Network Time Security
draft-ietf-ntp-network-time-security-06.txt

Abstract

This document describes Network Time Security (NTS), a collection of measures that enable secure time synchronization with time servers using protocols like the Network Time Protocol (NTP) or the Precision Time Protocol (PTP). Its design considers the special requirements of precise timekeeping which are described in Security Requirements of Time Protocols in Packet Switched Networks [RFC7384].

Requirements Language

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].

Status of This Memo

This Internet-Draft is submitted in full conformance with the provisions of BCP 78 and BCP 79.

Internet-Drafts are working documents of the Internet Engineering Task Force (IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet-Drafts is at http://datatracker.ietf.org/drafts/current/.

Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress."

This Internet-Draft will expire on July 20, 2015.

Copyright Notice

Copyright (c) 2015 IETF Trust and the persons identified as the document authors. All rights reserved.

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Table of Contents

• 1. Introduction
• 2. Security Threats
• 3. Objectives
• 4. Terms and Abbreviations
• 5. NTS Overview
• 6. Protocol Messages
• 6.1. Association Messages
• 6.1.1. Message Type: "client_assoc"
• 6.1.2. Message Type: "server_assoc"
• 6.2. Cookie Messages
• 6.2.1. Message Type: "client_cook"
• 6.2.2. Message Type: "server_cook"
• 6.3. Unicast Time Synchronisation Messages
• 6.3.1. Message Type: "time_request"
• 6.3.2. Message Type: "time_response"
• 6.4. Broadcast Parameter Messages
• 6.4.1. Message Type: "client_bpar"
• 6.4.2. Message Type: "server_bpar"
• 6.5. Broadcast Messages
• 6.5.1. Message Type: "server_broad"
• 6.6. Broadcast Key Check
• 6.6.1. Message Type: "client_keycheck"
• 6.6.2. Message Type: "server_keycheck"
• 7. Message Dependencies
• 8. Server Seed Considerations
• 9. Hash Algorithms and MAC Generation
• 9.1. Hash Algorithms
• 9.2. MAC Calculation
• 10. IANA Considerations
• 11. Security Considerations
• 11.1. Privacy
• 11.2. Initial Verification of the Server Certificates
• 11.3. Revocation of Server Certificates
• 11.4. Mitigating Denial-of-Service for broadcast packets
• 11.5. Delay Attack
• 12. Acknowledgements
• 13. References
• 13.1. Normative References
• 13.2. Informative References
• Appendix A. TICTOC Security Requirements
• Appendix B. Using TESLA for Broadcast-Type Messages
• B.1. Server Preparation
• B.2. Client Preparation
• B.3. Sending Authenticated Broadcast Packets
• B.4. Authentication of Received Packets
• Appendix C. Random Number Generation
• Authors' Addresses

1. Introduction

Time synchronization protocols are increasingly utilized to synchronize clocks in networked infrastructures. The reliable performance of such infrastructures can be degraded seriously by successful attacks against the time synchronization protocol. Therefore, time synchronization protocols have to be secured if they are applied in environments that are prone to malicious attacks. This can be accomplished either by utilization of external security protocols, like IPsec or TLS, or by intrinsic security measures of the time synchronization protocol.

The two most popular time synchronization protocols, the Network Time Protocol (NTP) [RFC5905] and the Precision Time Protocol (PTP) [IEEE1588], currently do not provide adequate intrinsic security precautions. This document specifies security measures which enable these protocols to verify the authenticity of the time server and the integrity of the time synchronization protocol packets.

The given measures are specified with the prerequisite in mind that precise timekeeping can only be accomplished with stateless time synchronization communication, which excludes the utilization of standard security protocols, like IPsec or TLS, for time synchronization messages. This prerequisite corresponds with the requirement that a security mechanism for timekeeping must be designed in such a way that it does not degrade the quality of the time transfer [RFC7384].

Note:

It is recommended that details on how to apply NTS to specific time synchronization protocols be formulated in separate documents, with one separate document for each protocol.

2. Security Threats

A profound analysis of security threats and requirements for time synchronization protocols can be found in the "Security Requirements of Time Protocols in Packet Switched Networks" [RFC7384].

3. Objectives

The objectives of the NTS specification are as follows:

• Authenticity: NTS enables a client/slave to authenticate its time server(s)/master(s).
• Integrity: NTS protects the integrity of time synchronization protocol packets via a message authentication code (MAC).
• Confidentiality: NTS does not provide confidentiality protection of the time synchronization packets.
• Integration with protocols: NTS can be used to secure different time synchronization protocols, specifically at least NTP and PTP. An client or server running an NTS-secured version of a time protocol does not negatively affect other participants who are running unsecured versions of that protocol.

