Internet Engineering Task Force (IETF) Y. Sheffer
Request for Comments: 6989 Porticor
Updates: 5996 S. Fluhrer
Category: Standards Track Cisco
ISSN: 2070-1721 July 2013 Additional Diffie-Hellman Tests
for the Internet Key Exchange Protocol Version 2 (IKEv2)
This document adds a small number of mandatory tests required for the
secure operation of the Internet Key Exchange Protocol version 2
(IKEv2) with elliptic curve groups. No change is required to IKE
implementations that use modular exponential groups, other than a few
rarely used so-called Digital Signature Algorithm (DSA) groups. This
document updates the IKEv2 protocol, RFC 5996.
Status of This Memo
This is an Internet Standards Track document.
This document is a product of the Internet Engineering Task Force
(IETF). It represents the consensus of the IETF community. It has
received public review and has been approved for publication by the
Internet Engineering Steering Group (IESG). Further information on
Internet Standards is available in Section 2 of RFC 5741.
Information about the current status of this document, any errata,
and how to provide feedback on it may be obtained at
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Table of Contents
1. Introduction ....................................................21.1. Conventions Used in This Document ..........................32. Group Membership Tests ..........................................32.1. Sophie Germain Prime MODP Groups ...........................32.2. MODP Groups with Small Subgroups ...........................32.3. Elliptic Curve Groups ......................................42.4. Transition .................................................42.5. Protocol Behavior ..........................................53. Side-Channel Attacks ............................................54. Security Considerations .........................................64.1. DH Key Reuse and Multiple Peers ............................64.2. DH Key Reuse: Variants .....................................74.3. Groups Not Covered by This RFC .............................74.4. Behavior upon Test Failure .................................75. IANA Considerations .............................................86. Acknowledgements ................................................87. References ......................................................97.1. Normative References .......................................97.2. Informative References .....................................91. Introduction
IKEv2 [RFC5996] consists of the establishment of a shared secret
using the Diffie-Hellman (DH) protocol, followed by authentication of
the two peers. Existing implementations typically use modular
exponential (MODP) DH groups, such as those defined in [RFC3526].
IKEv2 does not require that any tests be performed by a peer
receiving a public Diffie-Hellman key from the other peer. This is
fine for the common case of MODP groups. For other DH groups, when
peers reuse DH values across multiple IKE sessions, the lack of tests
by the recipient results in a potential vulnerability (see
Section 4.1 for more details). In particular, this is true for
Elliptic Curve (EC) groups, whose use is becoming ever more popular.
This document defines such tests for several types of DH groups.
In addition, this document describes another potential attack related
to the reuse of DH keys: a timing attack. This additional material
is taken from [RFC2412].
This document updates [RFC5996] by adding security requirements that
apply to many of the protocol's implementations.
1.1. Conventions Used in This Document
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in [RFC2119].
2. Group Membership Tests
This section describes the tests that need to be performed by IKE
peers receiving a Key Exchange (KE) payload. The tests are
RECOMMENDED for all implementations but only REQUIRED for those that
reuse DH private keys (as defined in [RFC5996], Section 2.12). The
tests apply to the recipient of a KE payload and describe how it
should check the received payload. They are listed here according to
the DH group being used.
2.1. Sophie Germain Prime MODP Groups
These are currently the most commonly used groups; all these groups
have the property that (p-1)/2 is also prime; this section applies to
any such MODP group. Each recipient MUST verify that the peer's
public value r is in the legal range (1 < r < p-1). According to
[Menezes], Section 2.2, even with this check there remains the
possibility of leaking a single bit of the secret exponent when DH
keys are reused; this amount of leakage is insignificant.
See Section 5 for the specific groups covered by this section.
2.2. MODP Groups with Small Subgroups
[RFC5114] defines modular exponential groups with small subgroups;
these are modular exponential groups with comparatively small
subgroups, and all have (p-1)/2 composite. Section 2.1 of [Menezes]
describes some informational leakage from a small-subgroup attack on
these groups if the DH private value is reused.
This leakage can be prevented if the recipient performs a test on the
peer's public value; however, this test is expensive (approximately
as expensive as what reusing DH private values saves). In addition,
the NIST standard ([NIST-800-56A], Section 126.96.36.199) requires that
test; hence, anyone needing to conform to that standard will need to
implement the test anyway.
