Network Working Group D. Harkins
Internet-Draft Aruba Networks
Intended status: Standards Track November 11, 2009
Expires: May 15, 2010
Secure PSK Authentication for IKE
draft-harkins-ipsecme-spsk-auth-00
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Abstract
This memo describes a secure pre-shared key authentication method for
IKE. It is resistant to dictionary attack and retains security even
when used with weak pre-shared keys.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1. Keyword Definitions . . . . . . . . . . . . . . . . . . . 3
2. Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3. Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4. Finite Cyclic Groups . . . . . . . . . . . . . . . . . . . . . 5
4.1. Elliptic Curve Groups . . . . . . . . . . . . . . . . . . 6
4.2. Prime Modulus Groups . . . . . . . . . . . . . . . . . . . 6
5. Random Numbers . . . . . . . . . . . . . . . . . . . . . . . . 7
6. The Random Function . . . . . . . . . . . . . . . . . . . . . 7
7. Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . 8
8. Secure Pre-Shared Key Authentication Message Exchange . . . . 8
8.1. Fixing the Secret Element, SKE . . . . . . . . . . . . . . 9
8.1.1. Elliptic Curve SKE . . . . . . . . . . . . . . . . . . 9
8.1.2. Prime Modulus SKE . . . . . . . . . . . . . . . . . . 11
8.2. Encoding of Elements . . . . . . . . . . . . . . . . . . . 11
8.3. Generation of a Commit . . . . . . . . . . . . . . . . . . 11
8.4. Generation of a Confirm . . . . . . . . . . . . . . . . . 12
8.5. Commit Payload . . . . . . . . . . . . . . . . . . . . . . 13
8.6. Confirm Payload . . . . . . . . . . . . . . . . . . . . . 13
8.7. IKEv1 Messaging . . . . . . . . . . . . . . . . . . . . . 14
8.8. IKEv2 Messaging . . . . . . . . . . . . . . . . . . . . . 15
9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 15
10. Security Considerations . . . . . . . . . . . . . . . . . . . 16
11. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 17
12. References . . . . . . . . . . . . . . . . . . . . . . . . . . 18
12.1. Normative References . . . . . . . . . . . . . . . . . . . 18
12.2. Informative References . . . . . . . . . . . . . . . . . . 18
Author's Address . . . . . . . . . . . . . . . . . . . . . . . . . 19
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1. Introduction
Both [RFC2409] and [RFC4306] allow for authentication of the IKE
peers using a pre-shared key. The exchanges, though, are susceptible
to dictionary attack and are therefore insecure.
To address this security issue, [RFC4306] recommends that the pre-
shared key used for authentication "contain as much unpredictability
as the strongest key being negotiated". That means any non-
hexidecimal key would require over 100 characters to provide enough
strength to generate a 128-bit key for AES. This is an unrealistic
requirement because humans have a hard time entering a string over 20
characters without error.
A pre-shared key authentication method built on top of a zero-
knowledge proof will provide resistance to dictionary attack and
still allow for security when used with weak pre-shared keys, such as
user-chosen passwords. Such an authentication method is described in
this memo.
Resistance to dictionary attack is achieved when an attacker gets
one, and only one, guess at the secret per active attack (see for
example, [BM92], [BMP00] and [BPR00]). Another way of putting this
is that any advantage the attacker can realize is through interaction
and not through computation. This is demonstrably different than the
technique from [RFC4306] of using a large, random number as the pre-
shared key. That can only make a dictionary attack less likely to
suceed, it does not prevent a dictionary attack. And, as [RFC4306]
notes, it is completely insecure when used with weak keys like user-
generated passwords.
1.1. Keyword Definitions
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 RFC 2119 [RFC2119].
2. Scenarios
[RFC4306] describes usage scenarios for IKEv2. These are:
1. "Security Gateway to Security Gateway Tunnel": the endpoints of
the IKE (and IPsec) communication are network nodes that protect
traffic on behalf of connected networks. Protected traffic is
between devices on the respective protected networks.
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2. "Endpoint-to-Endpoint Transport": the endpoints of the IKE (and
IPsec) communication are hosts according to [RFC4301]. Protected
traffic is between the two endpoints.
