Internet Engineering Task Force (IETF) V. Roca Request for Comments: 5776 A. Francillon Category: Experimental S. Faurite ISSN: 2070-1721 INRIA April 2010 Use of Timed Efficient Stream Loss-Tolerant Authentication (TESLA) in the Asynchronous Layered Coding (ALC) and NACK-Oriented Reliable Multicast (NORM) ProtocolsAbstract
This document details the Timed Efficient Stream Loss-Tolerant Authentication (TESLA) packet source authentication and packet integrity verification protocol and its integration within the Asynchronous Layered Coding (ALC) and NACK-Oriented Reliable Multicast (NORM) content delivery protocols. This document only considers the authentication/integrity verification of the packets generated by the session's sender. The authentication and integrity verification of the packets sent by receivers, if any, is out of the scope of this document. Status of This Memo This document is not an Internet Standards Track specification; it is published for examination, experimental implementation, and evaluation. This document defines an Experimental Protocol for the Internet community. 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). Not all documents approved by the IESG are a candidate for any level of Internet Standard; see 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 http://www.rfc-editor.org/info/rfc5776.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1. Scope of This Document . . . . . . . . . . . . . . . . . . 6 1.2. Conventions Used in This Document . . . . . . . . . . . . 7 1.3. Terminology and Notations . . . . . . . . . . . . . . . . 7 1.3.1. Notations and Definitions Related to Cryptographic Functions . . . . . . . . . . . . . . . . . . . . . . 7 1.3.2. Notations and Definitions Related to Time . . . . . . 8 2. Using TESLA with ALC and NORM: General Operations . . . . . . 9 2.1. ALC and NORM Specificities That Impact TESLA . . . . . . . 9 2.2. Bootstrapping TESLA . . . . . . . . . . . . . . . . . . . 10 2.2.1. Bootstrapping TESLA with an Out-Of-Band Mechanism . . 10 2.2.2. Bootstrapping TESLA with an In-Band Mechanism . . . . 11 2.3. Setting Up a Secure Time Synchronization . . . . . . . . . 11 2.3.1. Direct Time Synchronization . . . . . . . . . . . . . 12 2.3.2. Indirect Time Synchronization . . . . . . . . . . . . 12 2.4. Determining the Delay Bounds . . . . . . . . . . . . . . . 13 2.4.1. Delay Bound Calculation in Direct Time Synchronization Mode . . . . . . . . . . . . . . . . . 14 2.4.2. Delay Bound Calculation in Indirect Time Synchronization Mode . . . . . . . . . . . . . . . . . 14 2.5. Cryptographic Parameter Values . . . . . . . . . . . . . . 15 3. Sender Operations . . . . . . . . . . . . . . . . . . . . . . 16 3.1. TESLA Parameters . . . . . . . . . . . . . . . . . . . . . 16 3.1.1. Time Intervals . . . . . . . . . . . . . . . . . . . . 16 3.1.2. Key Chains . . . . . . . . . . . . . . . . . . . . . . 16 3.1.3. Time Interval Schedule . . . . . . . . . . . . . . . . 20 3.1.4. Timing Parameters . . . . . . . . . . . . . . . . . . 20 3.2. TESLA Signaling Messages . . . . . . . . . . . . . . . . . 21 3.2.1. Bootstrap Information . . . . . . . . . . . . . . . . 21 3.2.2. Direct Time Synchronization Response . . . . . . . . . 22 3.3. TESLA Authentication Information . . . . . . . . . . . . . 22 3.3.1. Authentication Tags . . . . . . . . . . . . . . . . . 23 3.3.2. Digital Signatures . . . . . . . . . . . . . . . . . . 23 3.3.3. Group MAC Tags . . . . . . . . . . . . . . . . . . . . 24 3.4. Format of TESLA Messages and Authentication Tags . . . . . 25 3.4.1. Format of a Bootstrap Information Message . . . . . . 26 3.4.2. Format of a Direct Time Synchronization Response . . . 31 3.4.3. Format of a Standard Authentication Tag . . . . . . . 32 3.4.4. Format of an Authentication Tag without Key Disclosure . . . . . . . . . . . . . . . . . . . . . . 33 3.4.5. Format of an Authentication Tag with a "New Key Chain" Commitment . . . . . . . . . . . . . . . . . . 34 3.4.6. Format of an Authentication Tag with a "Last Key of Old Chain" Disclosure . . . . . . . . . . . . . . . 35 4. Receiver Operations . . . . . . . . . . . . . . . . . . . . . 36 4.1. Verification of the Authentication Information . . . . . . 36