Because of the above, the IKE implementation MUST choose between one
of the following two options:
o It MUST check both that the peer's public value is in range (1 < r
< p-1) and that r^q = 1 mod p (where q is the size of the
subgroup, as listed in the RFC defining the group). DH private
values MAY then be reused. This option is appropriate if
conformance to [NIST-800-56A] is required.
o It MUST NOT reuse DH private values (that is, the DH private value
for each DH exchange MUST be generated from a fresh output of a
cryptographically secure random number generator), and it MUST
check that the peer's public value is in range (1 < r < p-1).
This option is more appropriate if conformance to [NIST-800-56A]
is not required.
See Section 5 for the specific groups covered by this section.
2.3. Elliptic Curve Groups
IKEv2 can be used with elliptic curve groups defined over a field
GF(p) [RFC5903] [RFC5114]. According to [Menezes], Section 2.3,
there is some informational leakage possible. A receiving peer MUST
check that its peer's public value is valid; that is, the x and y
parameters from the peer's public value satisfy the curve equation,
y^2 = x^3 + ax + b mod p (where for groups 19, 20, and 21, a=-3 (mod
p), and all other values of a, b, and p for the group are listed in
the RFC defining the group).
We note that an additional check to ensure that the public value is
not the point at infinity is not needed, because IKE (see Section 7
of [RFC5903]) does not allow for encoding this value.
See Section 5 for the specific groups covered by this section.
Existing implementations of IKEv2 with Elliptic Curve Diffie-Hellman
(ECDH) groups may be modified to include the tests described in the
current document, even if they do not reuse DH keys. The tests can
be considered as sanity checks and will prevent the code having to
handle inputs that it may not have been designed to handle.
ECDH implementations that do reuse DH keys MUST be enhanced to
include the above tests.
2.5. Protocol Behavior
The recipient of a DH public key that fails one of the above tests
must assume that the sender is either truly malicious or has a bug in
its implementation. The behavior defined below attempts to balance
resistance to attackers that are trying to disrupt the IKE exchange,
against the need to help a badly implemented peer by providing useful
If this error happens during the IKE_SA_INIT exchange, then the
recipient MUST drop the message that contains an invalid KE payload
and MUST NOT use that message when creating the IKE security
If the implementation employs the DoS-resistant behavior proposed in
Section 2.4 of [RFC5996], it may simply ignore the erroneous request
or response message, and continue waiting for a later message
containing a legitimate KE payload.
If DoS-resistant behavior is not implemented and the invalid KE
payload was in the IKE_SA_INIT request, the implementation MAY send
an INVALID_SYNTAX error notification back and remove the in-progress
IKE SA; if the invalid KE payload was in the IKE_SA_INIT response,
then the implementation MAY simply delete the half-created IKE SA and
re-initiate the exchange.
If the invalid KE payload is received during the CREATE_CHILD_SA
exchange (or any other exchange after the IKE SA has been
established) and the invalid KE payload is in the request message,
the Responder MUST reply with an INVALID_SYNTAX error notification
and drop the IKE SA. If the invalid KE payload is in a response, the
Initiator getting this reply MUST immediately delete the IKE SA by
sending an IKE SA Delete notification as a new exchange. In this
case, the sender evidently has an implementation bug, and dropping
the IKE SA makes it easier to detect.
3. Side-Channel Attacks
In addition to the small-subgroup attack, there is also a potential
timing attack on IKE peers when they are reusing Diffie-Hellman
secret values. This is a side-channel attack, which means that it
may or may not be a vulnerability in certain cases, depending on
implementation details and the threat model.
The remainder of this section is quoted from [RFC2412], Section 5,
with a few minor clarifications. This attack still applies to IKEv2
implementations, and both to MODP groups and ECDH groups. We also
note that more efficient countermeasures are available for EC groups
represented in projective form, but these are outside the scope of
the current document.
Timing attacks that are capable of recovering the exponent value used
in Diffie-Hellman calculations have been described by Paul Kocher
[Kocher]. In order to nullify the attack, implementors must take
pains to obscure the sequence of operations involved in carrying out
One potential method to foil these timing attacks is to use a
"blinding factor". In this method, a group element, r, is chosen at
random, and its multiplicative inverse modulo p is computed, which
we'll call r_inv. r_inv can be computed by the Extended Euclidean
Method, using r and p as inputs. When an exponent x is chosen, the
value r_inv^x is also calculated. Then, when calculating (g^y)^x,
the implementation will calculate this sequence:
A = r*g^y
B = A^x = (r*g^y)^x = (r^x)(g^(xy))
C = B*r_inv^x = (r^x)(r^(-1*x))(g^(xy)) = g^(xy)
The blinding factor is only necessary if the exponent x is used more
than 100 times.