3. "Endpoint to Securty Gateway Tunnel": one endpoint connects to a
protected network through a network node. The endpoints of the
IKE (and IPsec) communication are the endpoint and network node,
but the protected traffic is between the endpoint and another
device on the protected network behind the node.
[RFC4306] also defines an EAP authentication method which can use a
pre-shared key or password in a manner that is resistant to
dictionary attack. But this requires the IKE Responder to have a
certificate. Also, EAP is strictly a client-server protocol used for
network access where one side is, typically, has a human behind it
and the other side is a network node. And, for EAP to scale a server
that terminates the EAP conversation is typically located on the
protected network behind the network node. Therefore EAP
authentication is really only applicable to the "Endpoint to Security
Gateway Tunnel" usage scenario.
The authentication and key exchange described in this memo is
therefore suitable for both the "Security Gateway to Security Gateway
Tunnel" scenario and the "Endpoint-to-Endpoint Transport" scenario.
In both of those, there is no defined roles. Either party could
initiate an IKE connection to the other and there isn't necessarily a
human involved. Also, both sides will have access to the pre-shared
key (i.e. no external authentication server) and neither side is
required to have a certificate. While it is certainly possible to
use EAP authentication in these cases with an EAP method such as
[EAPPWD], it will be a pointless and problematic encapsulation-- it
requires implementation of both the EAP client and EAP server state
machines, requires support of at least one EAP method, requires
support for EAP fragmentation, etc.
[RFC2409] does not describe usage scenarios for IKEv1 but IKEv1 has,
traditionally, been used in the same "Security Gateway to Security
Gateway Tunnel" scenario and the "Endpoint-to-Endpoint Transport"
scenario. Its pre-shared key-based authentication method is
constrained to only allow keys identified by IP address. Also, it
lacks a robust way to do user authentication using a password,
prompting the definition of different insecure ways to do password
authentication. Therefore, a secure pre-shared key-based
authentication method in IKEv1 will mitigate the need to do insecure
password-based authentication and remove the requirement that a pre-
shared key in IKEv1 needs to be based on IP address.
There is a need to do secure pre-shared key-based authentication in
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IKE and it makes sense to do it as part of IKE and not by requiring
additional authentication protocols.
3. Notation
The following notation is used in this memo:
psk
The key shared between the two protocol participants.
a = H(b)
The binary string "b" is given to a function H which produces a
fixed-length output "a".
a | b
denotes concatenation of string "a" with string "b".
[a]b
indicates a string consisting of the single bit "a" repeated "b"
times.
len(x)
indicates the length in bits of the string x.
LSB(x)
returns the least-significant bit of the bitstring "x".
The convention for this memo to represent an element in a finite
cyclic group is to use an upper-case letter while a scalar is
indicated with a lower-case letter.
4. Finite Cyclic Groups
This protocol uses the same group (from the IANA repository created
by [RFC2409]) as the IKE exchange in which this authentication method
is used. Groups can be either based on exponentiation modulo a prime
or on an elliptic curve. These groups all define the following
operations:
o "scalar operation"-- taking a scalar and an element in the group
producing another element-- Z = scalar-op(x, Y).
o "element operation"-- taking two elements in the group to produce
a third-- Z = element-op(X, Y).
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o "inverse operation"-- take an element an return another element
such that the element operation on the two produces the identity
element of the group-- Y = inverse(X).
4.1. Elliptic Curve Groups
ECP elliptic curves are defined by a curve equation, y^2 = x^3 + ax +
b, for a defined "a" and "b". ECP groups have a generator G, a prime
p, an order r, and, optionally, a co-factor f. The scalar operation
is multiplication of a point on the curve by itself a number of
times, and the element operation is addition of two points on the
curve:
Z = scalar-op(x, Y) = x*Y
the point Y is multiplied x-times to produce another point on the
curve, Z.
Z = element-op(X, Y) = X + Y
points X and Y are summed to produce another point on the curve,
Z.
Elliptic curve groups require a mapping function, q = F(Q), to
convert a group element to an integer. The mapping function used in
this memo returns the x-coordinate of the point it is passed.
If a co-factor is given in the group definition it MUST be used as
the co-factor, f, when a co-factor is called for, otherwise the co-
factor, f, MUST be 1.