4. Terms and Abbreviations

MITM

Man In The Middle

NTS

Network Time Security

TESLA

Timed Efficient Stream Loss-tolerant Authentication

5. NTS Overview

NTS applies X.509 certificates to verify the authenticity of the time server/master and to exchange a symmetric key, the so-called cookie. This cookie is then used to protect the authenticity and the integrity of subsequent unicast-type time synchronization packets. This is done by means of a Message Authentication Code (MAC), which is attached to each time synchronization packet. The calculation of the MAC includes the whole time synchronization packet and the cookie which is shared between client and server. The cookie is calculated according to:[RFC7384]. See Section 8 for details on seed refreshing.

cookie = MSB_<b> (HMAC(server seed, H(certificate of client))),

with the server seed as the key, where H is a hash function, and where the function MSB_<b> cuts off the b most significant bits of the result of the HMAC function. The server seed is a random value of bit length b that the server possesses, which has to be kept secret. The cookie never changes as long as the server seed stays the same, but the server seed has to be refreshed periodically in order to provide key freshness as required in

Since the server does not keep a state of the client, it has to recalculate the cookie each time it receives a unicast time synchronization request from the client. To this end, the client has to attach the hash value of its certificate to each request (see Section 6.3).

For broadcast-type messages, authenticity and integrity of the time synchronization packets are also ensured by a MAC, which is attached to the time synchronization packet by the sender. Verification of the broadcast-type packets' authenticity is based on the TESLA protocol, in particular on its "not re-using keys" scheme, see Section 3.7.2 of [RFC4082]. TESLA uses a one-way chain of keys, where each key is the output of a one-way function applied to the previous key in the chain. The last element of the chain is shared securely with all clients. The server splits time into intervals of uniform duration and assigns each key to an interval in reverse order, starting with the penultimate. At each time interval, the server sends a broadcast packet appended by a MAC, calculated using the corresponding key, and the key of the previous disclosure interval. The client verifies the MAC by buffering the packet until disclosure of the key in its associated disclosure interval occurs. In order to be able to verify the validity of the key, the client has to be loosely time synchronized with the server. This has to be accomplished during the initial client server exchange between the broadcast client and the server. In addition, NTS uses another, more rigorous check than what is used in the TESLA protocol. For a more detailed description of how NTS employs and customizes TESLA, see Appendix B.

6. Protocol Messages

This section describes the types of messages needed for secure time synchronization with NTS.

For some guidance on how these message types can be realized in practice, and integrated into the communication flow of existing time synchronization protocols, see [I-D.ietf-ntp-cms-for-nts-message], a companion document for NTS. Said document describes ASN.1 encodings for those message parts that have to be added to a time synchronization protocol for security reasons as well as CMS (Cryptographic Message Syntax, see [RFC5652]) conventions that can be used to get the cryptographic aspects right.

6.1. Association Messages

In this message exchange, the hash and encryption algorithms that are used throughout the protocol are negotiated. In addition , the client receives the certification chain up to a trusted anchor. With the established certification chain the client is able to verify the server's signatures and, hence, the authenticity of future NTS messages from the server is ensured.

6.1.1. Message Type: "client_assoc"

The protocol sequence starts with the client sending an association message, called client_assoc. This message contains

• the NTS message ID "client_assoc",
• the version number of NTS that the client wants to use (this SHOULD be the highest version number that it supports),
• the hostname of the client,
• a selection of accepted hash algorithms, and
• a selection of accepted encryption algorithms.

6.1.2. Message Type: "server_assoc"

This message is sent by the server upon receipt of client_assoc. It contains

• the NTS message ID "server_assoc",
• the version number used for the rest of the protocol (which SHOULD be determined as the minimum over the client's suggestion in the client_assoc message and the highest supported by the server),
• the hostname of the server,
• the server's choice of algorithm for encryption and for cryptographic hashing, all of which MUST be chosen from the client's proposals,
• a signature, calculated over the data listed above, with the server's private key and according to the signature algorithm which is also used for the certificates that are included (see below), and
• a chain of certificates, which starts at the server and goes up to a trusted authority; each certificate MUST be certified by the one directly following it.

6.2. Cookie Messages

During this message exchange, the server transmits a secret cookie to the client securely. The cookie will later be used for integrity protection during unicast time synchronization.

6.2.1. Message Type: "client_cook"

This message is sent by the client upon successful authentication of the server. In this message, the client requests a cookie from the server. The message contains

• the NTS message ID "client_cook",
• the negotiated version number,
• the negotiated signature algorithm,
• the negotiated encryption algorithm,
• a nonce,
• the negotiated hash algorithm H,
• the client's certificate.

6.2.2. Message Type: "server_cook"

This message is sent by the server upon receipt of a client_cook message. The server generates the hash of the client's certificate, as conveyed during client_cook, in order to calculate the cookie according to Section 5. This message contains

• the NTS message ID "server_cook"
• the version number as transmitted in client_cook,
• a concatenated datum which is encrypted with the client's public key, according to the encryption algorithm transmitted in the client_cook message. The concatenated datum contains
  • the nonce transmitted in client_cook, and
  • the cookie.
• a signature, created with the server's private key, calculated over all of the data listed above. This signature MUST be calculated according to the transmitted signature algorithm from the client_cook message.

6.3. Unicast Time Synchronisation Messages

In this message exchange, the usual time synchronization process is executed, with the addition of integrity protection for all messages that the server sends. This message can be repeatedly exchanged as often as the client desires and as long as the integrity of the server's time responses is verified successfully.