4.1.1. Processing the Group MAC Tag . . . . . . . . . . . . . 36 4.1.2. Processing the Digital Signature . . . . . . . . . . . 37 4.1.3. Processing the Authentication Tag . . . . . . . . . . 37 4.2. Initialization of a Receiver . . . . . . . . . . . . . . . 38 4.2.1. Processing the Bootstrap Information Message . . . . . 38 4.2.2. Performing Time Synchronization . . . . . . . . . . . 38 4.3. Authentication of Received Packets . . . . . . . . . . . . 40 4.3.1. Discarding Unnecessary Packets Earlier . . . . . . . . 43 4.4. Flushing the Non-Authenticated Packets of a Previous Key Chain . . . . . . . . . . . . . . . . . . . . . . . . 43 5. Integration in the ALC and NORM Protocols . . . . . . . . . . 44 5.1. Authentication Header Extension Format . . . . . . . . . . 44 5.2. Use of Authentication Header Extensions . . . . . . . . . 45 5.2.1. EXT_AUTH Header Extension of Type Bootstrap Information . . . . . . . . . . . . . . . . . . . . . 45 5.2.2. EXT_AUTH Header Extension of Type Authentication Tag . . . . . . . . . . . . . . . . . . . . . . . . . 48 5.2.3. EXT_AUTH Header Extension of Type Direct Time Synchronization Request . . . . . . . . . . . . . . . 49 5.2.4. EXT_AUTH Header Extension of Type Direct Time Synchronization Response . . . . . . . . . . . . . . . 49 6. Security Considerations . . . . . . . . . . . . . . . . . . . 50 6.1. Dealing with DoS Attacks . . . . . . . . . . . . . . . . . 50 6.2. Dealing With Replay Attacks . . . . . . . . . . . . . . . 51 6.2.1. Impacts of Replay Attacks on TESLA . . . . . . . . . . 51 6.2.2. Impacts of Replay Attacks on NORM . . . . . . . . . . 52 6.2.3. Impacts of Replay Attacks on ALC . . . . . . . . . . . 53 6.3. Security of the Back Channel . . . . . . . . . . . . . . . 53 7. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 54 8. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 55 9. References . . . . . . . . . . . . . . . . . . . . . . . . . . 55 9.1. Normative References . . . . . . . . . . . . . . . . . . . 55 9.2. Informative References . . . . . . . . . . . . . . . . . . 56
1. Introduction
Many applications using multicast and broadcast communications require that each receiver be able to authenticate the source of any packet it receives as well as the integrity of these packets. This is the case with ALC [RFC5775] and NORM [RFC5740], two Content Delivery Protocols (CDPs) designed to transfer objects (e.g., files) reliably between a session's sender and several receivers. The NORM protocol is based on bidirectional transmissions. Each receiver acknowledges data received or, in case of packet erasures, asks for retransmissions. On the opposite, the ALC protocol is based on purely unidirectional transmissions. Reliability is achieved by means of the cyclic transmission of the content within a carousel and/or by the use of proactive Forward Error Correction (FEC) codes. Both protocols have in common the fact that they operate at the application level, on top of an erasure channel (e.g., the Internet) where packets can be lost (erased) during the transmission. The goal of this document is to counter attacks where an attacker impersonates the ALC or NORM session's sender and injects forged packets to the receivers, thereby corrupting the objects reconstructed by the receivers. Preventing this attack is much more complex in the case of group communications than it is with unicast communications. Indeed, with unicast communications, a simple solution exists: the sender and the receiver share a secret key to compute a Message Authentication Code (MAC) of all messages exchanged. This is no longer feasible in the case of multicast and broadcast communications since sharing a group key between the sender and all receivers implies that any group member can impersonate the sender and send forged messages to other receivers. The usual solution to provide the source authentication and message integrity services in the case of multicast and broadcast communications consists of relying on asymmetric cryptography and using digital signatures. Yet, this solution is limited by high computational costs and high transmission overheads. The Timed Efficient Stream Loss-tolerant Authentication (TESLA) protocol is an alternative solution that provides the two required services, while being compatible with high-rate transmissions over lossy channels. This document explains how to integrate the TESLA source authentication and packet integrity protocol to the ALC and NORM CDP. Any application built on top of ALC and NORM will directly benefit from the services offered by TESLA at the transport layer. In particular, this is the case of File Delivery over Unidirectional Transport (FLUTE).
