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The Extensible Authentication Protocol (EAP) describes a framework that allows the use of multiple authentication mechanisms. This document defines an authentication mechanism for EAP called EAP-EKE, based on the Encrypted Key Exchange (EKE) protocol. This method provides mutual authentication through the use of a short, easy to remember password.

The predominant access method for the Internet today is that of a human using a username and password to authenticate to a computer enforcing access control. Proof of knowledge of the password authenticates the human to the computer. Typically, these passwords are not stored on a user's computer for security reasons and must be entered each time the human desires network access. Therefore, the passwords must be ones that can be repeatedly entered by a human with a low probability of error. They will likely not possess high entropy and it may be assumed that an adversary with access to a dictionary will have the ability to guess a user's password. It is therefore desirable to have a robust authentication method that is secure even when used with a weak password in the presence of a strong adversary. EAP-EKE is an EAP method that addresses the problem of password-based authenticated key exchange, using a possibly weak password for authentication and to derive an authenticated and cryptographically strong shared secret. This problem was first described by Bellovin and Merritt in and . Subsequently, a number of other solution approaches have been proposed, for example , , , and others. This proposal is based on the original Encrypted Key Exchange (EKE) proposal, as described in . Some of the variants of the original EKE has been attacked, see e.g. , and improvements have been proposed. None of these subsequent improvements have been incorporated into the current protocol. However, we have used only the subset of (namely the variant described in Section 3.1) which has withstood the test of time and is believed secure as of this writing.

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 .

EAP is a two-party protocol spoken between an EAP peer and an EAP server (also known as "authenticator"). An EAP method defines the specific authentication protocol being used by EAP. This memo defines a particular method and therefore defines the messages sent between the EAP server and the EAP peer for the purpose of authentication and key derivation.

EAP-EKE defines three message exchanges: an Identity exchange, a Commit exchange and a Confirm exchange. A successful authentication is shown in . The peer and server use the EAP-EKE Identity exchange to learn each other's identities and to agree upon a ciphersuite to use in the subsequent exchanges. In the Commit exchange the peer and server exchange information to generate a shared key and also to bind each other to a particular guess of the password. In the Confirm exchange the peer and server prove liveness and knowledge of the password by generating and verifying verification data.

| | | | | | | | EAP-EKE-Commit/Request | | | |<------------------------------------| | | | | | | | EAP-EKE-Commit/Response | | | |------------------------------------>| | | | | | | | EAP-EKE-Confirm/Request | | | |<------------------------------------| | | | | | | | EAP-EKE-Confirm/Response | | | |------------------------------------>| | | | | | | | EAP-Success | | | |<------------------------------------| | +--------+ +--------+ ]]>

Schematically, the original exchange as described in (and with the roles reversed) is:

<- E(Password, Y_P), E(SharedSecret, Nonce_P) E(SharedSecret, Nonce_S | Nonce_P) -> <- E(SharedSecret, Nonce_S) ]]>

Where: Y_S and Y_P are the server's (and respectively, the peer's) ephemeral public key, i.e. g^x (mod p), g^y (mod p). Nonce_S, Nonce_P are random strings generated by the server and the peer as cryptographic challenges. SharedSecret is the secret created by the Diffie-Hellman algorithm, namely g^(x*y) (mod p). The current protocol extends the basic cryptographic protocol, and the regular successful exchange becomes:

P ID_S, CryptoProposals EAP-EKE-ID/Response: S <- P ID_P, CryptoSelection EAP-EKE-Commit/Request: S -> P E(Password, Y_S)) EAP-EKE-Commit/Response: S <- P E(Password, Y_P), E(Ke, Nonce_P) EAP-EKE-Confirm/Request: S -> P E(Ke, Nonce_S | Nonce_P), Auth_S EAP-EKE-Confirm/Response: S <- P E(Ke, Nonce_S), Auth_P ]]>

As shown in the exchange above, the following information elements are added to the original protocol: identity values for both protocol parties (ID_S, ID_P), negotiation of cryptographic protocols, and signature fields to protect the integrity of the negotiated parameters (Auth_S, Auth_P). In addition the shared secret is not used directly. Note that a few details have been omitted for clarity.