The inverse function for an elliptic group is defined such that the
sum of an element and its inverse is the "point at infinity", denoted
here as "O". In other words,
Q + inverse(Q) = "O"
Only ECP elliptic curve can be used by the secure pre-shared key
authentication method. EC2N elliptic curves SHALL NOT be used.
While such groups exist in the IANA registry their use is not
defined.
4.2. Prime Modulus Groups
Groups formed by a prime modulus have a generator G, a prime modulus
p, and an order r.
The scalar operation is exponentiation of a generator modulus a
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prime, and the element operation is modular multiplication:
Z = scalar-op(x, Y) = Y^x mod p
an element, Y taken to the x-th power modulo the prime returning
another element in the group, Z.
Z = element-op(X, Y) = (X * Y) mod p
two elements, X and Y, are multiplied modulo the prime returning
another element, Z.
If the order of the generator of the group is part of the group
definition that value MUST be used as the order of the group, r, when
an order is called for, otherwise the order, r, MUST be computed as
the prime minus one divided by two-- (p-1)/2.
Unlike elliptic curve groups, prime modulus groups do not require a
mapping function to convert an element into a scalar. But for the
purposes of notation in protocol definition, the function F, when
used below, shall just return the integer representation of an
element in a prime modulus group.
The inverse function for a prime modulus group is defined such that
the product of an element and its inverse modulo the group prime
equals one (1). In other words,
(Q * inverse(Q)) mod p = 1
5. Random Numbers
As with IKE itself, the security of the secure pre-shared key
authenticaiton method relies upon each participant in the protocol
producing quality secret random numbers. A poor random number chosen
by either side in a single exchange can compromise the shared secret
from that exchange and open up the possibility of dictionary attack.
Producing quality random numbers without specialized hardware entails
using a cryptographic mixing function (like a strong hash function)
to distill entropy from multiple, uncorrelated sources of information
and events. A very good discussion of this can be found in
[RFC4086].
6. The Random Function
The protocol described in this memo uses a random function, H. This
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is a "random oracle" as defined in [RANDOR]. At first glance one may
view this as a hash function. As noted in [RANDOR], though, hash
functions are too structured to be used directly as a random oracle.
But they can be used to instantiate a random oracle.
The random function, H, in this memo is instantiated by HMAC-SHA256
(see [RFC4634]) with a key whose length is 32 octets and whose value
is zero. In other words,
H(x) = HMAC-SHA-256([0]32, x)
7. Assumptions
The security of the protocol relies on certain assumptions. They
are:
1. Function H maps a binary string of indeterminate length onto a
fixed binary string that is x bits in length.
H: {0,1}^* --> {0,1}^x
2. Function H is a "random oracle" (see [RANDOR]). Given knowledge
of the input to H an adversary is unable to distinguish the
output of H from a random data source.
3. The discrete logarithm problem for the chosen finite cyclic group
is hard. That is, given G, p and Y = G^x mod p it is
computationally infeasible to determine x. Similarly for an
elliptic curve group given the curve definition, a generator G,
and Y = x * G it is computationally infeasible to determine x.
4. The pre-shared key is drawn from a finite pool of potential keys.
Each possible key in the pool has equal probability of being the
shared key. All potential attackers have access to this pool of
keys.
8. Secure Pre-Shared Key Authentication Message Exchange
To perform secure pre-shared key authentication each side must
generate a shared and secret element in the chosen group based on the
pre-shared key. This element, called the Secret Key Element, or SKE,
is then used in an authentication and key exchange protocol. The key
exchange protocol consists of each side exchanging two data, a
"Commit" and a "Confirm".
The "Commit" contributes ephemeral information to the exchange and
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binds the sender to a single value of the pre-shared key from the
pool of potential pre-shared keys. The "Confirm" proves that the
pre-shared key is known and completes the zero-knowledge proof.
8.1. Fixing the Secret Element, SKE
The method of fixing SKE depends on the type of group, either MODP or
ECP. For the sake of convenience, we will use a single notation of
prf+() to denote the function prf+() from [RFC4306] as well as the
function prf() from [RFC2409], depending on whether the exchange is
being performed in IKEv2 or IKEv1, respectively.