For more information on the TESLA protocol and its principles, please refer to [RFC4082] and [Perrig04]. For more information on ALC and NORM, please refer to [RFC5775], [RFC5651], and [RFC5740], respectively. For more information on FLUTE, please refer to [RMT-FLUTE].1.1. Scope of This Document
This specification only considers the authentication and integrity verification of the packets generated by the session's sender. This specification does not consider the packets that may be sent by receivers, for instance, NORM's feedback packets. [RMT-SIMPLE-AUTH] describes several techniques that can be used to that purpose. Since this is usually a low-rate flow (unlike the downstream flow), using computing intensive techniques like digital signatures, possibly combined with a Group MAC scheme, is often acceptable. Finally, Section 5 explains how to use several authentication schemes in a given session thanks to the "ASID" (Authentication Scheme IDentifier) field. This specification relies on several external mechanisms, for instance: o to communicate securely the public key or a certificate for the session's sender (Section 2.2.2); o to communicate securely and confidentially the group key, K_g, used by the Group MAC feature, when applicable (Section 3.3.3). In some situations, this group key will have to be periodically refreshed; o to perform secure time synchronization in indirect mode (Section 2.3.2) or in direct mode (Section 2.3.1) to carry the request/response messages with ALC, which is purely unidirectional; These mechanisms are required in order to bootstrap TESLA at a sender and at a receiver and must be deployed in parallel to TESLA. Besides, the randomness of the Primary Key of the key chain (Section 3.1.2) is vital to the security of TESLA. Therefore, the sender needs an appropriate mechanism to generate this random key. Several technical details of TESLA, like the most appropriate way to alternate between the transmission of a key disclosure and a commitment to a new key chain, or the transmission of a key disclosure and the last key of the previous key chain, or the disclosure of a key and the compact flavor that does not disclose any key, are specific to the target use case (Section 3.1.2). For
instance, it depends on the number of packets sent per time interval, on the desired robustness and the acceptable transmission overhead, which can only be optimized after taking into account the use-case specificities.1.2. 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].1.3. Terminology and Notations
The following notations and definitions are used throughout this document.1.3.1. Notations and Definitions Related to Cryptographic Functions
Notations and definitions related to cryptographic functions [RFC4082][RFC4383]: o PRF is the Pseudo Random Function; o MAC is the Message Authentication Code; o HMAC is the keyed-Hash Message Authentication Code; o F is the one-way function used to create the key chain (Section 3.1.2.1); o F' is the one-way function used to derive the HMAC keys (Section 3.1.2.1); o n_p is the length, in bits, of the F function's output. This is therefore the length of the keys in the key chain; o n_f is the length, in bits, of the F' function's output. This is therefore the length of the HMAC keys; o n_m is the length, in bits, of the truncated output of the MAC [RFC2104]. Only the n_m most significant bits of the MAC output are kept; o N is the length of a key chain. There are N+1 keys in a key chain: K_0, K_1, ..., K_N. When several chains are used, all the chains MUST have the same length and keys are numbered consecutively, following the time interval numbering;
o n_c is the number of keys in a key chain. Therefore, n_c = N+1; o n_tx_lastkey is the number of additional intervals during which the last key of the old key chain SHOULD be sent, after switching to a new key chain and after waiting for the disclosure delay d. These extra transmissions take place after the interval during which the last key is normally disclosed. The n_tx_lastkey value is either 0 (no extra disclosure) or larger. This parameter is sender specific and is not communicated to the receiver; o n_tx_newkcc is the number of intervals during which the commitment to a new key chain SHOULD be sent, before switching to the new key chain. The n_tx_newkcc value is either 0 (no commitment sent within authentication tags) or larger. This parameter is sender specific and is not communicated to the receiver; o K_g is a shared group key, communicated to all group members, confidentially, during the TESLA bootstrapping (Section 2.2); o n_w is the length, in bits, of the truncated output of the MAC of the optional group authentication scheme: only the n_w most significant bits of the MAC output are kept. n_w is typically small, a multiple of 32 bits (e.g., 32 bits).1.3.2. Notations and Definitions Related to Time