The EAP-EKE header consists of the standard EAP header (see Section 4 of ), followed an EAP-EKE exchange type. The header has the following structure:

The Code, Identifier, Length, and Type fields are all part of the EAP header, and defined in . The Type field in the EAP header MUST be the value allocated by IANA for EAP-EKE version 1. The EKE-Exch field identifies the type of EAP-EKE payload encapsulated in the Data field. This document defines the following values for the EKE-Exch field: 0x00: Reserved 0x01: EAP-EKE-ID exchange 0x02: EAP-EKE-Commit exchange 0x03: EAP-EKE-Confirm exchange 0x04: EAP-EKE-Failure message 0x05: EAP-EKE-Protected-Failure message Further values of this EKE-Exch field are available via IANA registration.

EAP-EKE payloads all contain the EAP-EKE header and encoded information, which differs for the different exchanges.

The EAP-EKE-ID payload contains the following fields: The NumProposals field contains the number of proposals subsequently contained in the Proposal field. In the EAP-EKE-ID/Request the NumProposals field MUST NOT be set to zero (0) and in the EAP-EKE-ID/Response message the NumProposals field MUST be set to one (1). The offered proposals in the Request are listed contiguously in priority order, most preferable first. The selected proposal in the Response MUST be fully identical with one of the offered proposals. Each proposal consists of four one-octet fields, in this order: This field's value is taken from the IANA registry for Diffie-Hellman groups defined in . This field's value is taken from the IANA registry for encryption algorithms defined in . This field's value is taken from the IANA registry for pseudo random functions defined in . This field's value is taken from the IANA registry for keyed message digest algorithms defined in used to provide integrity protection. Denotes the Identity type. This is taken from the IANA registry defined in . The server and the peer MAY use different identity types. The Identity field is always printable, and its meaning depends on the values of the Code and IDType fields. EAP-EKE-ID/Request: server ID EAP-EKE-ID/Response: peer ID The server SHOULD assert its own identity (e.g. its host name), or it MAY use the peer's identity if it knows it before the protocol starts. The length of the Identity is computed from the Length field in the EAP header.

In this exchange both parties send their encrypted ephemeral public key, and the peer also includes a Challenge.

This field contains the password-encrypted Diffie-Hellman public key, see . This field only appears in the response, and contains the encrypted challenge value sent by the peer. See .

In this exchange both parties complete the authentication by generating a shared temporary key, authenticating the entire protocol, and generating key material for the EAP consumer protocol.

This field contains the encrypted response to the other peer's challenge, see and . This field signs the Identity and the negotiated fields, to prevent downgrade attacks. See and .

The EAP-EKE-Failure message format is defined as follows:

The EAP-EKE-Protected-Failure payload format is defined as follows:

The MAC field contains the keyed message digest computed with the MAC algorithm selected during the initial exchange computed over the Failure-Code using the MAC key (see on how this key is derived). A protected failure response can only be returned once the MAC key has been derived. Currently the following Failure-Code values are defined: 0x00000000: Reserved 0x00000001: No Error 0x00000002: Protocol Error 0x00000003: Password Not Found 0x00000004: Authentication Failure 0x00000005: Authorization Failure 0x00000006: No Proposal Chosen Additional values of this field are available via IANA registration. "No Error" is used for failure acknowledgement, see below. "Protocol Error" indicates a failure to parse or understand a protocol message or one of its payloads. "Password Not Found" indicates a password for a particular user could not be located, making authentication impossible. "Authentication Failure" indicates failure in the cryptographic computation most likely caused by an incorrect password, or an inappropriate identity type. "Authorization Failure" indicates that while the password being used is correct, the user is not authorized to connect. "No Proposal Chosen" indicates that the peer is unwilling to select any of the cryptographic proposals offered by the server. When the peer encounters an error situation, it MUST respond with either EAP-EKE-Failure or EAP-EKE-Protected-Failure, depending on whether it believes a common MAC key has been agreed upon. The server MUST send an EAP-Failure message to end the exchange. When the server encounters an error situation, it MUST respond with either EAP-EKE-Failure or EAP-EKE-Protected-Failure, depending on whether it believes a common MAC key has been agreed upon. The peer MUST send back either EAP-EKE-Failure or EAP-EKE-Protected-Failure (corresponding to the server's selection), containing a "No Error" failure code. Then the server MUST send an EAP-Failure message to end the exchange.