8.1.1. Elliptic Curve SKE
For a finite cyclic group based on an elliptic curve it is necessary
to use an iterative hunt-and-peck technique to fix the secret key
element.
First, an 8-bit counter is set to the value one (1). Then, the
random function is used to generate a secret seed using the counter,
the pre-shared key, and the two nonces exchange by the Initiator and
the Responder:
ske-seed = H(psk | counter | Ni | Nr)
Then, the swe-seed is expanded using prf+ to create an ske-value:
ske-value = prf+(ske-seed, "IKE SKE Hunting And Pecking")
where len(ske-value) is the same as len(p), the length of the prime
of the curve.
If the ske-value is greater than or equal to the prime, p, the
counter is incremented, and a new ske-seed is gnerated and the
hunting-and-pecking continues. If ske-value is less than the prime,
p, it is used as the x-coordinate, x, with the equation for the
elliptic curve, with parameters a and b from the definition of the
curve, to solve for a y-coordinate, y. If there is no solution to
the quadratic equation the counter is incremented, a new ske-seed is
generated and the hunting and pecking continues. If a solution is
found then an ambiguity exists as there are technically two solutions
to the equation and ske-seed is used to unambiguously select one of
them. If the low-order bit of ske-seed is equal to the low-order bit
of y then a candidate SKE is defined as the point (x, y); if the low-
order bit of ske-seed differs from the low-order bit of y then a
candidate SKE is defined as the point (x, p - y), where p is the
prime over which the curve is defined. If the co-factor equals 1
then the candidate SKE becomes the SKE and hunting and pecking
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terminates. If the co-factor of the curve is not equal to one the
order of the candidate SKE is checked to make sure it can safely be
used as a generator in the protocol. If the co-factor of the curve
multiplied by the candidate SKE equals the point-at-infinity then the
candidate SKE is discarded, the counter is incremented, a new ske-
seed is generated and the hunting and pecking continues. If it does
not equal the point-at-infinity the candidate SKE becomes the SKE and
hunting and pecking terminates. (Note: the point multiplied by the
co-factor does not become SKE, it is only used to determine the order
of the group defined with SKE as a generator).
Algorithmically, the process looks like this:
found = 0
counter = 1
do {
ske-seed = H(psk | counter | Ni | Nr)
ske-value = prf+(swd-seed, "IKE SKE Hunting And Pecking")
if (ske-value < p)
then
x = ske-value
if ( (y = sqrt(x^3 + ax + b)) != FAIL)
then
if (LSB(y) == LSB(ske-seed))
then
SKE = (x,y)
else
SKE = (x, p-y)
fi
if (f == 1)
then
found = 1
else
P = f*SKE
if (P != "O")
then
found = 1
fi
fi
fi
fi
counter = counter + 1
} while (found == 0)
Figure 1: Fixing SKE for Elliptic Curves
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8.1.2. Prime Modulus SKE
For a finite cyclic group based on exponentiation of a generator, G,
modulo a large prime p it is not necessary to hunt-and-peck to find
SKE. An SKE can be computed in a sub-field of the group directly
using the prime, p, and order r.
First, the random function is used to generate a seed:
ske-seed = H(psk | Ni | Nr)
Then the ske-seed is expanded using prf+ to the length of the prime,
modulo the prime.
ske-gen = prf+(ske-seed, "IKE Affixing the SKE")
ske-gen = ske-gen mod p
The ske is then computed by exponentiating the ske-gen to the value
((p-1)/r) modulo the prime.
SKE = ske-gen ^ ((p-1)/r) mod p
8.2. Encoding of Elements
Encoding of an element in a finite cyclic group depends on the type
of group.
For MODP groups the element is treated as an unsigned integer less
than the prime that defines the group. The length of each MODP
element MUST have a bit length equal to the bit length of the prime.
This length is enforced, if necessary, by prepending the integer with
zeros until the required length is achieved.
For ECP groups the element is treated as two unsigned integers, each
less than the prime that defines the group, representing the
coordinates of the point. The first is the x-coordinate and the
second is the y-coordinate. Each of these two integers MUST have a
bit length equal to the bit length of the prime. This length is
enforced, if necessary, by prepending the integer with zeros until
the required length is achieved.
