-2Dmadden-2Djose-2Decdh-2D1pu-2D03&amp;d=3DDwMFaQ&amp;c=3DyzoHOc_Z=
K-sxl-kfGNSEvlJYanssXN3q-lhj0sp26wE&amp;r=3Dmf6j6fOClApRsArWE9wqI1rEGUVkfxZ=
0aXWmn35nK_c&amp;m=3DKlOwyf9hUXlVGjlgt8Wi940vBk4gshSudWFblTPOqqw&amp;s=3Dhl=
600UzfUwE0mwdBn12J1fBTXatCOOKthaRGKw9n6ZM&amp;e=3D" target=3D"_blank">https=
://tools.ietf.org/html/draft-madden-jose-ecdh-1pu-03</a><o:p></o:p></p></di=
v><div><p class=3DMsoNormal><o:p>&nbsp;</o:p></p></div><div><p class=3DMsoN=
ormal>Kind regards,<o:p></o:p></p></div><div><p class=3DMsoNormal><o:p>&nbs=
p;</o:p></p></div><div><p class=3DMsoNormal>Neil Madden<o:p></o:p></p></div=
></div><p class=3DMsoNormal>_______________________________________________=
<br>Cfrg mailing list<br><a href=3D"mailto:Cfrg@irtf.org" target=3D"_blank"=
>Cfrg@irtf.org</a><br><a href=3D"https://urldefense.proofpoint.com/v2/url?u=
=3Dhttps-3A__www.irtf.org_mailman_listinfo_cfrg&amp;d=3DDwMFaQ&amp;c=3DyzoH=
Oc_ZK-sxl-kfGNSEvlJYanssXN3q-lhj0sp26wE&amp;r=3Dmf6j6fOClApRsArWE9wqI1rEGUV=
kfxZ0aXWmn35nK_c&amp;m=3DKlOwyf9hUXlVGjlgt8Wi940vBk4gshSudWFblTPOqqw&amp;s=
=3DZsd48TBtVxnczibcn8zmbWpsdpRyprK6NbobiMEqaec&amp;e=3D" target=3D"_blank">=
https://www.irtf.org/mailman/listinfo/cfrg</a><o:p></o:p></p></blockquote><=
/div></div></blockquote></div><p class=3DMsoNormal><o:p>&nbsp;</o:p></p></d=
iv></div></div>
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