Keying material will always be derived as the output of the negotiated prf algorithm. Since the amount of keying material needed may be greater than the size of the output of the prf algorithm, we will use the prf iteratively. We will use the terminology prf+ to describe the function that outputs a pseudo-random stream based on the inputs to a prf as follows: (where | indicates concatenation) prf+ (K,S) = T1 | T2 | T3 | T4 | ... where: T1 = prf(K, S | 0x01) T2 = prf(K, T1 | S | 0x02) T3 = prf(K, T2 | S | 0x03) T4 = prf(K, T3 | S | 0x04) continuing as needed to compute all required keys. The keys are taken from the output string without regard to boundaries (e.g., if the required keys are a 256-bit Advanced Encryption Standard (AES) key and a 160-bit HMAC key, and the prf function generates 160 bits, the AES key will come from T1 and the beginning of T2, while the HMAC key will come from the rest of T2 and the beginning of T3). The constant concatenated to the end of each string feeding the prf is a single octet. prf+ in this document is not defined beyond 255 times the size of the prf output.

The server computes Y_S = g^x mod N, where 'x' is a randomly chosen number in the range 2 .. N-1. The randomly chosen number is the private key, and the calculated field is the corresponding public key. The calculated value MUST NOT be zero modulo N. If the peer receives a bad value for this field, it MUST take action to disconnect or disable the link. Each of the peers MUST use a fresh, random value for this field on each run of the protocol. Note: If Elliptic Curve Diffie-Hellman is used, the corresponding additive group operations are to be understood. The server transmits DHComponent_S = E(prf+(password, "EAP-EKE Password"), Y_S), encrypted using the algorithm negotiated during the previous exchange. If required by the encryption algorithm/mode, the encrypted field is preceded by an Initialization Vector (IV), whose length depends on the algorithm. The IV value MUST be unpredictable. When using block ciphers, it may be necessary to pad Y_S on the right, to fit the encryption algorithm's block size. In such cases, random padding MUST be used, and this randomness is critical to the security of the protocol. Randomness recommendations can be found in . When decrypting this field, the real length of Y_S is determined according to the negotiated Diffie Hellman group. If the password needs to be stored on the server, it is RECOMMENDED to store the randomized password value, i.e. prf+(password, ...), as a password-equivalent, rather than the cleartext password.

The peer computes Y_P = g^y mod N and sends DHComponent_P = E(prf+(password, "EAP-EKE Password"), Y_P) If the password is non-ASCII, it SHOULD be normalized by the peer before the EAP-EKE message is constructed. The normalization method is SASLprep, . Note that the password is not null-terminated. Both sides calculate SharedSecret = g^(x*y) mod N The encryption key is computed: Ke = prf+(SharedSecret, "EAP-EKE Ke" | ID_S | ID_P) The MAC key is computed: MAC = prf+(SharedSecret, "EAP-EKE MAC" | ID_S | ID_P) And the peer generates Challenge_P = E(Ke, Nonce_P), where Nonce_P is a randomly generated binary string. Nonce_P has length equal to the block size of E for block ciphers, or 32 octets if E is a stream cipher.

The server sends: Commit_S = E(Ke, Nonce_P | Nonce_S), where Nonce_S is a randomly generated string, similar to Nonce_P. It computes: Ka = prf+(SharedSecret, "EAP-EKE Ka" | ID_S | ID_P | Nonce_P | Nonce_S) And sends: Auth_S = prf(Ka, "EAP-EKE server" | EAP-EKE-ID/Request | EAP-EKE-ID/Response | EAP-EKE-Commit/Request | EAP-EKE-Commit/Response), where the literal string is encoded using ASCII with no zero terminator. The messages are included in full, starting with the EAP header, and including any possible future extensions.

The peer computes Ka, and sends: Commit_P = E(Ke, Nonce_S) Auth_P = prf(Ka, "EAP-EKE peer" | EAP-EKE-ID/Request | EAP-EKE-ID/Response | EAP-EKE-Commit/Request | EAP-EKE-Commit/Response)

Following the last message of the protocol, both sides compute and export the shared keys, each 512 bits in length: MSK = prf+(SharedSecret, "EAP-EKE MSK" | ID_S | ID_P | Nonce_P | Nonce_S) EMSK = prf+(SharedSecret, "EAP-EKE EMSK" | ID_S | ID_P | Nonce_P | Nonce_S)

Many of the commonly used Diffie Hellman groups are inappropriate for use in EKE. Most of these groups use a generator which is not a primitive element of the group. As a result, an attacker running a dictionary attack would be able to learn at least 1 bit of information for each decrypted password guess. Any MODP Diffie Hellman group defined for use in this protocol MUST have the following properties, to ensure that it does not leak a usable amount of information about the password: The generator is a primitive element of the group. The most significant 64 bits of the prime number are 1. The group's order p is a "safe prime", i.e. (p-1)/2 is also prime. The last requirement is related to the strength of the Diffie Hellman algorithm, rather than the password encryption. It also makes it easy to verify that the generator is primitive. We have defined the following groups: DHGROUP_EKE_14 is defined by: the prime number of Group 14 , with the generator 11 (decimal). Additional groups will be defined by future versions of this document.