8.3. Generation of a Commit
A Commit has two components, a Scalar and an Element. To generate a
Commit, two random numbers, a "private" value and a "mask" value, are
generated (see Section 5). Their sum modulo the order of the group,
r, becomes the Scalar component:
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Scalar = (private + mask) mod r
and the inverse of the scalar operation with the mask and SWE becomes
the Element component.
Element = inverse(scalar-op(mask, SKE))
The Commit payload consists of the Scalar followed by the Element.
8.4. Generation of a Confirm
After receipt of a peer's Commit and generation of one's own Commit a
candidate shared secret to authenticate the peer is derived. Using
SKE, the "private" value generated as part of Commit generation, and
the peer's Scalar and Element from its Commit, peer-scalar and peer-
element, respectively, the shared secret, ss, is generated as:
ss = scalar-op(private, element-op(peer-element, scalar-op(peer-
scalar, SKE)))
For the purposes of subsequent computation, the bit length of ss
SHALL be equal to the bit length of the prime, p, used in either a
MODP or ECP group. This bit length SHALL be enforced, if necessary,
by prepending zeros to the value until the required length is
achieved.
Using the shared secret, ss, and the generated Scalar and Element,
self-scalar and self-element, respectively, and the received Scalar
and Element, peer-scalar and peer-element, respectively, an
authenticating Tag is generated as:
Tag = H(self-scalar | peer-scalar | F(self-element) | F(peer-
element) | ss)
The Commit payload consists of the authenticating Tag.
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8.5. Commit Payload
The Commit Payload is defined as follows:
1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
! Next Payload !C! RESERVED ! Payload Length !
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
~ Scalar ~
| |
~ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ ~
| |
~ Element ~
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
The Commit Payload SHALL be indicated in both IKEv1 and IKEv2 with
TBD1 from the [IKEV2-IANA] registry maintained by IANA.
The Scalar SHALL be encoded as an unsigned integer with a bit length
equal to the bit length of the order of the group used in the
exchange. This length is enforced, if necessary, by prepending the
integer with zeros until the required length is achieved. The
Element is encoded according to Section 8.2.
8.6. Confirm Payload
The Confirm Payload is defined as follows:
1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
! Next Payload !C! RESERVED ! Payload Length !
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
! !
~ Tag ~
! !
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
The Confirm Payload SHALL be indicated in both IKEv1 and IKEv2 with
TBD2 from the [IKEV2-IANA] registry maintained by IANA.
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8.7. IKEv1 Messaging
Secure pre-shared key authentication can be used in either Main Mode
(see Figure 2) or Aggressive Mode (see Figure 3) with IKEv1 and SHALL
be indicated by negotiation of the TBD3 Authentication Method from
the [IKEV1-IANA] registry maintained by IANA, in the SA payload.
When using IKEv1 the "C" (critical) bit from Section 8.5 and
Section 8.6 MUST be clear (i.e. a value of zero).
Initiator Responder
----------- -----------
HDR, SAi -->
<-- HDR, SAr
HDR, KEi, Ni -->
<-- HDR, KEr, Nr
HDR*, IDii, Commit -->
<-- HDR*, IDir, Commit, Confirm
HDR*, Confirm, HASH_I -->
<-- HDR*, HASH_R
Figure 2: Secure PSK in Main Mode
Initiator Responder
----------- -----------
HDR, SAi, KEi, Ni, IDii,
Commit -->
<-- HDR, SAr, KEr, Nr, IDir,
Commit, Confirm
HDR, Confirm, HASH_I -->
<-- HDR, HASH_R
Figure 3: Secure PSK in Aggressive Mode
For secure pre-shared key authentication with IKEv1 the SKEYID value
is computed as follows:
SKEYID = prf(Ni_b | Nr_b, g^xy)
And HASH_I and HASH_R are computed as follows:
HASH_I = prf(SKEYID, ss | g^xi | g^xr | CKY-I | CKY-R | SA_ib |
IDii_b)
HASH_R = prf(SKEYID, ss | g^xr | g^xi | CKY-R | CKY-I | SA_ib |
IDir_b)
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Where "ss" is the shared secret derived in Section 8.4.
