Kerberos SPAKE with Two-Factor Authentication

Introduction A password-derived long-term key is commonly used in the Kerberos pre-authentication stage to protect messages exchanged between a Kerberos client and a Key Distribution Center (KDC). As noted in , an attacker can mount brute-force password attacks via eavesdropping a legitimate credential returned by the KDC or a legitimate authentication message sent by the client, which are both encrypted by the long-term key. A Kerberos SPAKE pre-authentication mechanism is proposed in , it uses a simple password-authenticated key exchange (SPAKE) to protect against brute-force password attacks, and additionally enables two-factor authentication (2FA). For example, the second-factor (SF) authentication may include one-time passwords, challenge/response signatures, and biometric data. As suggested in , the SF authentication data can be first encrypted using the key established by the SPAKE and then securely transferred from the client to the KDC for verification, where the password verification happens implicitly by a successful decryption of the SF authentication data. However, this 2FA methodology does not achieve the security of true two-factor authentication, which requires that the compromise of any factor will not affect the security of whole 2FA protocol. More specifically, in case of password leakage, an attacker can use the leaked password to successfully perform a man-in-the-middle (MITM) attack against the Kerberos SPAKE, i.e., the client establishes a Kerberos SPAKE session A with the attacker and the attacker establishes a Kerberos SPAKE session B with the KDC. In this case, the attacker can obtain the SF authentication data in plaintext from the session A, and can use it as a valid second-factor in session B. Therefore, only the password factor allows the attacker to pass the KDC's two-factor authentication. To remedy the above problem, this document defines a new two-factor authentication mechanism for the Kerberos SPAKE pre-authentication, which uses the widely deployed time-based one-time password (TOTP) as a second factor. The mechanism combines the second factor with the password factor in the following way: the resulting TOTP value is combined with the password-derived long-term key to derive a shared secret, which will be used as an input of the SPAKE algorithm. Therefore, the password and the TOTP value are both protected by the SPAKE to defend against brute-force attacks and required to compute the SPAKE result, and the final encryption keys contain the entropy of both factors. As a result, if an attacker compromises either of factors, it also needs to obtain another factor's authentication data to derive the final encryption keys, which are necessary to pass the two-factor authentication or obtain the TGT's session key. But this is hard to do if the authentication of another factor is still secure.

Terminology The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in BCP 14 when, and only when, they appear in all capitals, as shown here. The terms "encryption type" and "random-to-key" are defined in .

Kerberos SPAKE Pre-authentication with Second-Factor TOTP

Two-Factor Authentication Overview The SPAKE algorithm combined with the TOTP algorithm can be generally described in the following steps:

Calculation of a shared TOTP value.
Calculation of an update reply key from the initial reply key and the TOTP value.
Calculation and exchange of the public key using the update reply key.
Calculation of a shared SPAKE result (K).
Derivation of an encryption key (K').
Verification of the derived encryption key (K').

In this mechanism, key verification happens implicitly by a successful decryption of the SF challenge data specific to the second-factor TOTP.

Introduction of the TOTP Algorithm As defined in , the HOTP algorithm is based on the HMAC-SHA-1 algorithm and is computed as follows: where K and C represent the shared secret and counter value, and Truncate represents the function that can convert an HMAC-SHA-1 value into an HOTP value; see for detailed definitions. Recall that in , the TOTP algorithm is defined as TOTP = HOTP(K, T), where T is an integer and represents the number of time steps between the initial counter time T0 (default value is 0, i.e., the Unix epoch) and the current Unix time. Note that TOTP implementations MAY use HMAC-SHA-256 or HMAC-SHA-512 functions, please refer to .

Definition of the Second-Factor TOTP Recall that in , each second factor is represented by a SPAKESecondFactor. The type field is a unique integer that identifies the second-factor type, and the data field contains optional challenge data. This document defines the type as an integer 2 to identify the second-factor TOTP, and defines the data as a random nonce whose length SHOULD match the multiplier length of the negotiated group, where the multiplier length is defined in .

SPAKE Parameters and Conversions Note that the TOTP value is a low-entropy secret, so it can also be protected by the SPAKE to protect against brute-force attacks. More specifically, an update reply key is produced from the initial reply key and the TOTP value as follows, which is used as an input to the SPAKE.

A pepper string is generated by concatenating the string "SF-TOTP" and the TOTP value as an octet string.
An octet string is derived using PRF+(initial-reply-key, pepper), where PRF+ is defined in .
An update reply key is produced from the octet string using the random-to-key function, which has the same encryption type as the initial reply key.

The SPAKE algorithm requires a shared secret input w to be used as a scalar multiplier. Similar to the computation in , this value MUST be produced from the update reply key as follows:

Determine the length of the multiplier octet string as defined in the "Kerberos SPAKE Groups" registry (see ).
Compose a pepper string by concatenating the string "SPAKEsecret" and the group number as a big-endian four-byte two's complement binary number.
Produce an octet string of the required length using PRF+(update-reply-key, pepper), where PRF+ is as defined in .
Convert the octet string to a multiplier scalar using the multiplier conversion method defined in the "Kerberos SPAKE Groups" registry (see ).

Key Derivation The 2FA protocol requires encryption keys to be used for client verification and TGT issuance. Similar to the computation in , the key K'[n] is computed as follows:

The key K'[n] has the same encryption type as the update reply key, and has the value KRB-FX-CF2(update-reply-key, intermediate-key, "SPAKE", "keyderiv"), where KRB-FX-CF2 is defined in .

Note that the update reply key and the intermediate key both contain the entropy of the password and TOTP factors.

Second-Factor Types This document defines one second-factor type: This second-factor type indicates that the TOTP second factor is used.

IANA Considerations This document defines a new second-factor type "SF-TOTP" with the following contents, and requests that IANA add it to the "Kerberos Second-Factor Types" Registry defined in .