To facilitate interoperability, the following algorithms are mandatory to implement: ENCR_AES128_CBC (encryption algorithm) PRF_HMAC_SHA1 (pseudo random function and keyed message digest) DHGROUP_EKE_14 (DH-group)

This document allocates an EAP method type, for "EAP-EKE Version 1". This document requires IANA to create the registries described in the subsequent sections. Values can be added or modified in these registries per Specification Required .

This section defines an IANA registry for encryption algorithms:

This section defines an IANA registry for pseudo random function algorithms:

This section defines an IANA registry for keyed message digest algorithms:

This section defines an IANA registry for Diffie-Hellman groups:

In addition, an identity type registry is defined:

This section defines an IANA registry for the Failure-Code registry, a 32-bit long code. Initial values are defined in . All values up to 0xff000000 are available for allocation via IANA. The remaining values up to 0xffffffff are available for private use.

Any protocol that claims to solve the problem of password-authenticated key exchange must be resistant to active, passive and dictionary attack and have the quality of forward secrecy. These characteristics are discussed further in the following paragraphs. A passive attacker is one that merely relays messages back and forth between the peer and server, faithfully, and without modification. The contents of the messages are available for inspection, but that is all. To achieve resistance to passive attack, such an attacker must not be able to obtain any information about the password or anything about the resulting shared secret from watching repeated runs of the protocol. Even if a passive attacker is able to learn the password, she will not be able to determine any information about the resulting secret shared by the peer and server. An active attacker is able to modify, add, delete, and replay messages sent between protocol participants. For this protocol to be resistant to active attack, the attacker must not be able to obtain any information about the password or the shared secret by using any of its capabilities. In addition, the attacker must not be able to fool a protocol participant into thinking that the protocol completed successfully. It is always possible for an active attacker to deny delivery of a message critical in completing the exchange. This is no different than dropping all messages and is not an attack against the protocol. For this protocol to be resistant to dictionary attack any advantage an adversary can gain must be directly related to the number of interactions she makes with an honest protocol participant and not through computation. The adversary will not be able to obtain any information about the password except whether a single guess from a single protocol run is correct or incorrect. Compromise of the password must not provide any information about the secrets generated by earlier runs of the protocol. requires that documents describing new EAP methods clearly articulate the security properties of the method. In addition, for use with wireless LANs, mandates and recommends several of these. The claims are: Mechanism: password. Claims: Mutual authentication: the peer and server both authenticate each other by proving possession of a shared password. This is REQUIRED by . Forward secrecy: compromise of the password does not reveal the secret keys (MSK and EMSK) from earlier runs of the protocol. Replay protection: an attacker is unable to replay messages from a previous exchange either to learn the password or a key derived by the exchange. Similarly the attacker is unable to induce either the peer or server to believe the exchange has successfully completed when it hasn't. Key derivation: a shared secret is derived by performing a group operation in a finite cyclic group (e.g. exponentiation) using secret data contributed by both the peer and server. An MSK and EMSK are derived from that shared secret. This is REQUIRED by . Dictionary attack resistance: an attacker can only make one password guess per active attack, and the protocol is designed so that the attacker does not gain any confirmation of her guess by observing the decrypted Y_x value (see below). The advantage she can gain is through interaction not through computation. This is REQUIRED by . Session independence: this protocol is resistant to active and passive attacks and does not enable compromise of subsequent or prior MSKs or EMSKs from either passive or active attacks. Denial of Service resistance: it is possible for an attacker to cause a server to allocate state and consume CPU. Such an attack is gated, though, by the requirement that the attacker first obtain connectivity through a lower-layer protocol (e.g. 802.11 authentication followed by 802.11 association, or 802.3 "link-up") and respond to two EAP messages--the EAP-ID/ Request and the EAP-EKE-ID/Request. Man-in-the-Middle Attack resistance: this exchange is resistant to active attack, which is a requirement for launching a man-in-the-middle attack. This is REQUIRED by . Shared state equivalence: upon completion of EAP-EKE the peer and server both agree on MSK, EMSK. The peer has authenticated the server based on the Server_ID and the server has authenticated the peer based on the Peer_ID. This is due to the fact that Peer_ID, Server_ID, and the generated shared secret are all combined to make the authentication element which must be shared between the peer and server for the exchange to complete. This is REQUIRED by . Fragmentation: this protocol does not define a technique for fragmentation and reassembly. Resistance to "Denning-Sacco" attack: learning keys distributed from an earlier run of the protocol, such as the MSK or EMSK, will not help an adversary learn the password. Key strength: the strength of the resulting key depends on the finite cyclic group chosen. Sufficient key strength is REQUIRED by . Key hierarchy: MSKs and EMSKs are derived from the secret values generated during the protocol run, using a negotiated pseudo-random function. Vulnerabilities (note that none of these are REQUIRED by ): Protected ciphersuite negotiation: the ciphersuite proposal made by the server is not protected from tampering by an active attacker. However if a proposal was modified by an active attacker it would result in a failure to confirm the message sent by the other party, since the proposal is bound by each side into its Confirm message, and the protocol would fail as a result. Confidentiality: none of the messages sent in this protocol are encrypted. Integrity protection: all messages in this protocol are integrity protected. Channel binding: this protocol does not enable the exchange of integrity-protected channel information that can be compared with values communicated via out-of-band mechanisms. Fast reconnect: this protocol does not provide a fast reconnect capability. Cryptographic binding: this protocol is not a tunneled EAP method and therefore has no cryptographic information to bind. Identity protection: the EAP-EKE-ID exchange is not protected. An attacker will see the server's identity in the EAP-EKE-ID/Request and see the peer's identity in EAP-EKE-ID/ Response.