Notations and definitions related to time: o i is the time interval index. Interval numbering starts at 0 and increases consecutively. Since the interval index is stored as a 32-bit unsigned integer, wrapping to 0 might take place in long sessions. o t_s is the sender local time value at some absolute time (in NTP timestamp format); o t_r is the receiver local time value at the same absolute time (in NTP timestamp format); o T_0 is the start time corresponding to the beginning of the session, i.e., the beginning of time interval 0 (in NTP timestamp format); o T_int is the interval duration (in milliseconds); o d is the key disclosure delay (in number of intervals);
o D_t is the upper bound of the lag of the receiver's clock with respect to the clock of the sender; o S_sr is an estimated bound of the clock drift between the sender and a receiver throughout the duration of the session; o D^O_t is the upper bound of the lag of the sender's clock with respect to the time reference in indirect time synchronization mode; o D^R_t is the upper bound of the lag of the receiver's clock with respect to the time reference in indirect time synchronization mode; o D_err is an upper bound of the time error between all the time references, in indirect time synchronization mode; o NTP timestamp format consists in a 64-bit unsigned fixed-point number, in seconds relative to 0h on 1 January 1900. The integer part is in the first 32 bits, and the fraction part in the last 32 bits [RFC1305].2. Using TESLA with ALC and NORM: General Operations
2.1. ALC and NORM Specificities That Impact TESLA
The ALC and NORM protocols have features and requirements that largely impact the way TESLA can be used. In the case of ALC: o ALC is massively scalable: nothing in the protocol specification limits the number of receivers that join a session. Therefore, an ALC session potentially includes a huge number (e.g., millions or more) of receivers; o ALC can work on top of purely unidirectional transport channels: this is one of the assets of ALC, and examples of unidirectional channels include satellite (even if a back channel might exist in some use cases) and broadcasting networks like Digital Video Broadcasting - Handhelds / Satellite services to Handhelds (DVB- H/SH); o ALC defines an on-demand content delivery model [RFC5775] where receivers can arrive at any time, at their own discretion, download the content and leave the session. Other models (e.g., push or streaming) are also defined;
o ALC sessions are potentially very long: a session can last several days or months during which the content is continuously transmitted within a carousel. The content can be either static (e.g., a software update) or dynamic (e.g., a web site). Depending on the use case, some of the above features may not apply. For instance, ALC can also be used over a bidirectional channel or with a limited number of receivers. In the case of NORM: o NORM has been designed for medium-size sessions: indeed, NORM relies on feedback messages and the sender may collapse if the feedback message rate is too high; o NORM requires a bidirectional transport channel: the back channel is not necessarily a high-data rate channel since the control traffic sent over it by a single receiver is an order of magnitude lower than the downstream traffic. Networks with an asymmetric connectivity (e.g., a high-rate satellite downlink and a low-rate return channel) are appropriate.2.2. Bootstrapping TESLA
In order to initialize the TESLA component at a receiver, the sender MUST communicate some key information in a secure way, so that the receiver can check the source of the information and its integrity. Two general methods are possible: o by using an out-of-band mechanism, or o by using an in-band mechanism. The current specification does not recommend any mechanism to bootstrap TESLA. Choosing between an in-band and out-of-band scheme is left to the implementer, depending on the target use case. However, it is RECOMMENDED that TESLA implementations support the use of the in-band mechanism for interoperability purposes.2.2.1. Bootstrapping TESLA with an Out-Of-Band Mechanism
For instance, [RFC4442] describes the use of the MIKEY (Multimedia Internet Keying) protocol to bootstrap TESLA. As a side effect, MIKEY also provides a loose time synchronization feature from which TESLA can benefit. Other solutions, for instance, based on an extended session description, are possible, on the condition that these solutions provide the required security level.