4. Security Considerations
This entire document is concerned with the IKEv2 security protocol
and the need to harden it in some cases.
4.1. DH Key Reuse and Multiple Peers
This section describes one variant of the attack prevented by the
tests defined above.
Suppose that IKE peer Alice maintains IKE security associations with
peers Bob and Eve. Alice uses the same secret ECDH key for both SAs,
which is allowed with some restrictions. If Alice does not implement
these tests, Eve will be able to send a malformed public key, which
would allow her to efficiently determine Alice's private key (as
described in Section 2 of [Menezes]). Since the key is shared, Eve
will be able to obtain Alice's shared IKE SA key with Bob.
4.2. DH Key Reuse: Variants
Private DH keys can be reused in different ways, with subtly
different security implications. For example:
1. DH keys are reused for multiple connections (IKE SAs) to the same
peer and for connections to different peers.
2. DH keys are reused for multiple connections to the same peer
(e.g., when the peer is identified by its IP address) but not for
3. DH keys are reused only when they had not been used to complete
an exchange, e.g., when the peer replies with an
Both the small-subgroup attack and the timing attack described in
this document apply at least to options #1 and #2.
4.3. Groups Not Covered by This RFC
There are a number of group types that are not specifically addressed
by this RFC. A document that defines such a group MUST describe the
tests required by that group.
One specific type of group would be an even-characteristic elliptic
curve group. Now, these curves have cofactors greater than 1; this
leads to a possibility of some information leakage. There are
several ways to address this information leakage, such as performing
a test analogous to the test in Section 2.2 or adjusting the ECDH
operation to avoid this leakage (such as Elliptic Curve Cryptography
Cofactor Diffie-Hellman (ECC CDH), where the shared secret really is
hxyG). Because the appropriate test depends on how the group is
defined, we cannot document it in advance.
4.4. Behavior upon Test Failure
The behavior recommended in Section 2.5 is in line with generic error
treatment during the IKE_SA_INIT exchange, per Section 2.21.1 of
[RFC5996]. The sender is not required to send back an error
notification, and the recipient cannot depend on this notification
because it is unauthenticated and may in fact have been sent by an
attacker trying to launch a DoS attack on the connection. Thus, the
notification is only useful to debug implementation errors.
On the other hand, the error notification is secure in the sense that
no secret information is leaked. All IKEv2 Diffie-Hellman groups are
publicly known, and none of the tests defined here depend on any
private key. In fact, the tests can all be performed by an
The situation when the failure occurs in the CREATE_CHILD_SA exchange
is different, since everything is protected by an IKE SA. The peers
are authenticated, and error notifications can be relied on. See
Section 2.21.3 of [RFC5996] for more details on error handling in
5. IANA Considerations
IANA has added a column named "Recipient Tests" to the Transform
Type 4 - Diffie-Hellman Group Transform IDs registry for IKEv2
This column has been initially populated as follows.
| Number | Recipient Tests |
| 1, 2, 5, 14, 15, 16, 17, 18 | RFC 6989, Section 2.1 |
| 22, 23, 24 | RFC 6989, Section 2.2 |
| 19, 20, 21, 25, 26, 27, 28, 29, 30 | RFC 6989, Section 2.3 |
Groups 27-30 are defined in [RFC6954].
Future documents that define new DH groups for IKEv2 are REQUIRED to
provide this information for each new group, possibly by referring to
the current document.
We would like to thank Dan Harkins, who initially raised this issue
on the IPsec mailing list. Thanks to Tero Kivinen and Rene Struik
for their useful comments. Much of the text in Section 3 is taken
from [RFC2412], and we would like to thank its author, Hilarie Orman.
The document was originally prepared using the lyx2rfc tool, created
by Nico Williams.
[RFC5903] Fu, D. and J. Solinas, "Elliptic Curve Groups modulo a
Prime (ECP Groups) for IKE and IKEv2", RFC 5903,
[RFC6954] Merkle, J. and M. Lochter, "Using the Elliptic Curve
Cryptography (ECC) Brainpool Curves for the Internet Key
Exchange Protocol Version 2 (IKEv2)", RFC 6954, July 2013.
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