When analyzing the Commit exchange, it should be noted that the base security assumptions are different from "normal" cryptology. Normally, we assume that the key has strong security properties, and that the data may have little. Here, we assume that the key has weak security properties (the attacker may have a list of possible keys), and hence we need to ensure that the data has strong properties (indistinguishable from random). This difference may mean that conventional wisdom in cryptology might not apply in this case. This also imposes severe constraints on the protocol, e.g. the mandatory use of random padding, and the need to define specific finite groups.

It is fundamental to the dictionary attack resistance that the Diffie Hellman public values Y_S and Y_P are indistinguishable from a random string. If this condition is not met, then a passive attacker can do trial-decryption of the encrypted DHComponent_P, DHComponent_S values based on a password guess, and if they decrypt to a value which in not a valid public value, they know that the password guess was incorrect. For MODP groups, gives conditions on the group to make sure that this criterion is met. For other groups (for example, Elliptic Curve groups), some other means of ensuring this must be employed. The standard way of expressing Elliptic Curve public values does not meet this criterion, as a valid Elliptic Curve X coordinate can be distinguished from a random string with probability approximately 0.5. A future version of this document might introduce a group representation, and/or a slight modification of the password encryption scheme, so that Elliptic Curve groups can be accommodated. presents several alternative solutions for this problem.

Much of this document was unashamedly picked from and , and we would like to acknowledge the authors of these documents: Dan Harkins, Glen Zorn, James Carlson, Bernard Aboba and Henry Haverinen. We would like to thank David Jacobson and Steve Bellovin for their useful comments.

&rfc2104; &rfc2119; &rfc2284; &rfc3526; &rfc3748; &rfc4013; &rfc4282; &rfc4017; &rfc4306; &rfc4086; &rfc5114; &draft-harkins-emu-eap-pwd; &rfc5226;

Revised following comments raised on the CFRG mailing list. In particular, added security considerations and a new DH group definition, to resolve the vulnerability in case the group's generator is not a primitive element.

Initial version.

We have looked at three options: 2 round trips, 3 round trips, and a normal run of 2 round trips with an optional third. Some of the decision factors include: Performance (latency). Crypto-agility, the ability to negotiate cryptographic algorithms. Ideally this applies to both the symmetric and asymmetric algorithms. Complexity of the protocol state machine, when some messages are optional. Dependence on a higher-level protocol sending the peer's identity before EAP-EKE starts, so that the correct password can be used. The initial version of this protocol has 3 round trips, primarily for simplicity.

While similar documents ( ) provide fragmentation support at the level of the EAP method, we have decided that such support is unnecessary given the expected size of messages in EAP-EKE.