2.2.2. Bootstrapping TESLA with an In-Band Mechanism
This specification describes an in-band mechanism. In some use cases, it might be desired that bootstrapping take place without requiring the use of an additional external mechanism. For instance, each device may feature a clock with a known time-drift that is negligible in front of the time accuracy required by TESLA, and each device may embed the public key of the sender. It is also possible that the use case does not feature a bidirectional channel that prevents the use of out-of-band protocols like MIKEY. For these two examples, the exchange of a bootstrap information message (described in Section 3.4.1) and the knowledge of a few additional parameters (listed below) are sufficient to bootstrap TESLA at a receiver. Some parameters cannot be communicated in-band. In particular: o the sender or group controller MUST either communicate the public key of the sender or a certificate (which also means that a PKI has been set up) to all receivers, so that each receiver be able to verify the signature of the bootstrap message and direct time synchronization response messages (when applicable). o when time synchronization is performed with NTP/SNTP (Simple Network Time Protocol), the sender or group controller MUST communicate the list of valid NTP/SNTP servers to all the session members (sender included), so that they are all able to synchronize themselves on the same NTP/SNTP servers. o when the Group MAC feature is used, the sender or group controller MUST communicate the K_g group key to all the session members (sender included). This group key may be periodically refreshed. The way these parameters are communicated is out of the scope of this document.2.3. Setting Up a Secure Time Synchronization
The security offered by TESLA heavily relies on time. Therefore, the session's sender and each receiver need to be time synchronized in a secure way. To that purpose, two general methods exist: o direct time synchronization, and o indirect time synchronization. It is also possible that a given session includes receivers that use the direct time synchronization mode while others use the indirect time synchronization mode.
2.3.1. Direct Time Synchronization
When direct time synchronization is used, each receiver asks the sender for a time synchronization. To that purpose, a receiver sends a direct time synchronization request (Section 4.2.2.1). The sender then directly answers each request with a direct time synchronization response (Section 3.4.2), signing this reply. Upon receiving this response, a receiver first verifies the signature, and then calculates an upper bound of the lag of his clock with respect to the clock of the sender, D_t. The details on how to calculate D_t are given in Section 2.4.1. This synchronization method is both simple and secure. Yet, there are two potential issues: o a bidirectional channel must exist between the sender and each receiver, and o the sender may collapse if the incoming request rate is too high. Relying on direct time synchronization is not expected to be an issue with NORM since (1) bidirectional communications already take place, and (2) NORM scalability is anyway limited. Yet, it can be required that a mechanism, that is out of the scope of this document, be used to spread the transmission of direct time synchronization request messages over time if there is a risk that the sender may collapse. But direct time synchronization is potentially incompatible with ALC since (1) there might not be a back channel, and (2) there are potentially a huge number of receivers and therefore a risk that the sender will collapse.2.3.2. Indirect Time Synchronization
When indirect time synchronization is used, the sender and each receiver must synchronize securely via an external time reference. Several possibilities exist: o sender and receivers can synchronize through an NTPv3 (Network Time Protocol version 3) [RFC1305] hierarchy of servers. The authentication mechanism of NTPv3 MUST be used in order to authenticate each NTP message individually. It prevents, for instance, an attacker from impersonating an NTP server; o they can synchronize through an NTPv4 (Network Time Protocol version 4) [NTP-NTPv4] hierarchy of servers. The Autokey security protocol of NTPv4 MUST be used in order to authenticate each NTP message individually;
o they can synchronize through an SNTPv4 (Simple Network Time Protocol version 4) [RFC4330] hierarchy of servers. The authentication features of SNTPv4 must then be used. Note that TESLA only needs a loose (but secure) time synchronization, which is in line with the time synchronization service offered by SNTP; o they can synchronize through a GPS or Galileo (or similar) device that also provides a high precision time reference. Spoofing attacks on the GPS system have recently been reported. Depending on the use case, the security achieved will or will not be acceptable; o they can synchronize thanks to a dedicated hardware, embedded on each sender and receiver, that provides a clock with a time-drift that is negligible in front of the TESLA time accuracy requirements. This feature enables a device to synchronize its embedded clock with the official time reference from time to time (in an extreme case once, at manufacturing time), and then to remain autonomous for a duration that depends on the known maximum clock drift. A bidirectional channel is required by the NTP/SNTP schemes. On the opposite, with the GPS/Galileo and high precision clock schemes, no such assumption is made. In situations where ALC is used on purely unidirectional transport channels (Section 2.1), using the NTP/SNTP schemes is not possible. Another aspect is the scalability requirement of ALC, and to a lesser extent of NORM. From this point of view, the above mechanisms usually do not raise any problem, unlike the direct time synchronization schemes. Therefore, using indirect time synchronization can be a good choice. It should be noted that the NTP/SNTP schemes assume that each client trusts the sender and accepts aligning its NTP/SNTP configuration to that of the sender. If this assumption does not hold, the sender SHOULD offer an alternative solution. The details on how to calculate an upper bound of the lag of a receiver's clock with respect to the clock of the sender, D_t, are given in Section 2.4.2.2.4. Determining the Delay Bounds
Let us assume that a secure time synchronization has been set up. This section explains how to define the various timing parameters that are used during the authentication of received packets.