8.8. IKEv2 Messaging
The specific authentication method being employed in IKEv2 is not
negotiated, like in IKEv1. It is inferred from the components of the
message. The presence of a Commit payload in second message sent by
the Initiator indicates an intention to perform secure pre-shared key
authentication (see Figure 4). The critical bit is used in both the
Commit and Confirm payloads to allow for backwards compatibility and
MUST be set (i.e. a value of one).
Initiator Responder
----------- -----------
HDR, SAi1, KEi, Ni -->
<-- HDR, SAr1, KEr, Nr, [CERTREQ]
HDR, SK {IDi, Commit, [IDr,]
SAi2, TSi, TSr} -->
<-- HDR, SK {IDr, Commit, Confirm}
HDR, SK {Confirm, AUTH} -->
<-- HDR, SK {AUTH, SAr2, TSi, TSr}
Figure 4: Secure PSK in IKEv2
In the case of secure pre-shared key authentication the AUTH value is
computed as:
AUTH = prf(ss, )
Where "ss" is the shared secret derived in Section 8.4. The
Authentication Method indicated in the AUTH payload SHALL be TBD4
from the [IKEV2-IANA] registry maintained by IANA.
9. IANA Considerations
IANA SHALL assign values for the Commit payload (Section 8.5) and the
Confirm payload (Section 8.6), and replace TBD1 and TBD2,
respectively, above, from the [IKEV2-IANA] of "IKEv2 Payload Types".
IANA SHALL assign a value for "Secure Shared Key Authentication",
replacing TBD3 above, from the IPSEC Authentication Method registry
in [IKEV1-IANA].
IANA SHALL assign a value for "Secure Shared Key Authentication",
replacing TBD4 above, from the IKEv2 Authentication Method registry
in [IKEV2-IANA].
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10. Security Considerations
Both the Initiator and Responder obtain a shared secret, "ss" (see
Section 8.4) based on a secret group element and their own private
values contributed to the exchange. If they do not share the same
pre-shared key they will be unable to derive the same secret group
element and if they do not share the same secret group element they
will be unable to derive the same shared secret.
Resistance to dictionary attack means that the attacker must launch
an active attack to make a single guess at the pre-shared key. If
the size of the pool from which the key was extracted was D, and each
key in the pool has an equal probability of being chosen, then the
probability of success after a single guess is 1/D. After X guesses,
and removal of failed guesses from the pool of possible keys, the
probability becomes 1/(D-X). As X grows so does the probability of
success. Therefore it is possible for an attacker to determine the
pre-shared key through repeated brute-force, active, guessing
attacks. This authentication method does not presume to be secure
against this and implementations SHOULD ensure the size of D is
sufficiently large to prevent this attack. Implementations SHOULD
also take countermeasures, for instance refusing authentication
attempts for a certain amount of time, after the number of failed
authentication attempts reaches a certain threshold. No such
threshold or amount of time is recommended in this memo.
An active attacker can impersonate the Initiator of the exchange and
send a forged Commit payload. The attacker then waits until it
receives a Commit and a Confirm from the Responder. Now the attacker
can attempt to run through all possible values of the pre-shared key,
computing SKE (see Section 8.1), computing "ss" (see Section 8.4),
and attempting to recreate the Confirm payload from the Responder.
But the attacker committed to a single guess of the pre-shared key
with her forged Commit. That value was used by the Responder in his
computation of "ss" which was used to construct his Confirm. Any
guess of the pre-shared key which differs from the one used in the
forged Commit would result in each side using a different secret
element in the computation of "ss" and therefore the Confirm could
not be verified as correct, even if a subsequent guess, while running
through all possible values, was correct. The attacker gets one
guess, and one guess only, per active attack.
An attacker, acting as either the Initiator or Responder, can take
the Element from the Commit message received from the other party,
reconstruct the random "mask" value used in its construction and then
recover the other party's "private" value from the Scalar in the
Commit message. But this requires the attacker to solve the discrete
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logarithm problem which we assumed was intractable above (Section 7).
Instead of attempting to guess at pre-shared keys an attacker can
attempt to determine SKE and then launch an attack. But SKE is
determined by the output of the random function, H, which is assumed
to be indistinguishable from a random source (Section 7). Therefore,
each element of the finite cyclic group will have an equal
probability of being the SKE. The probability of guessing SKE will
be 1/r, where r is the order of the group. This is the same
probability of guessing the solution to the discrete logarithm which
is assumed to be intractable (Section 7). The attacker would have a
better chance of success at guessing the input to H, i.e. the pre-
shared key, since the order of the group will be many orders of
magnitude greater than the size of the pool of pre-shared keys.
The implications of resistance to dictionary attack are significant.
An implementation can provision a pre-shared key in a practical and
realistic manner-- i.e. it MAY be a character string and it MAY be
relatively short-- and still maintain security. The nature of the
pre-share key determines the size of the pool, D, and countermeasures
can prevent an attacker from determining the secret in the only
possible way: repeated, active, guessing attacks. For example, a
simple four character string using lower-case English characters, and
assuming random selection of those characters, will result in D of
over four hundred thousand. An attacker would need to mount over one
hundred thousand active, guessing attacks (which will easily be
detected) before gaining any significant advantage in determining the
pre-shared key.
For a more detailed discussion of the security of the key exchange
underlying this authentication method see [SAE] and [EAPPWD].
11. Acknowledgements
The author would like to thank Scott Fluhrer and Hideyuki Suzuki for
their insight in discovering flaws in earlier versions of the key
exchange that underlies this authentication method and for their
helpful suggestions in improving it. Lily Chen provided useful
advice on how to "hash into an element" in a finite cyclic group.
Hugo Krawczyk suggested the particular instantiation of the random
function, H.
12. References
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12.1. Normative References
[IKEV1-IANA]
"Internet Assigned Numbers Authority, Internet Key
Exchange (IKE) Attributes",
.
[IKEV2-IANA]
"Internet Assigned Numbers Authority, IKEv2 Parameters",
.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
[RFC2409] Harkins, D. and D. Carrel, "The Internet Key Exchange
(IKE)", RFC 2409, November 1998.
[RFC4301] Kent, S. and K. Seo, "Security Architecture for the
Internet Protocol", RFC 4301, December 2005.
[RFC4306] Kaufman, C., "Internet Key Exchange (IKEv2) Protocol",
RFC 4306, December 2005.
[RFC4634] Eastlake, D. and T. Hansen, "US Secure Hash Algorithms
(SHA and HMAC-SHA)", RFC 4634, July 2006.
12.2. Informative References
[BM92] Bellovin, S. and M. Merritt, "Encrypted Key Exchange:
Password-Based Protocols Secure Against Dictionary
Attack", Proceedings of the IEEE Symposium on Security and
Privacy, Oakland, 1992.
[BMP00] Boyko, V., MacKenzie, P., and S. Patel, "Provably Secure
Password Authenticated Key Exchange Using Diffie-Hellman",
Proceedings of Eurocrypt 2000, LNCS 1807 Springer-Verlag,
2000.
[BPR00] Bellare, M., Pointcheval, D., and P. Rogaway,
"Authenticated Key Exchange Secure Against Dictionary
Attacks", Advances in Cryptology -- Eurocrypt '00, Lecture
Notes in Computer Science Springer-Verlag, 2000.
[EAPPWD] Harkins, D. and G. Zorn, "EAP Authentication Using Only A
Password", draft-harkins-emu-eap-pwd-12 (work in
progress), October 2009.
[RANDOR] Bellare, M. and P. Rogaway, "Random Oracles are Practical:
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A Paradigm for Designing Efficient Protocols", Proceedings
of the 1st ACM Conference on Computer and Communication
Security, ACM Press, 1993,
.
[RFC4086] Eastlake, D., Schiller, J., and S. Crocker, "Randomness
Requirements for Security", BCP 106, RFC 4086, June 2005.
[SAE] Harkins, D., "Simultaneous Authentication of Equals: A
Secure, Password-Based Key Exchange for Mesh Networks",
Proceedings of the 2008 Second International Conference on
Sensor Technologies and Applications Volume 00, 2008.
Author's Address
Dan Harkins
Aruba Networks
1322 Crossman Avenue
Sunnyvale, CA 94089-1113
United States of America
Email: dharkins@arubanetworks.com
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