2.4.1. Delay Bound Calculation in Direct Time Synchronization Mode
In direct time synchronization mode, synchronization between a receiver and the sender follows the following protocol [RFC4082]: o The receiver sends a direct time synchronization request message to the sender, that includes t_r, the receiver local time at the moment of sending (Section 4.2.2.1). o Upon receipt of this message, the sender records its local time, t_s, and sends to the receiver a direct time synchronization response that includes t_r (taken from the request) and t_s, signing this reply (Section 3.4.2). o Upon receiving this response, the receiver first verifies that he actually sent a request with t_r and then checks the signature. Then he calculates D_t = t_s - t_r + S_sr, where S_sr is an estimated bound of the clock drift between the sender and the receiver throughout the duration of the session. This document does not specify how S_sr is estimated. After this initial synchronization, at any point throughout the session, the receiver knows that: T_s < T_r + D_t, where T_s is the current time at the sender and T_r is the current time at the receiver.2.4.2. Delay Bound Calculation in Indirect Time Synchronization Mode
In indirect time synchronization, the sender and the receivers must synchronize indirectly using one or several time references.2.4.2.1. Single Time Reference
Let us assume that there is a single time reference. 1. The sender calculates D^O_t, the upper bound of the lag of the sender's clock with respect to the time reference. This D^O_t value is then communicated to the receivers (Section 3.2.1). 2. Similarly, a receiver R calculates D^R_t, the upper bound of the lag of the receiver's clock with respect to the time reference. 3. Then, for receiver R, the overall upper bound of the lag of the receiver's clock with respect to the clock of the sender, D_t, is the sum: D_t = D^O_t + D^R_t.
The D^O_t and D^R_t calculation depends on the time synchronization mechanism used (Section 2.3.2). In some cases, the synchronization scheme specifications provide these values. In other cases, these parameters can be calculated by means of a scheme similar to the one specified in Section 2.4.1, for instance, when synchronization is achieved via a group controller [RFC4082].2.4.2.2. Multiple Time References
Let us now assume that there are several time references (e.g., several NTP/SNTP servers). The sender and receivers first synchronize with the various time references, independently. It results in D^O_t and D^R_t. Let D_err be an upper bound of the time error between all of the time references. Then, the overall value of D_t within receiver R is set to the sum: D_t = D^O_t + D^R_t + D_err. In some cases, the D_t value is part of the time synchronization scheme specifications. For instance, NTPv3 [RFC1305] defines algorithms that are "capable of accuracies in the order of a millisecond, even after extended periods when synchronization to primary reference sources has been lost". In practice, depending on the NTP server stratum, the accuracy might be a little bit worse. In that case, D_t = security_factor * (1ms + 1ms), where the security_factor is meant to compensate several sources of inaccuracy in NTP. The choice of the security_factor value is left to the implementer, depending on the target use case.2.5. Cryptographic Parameter Values
The F (resp. F') function output length is given by the n_p (resp. n_f) parameter. The n_p and n_f values depend on the PRF function chosen, as specified below: +------------------------+---------------------+ | PRF name | n_p and n_f | +------------------------+---------------------+ | HMAC-SHA-1 | 160 bits (20 bytes) | | HMAC-SHA-224 | 224 bits (28 bytes) | | HMAC-SHA-256 (default) | 256 bits (32 bytes) | | HMAC-SHA-384 | 384 bits (48 bytes) | | HMAC-SHA-512 | 512 bits (64 bytes) | +------------------------+---------------------+ The computing of regular MAC (resp. Group MAC) makes use of the n_m (resp. n_w) parameter, i.e., the length of the truncated output of the function. The n_m and n_w values depend on the MAC function chosen, as specified below:
+------------------------+---------------------+-------------------+ | MAC name | n_m (regular MAC) | n_w (Group MAC) | +------------------------+---------------------+-------------------+ | HMAC-SHA-1 | 80 bits (10 bytes) | 32 bits (4 bytes) | | HMAC-SHA-224 | 112 bits (14 bytes) | 32 bits (4 bytes) | | HMAC-SHA-256 (default) | 128 bits (16 bytes) | 32 bits (4 bytes) | | HMAC-SHA-384 | 192 bits (24 bytes) | 32 bits (4 bytes) | | HMAC-SHA-512 | 256 bits (32 bytes) | 32 bits (4 bytes) | +------------------------+---------------------+-------------------+