6.3.1. Message Type: "time_request"

This message is sent by the client when it requests a time exchange. It contains

• the NTS message ID "time_request",
• the negotiated version number,
• a nonce,
• the negotiated hash algorithm H,
• the hash of the client's certificate under H.

6.3.2. Message Type: "time_response"

This message is sent by the server after it has received a time_request message. Prior to this the server MUST recalculate the client's cookie by using the hash of the client's certificate and the transmitted hash algorithm. The message contains

• the NTS message ID "time_response",
• the version number as transmitted in time_request,
• the server's time synchronization response data,
• the nonce transmitted in time_request,
• a MAC (generated with the cookie as key) for verification of all of the above data.

6.4. Broadcast Parameter Messages

In this message exchange, the client receives the necessary information to execute the TESLA protocol in a secured broadcast association. The client can only initiate a secure broadcast association after a successful unicast run.

See Appendix B for more details on TESLA.

6.4.1. Message Type: "client_bpar"

This message is sent by the client in order to establish a secured time broadcast association with the server. It contains

• the NTS message ID "client_bpar",
• the NTS version number negotiated during association in unicast mode,
• the client's hostname, and
• the signature algorithm negotiated during unicast.

6.4.2. Message Type: "server_bpar"

This message is sent by the server upon receipt of a client_bpar message during the broadcast loop of the server. It contains

• the NTS message ID "server_bpar",
• the version number as transmitted in the client_bpar message,
• the one-way functions used for building the key chain, and
• the disclosure schedule of the keys. This contains:
  • the last key of the key chain,
  • time interval duration,
  • the disclosure delay (number of intervals between use and disclosure of a key),
  • the time at which the next time interval will start, and
  • the next interval's associated index.
• The message also contains a signature signed by the server with its private key, verifying all the data listed above.

6.5. Broadcast Messages

Via this message, the server keeps sending broadcast time synchronization messages to all participating clients.

6.5.1. Message Type: "server_broad"

This message is sent by the server over the course of its broadcast schedule. It is part of any broadcast association. It contains

• the NTS message ID "server_broad",
• the version number that the server is working under,
• time broadcast data,
• the index that belongs to the current interval (and therefore identifies the current, yet undisclosed, key),
• the disclosed key of the previous disclosure interval (current time interval minus disclosure delay),
• a MAC, calculated with the key for the current time interval, verifying
  • the message ID,
  • the version number, and
  • the time data.

6.6. Broadcast Key Check

This message exchange is performed for an additional check of packet timeliness in the course of the TESLA scheme, see Appendix B.

6.6.1. Message Type: "client_keycheck"

A message of this type is sent by the client in order to initiate an additional check of packet timeliness for the TESLA scheme. It contains

• the NTS message ID "client_keycheck",
• the NTS version number negotiated during association in unicast mode,
• a nonce,
• an interval number from the TESLA disclosure schedule,
• the hash algorithm H negotiated in unicast mode, and
• the hash of the client's certificate under H.

6.6.2. Message Type: "server_keycheck"

A message of this type is sent by the server upon receipt of a client_keycheck message during the broadcast loop of the server. Prior to this, the server MUST recalculate the client's cookie by using the hash of the client's certificate and the transmitted hash algorithm. It contains

• the NTS message ID "server_keycheck"
• the version number as transmitted in "client_keycheck,
• the nonce transmitted in the client_keycheck message,
• the interval number transmitted in the client_keycheck message, and
• a MAC (generated with the cookie as key) for verification of all of the above data.

7. Message Dependencies

          +--------------------+
          |Association Exchange|
          +--------------------+
                    |
         At least one successful
                    |
                    v
            +---------------+
            |Cookie Exchange|
            +---------------+
                    |
         At least one successful
                    |
                    v
+----------------------------------------+
|Unicast Time Synchronization Exchange(s)|
+----------------------------------------+
                    |
Until sufficient accuracy has been reached
                    |
                    v
      +----------------------------+
      |Broadcast Parameter Exchange|
      +----------------------------+
                    |
        One successful per client
                    |
                    v
+----------------------------------------+
|Broadcast Time Synchronization Reception|
+----------------------------------------+
                    |
        Whenever deemed necessary
                    |
                    v
           +-----------------+
           |Keycheck Exchange|
           +-----------------+

8. Server Seed Considerations

The server has to calculate a random seed which has to be kept secret. The server MUST generate a seed for each supported hash algorithm, see Section 9.1.

According to the requirements in [RFC7384], the server MUST refresh each server seed periodically. Consequently, the cookie memorized by the client becomes obsolete. In this case, the client cannot verify the MAC attached to subsequent time response messages and has to respond accordingly by re-initiating the protocol with a cookie request (Section 6.2).

9. Hash Algorithms and MAC Generation

9.1. Hash Algorithms

Hash algorithms are used at different points: calculation of the cookie and the MAC, and hashing of the client's certificate. The client and the server negotiate a hash algorithm H during the association message exchange (Section 6.1) at the beginning of a unicast run. The selected algorithm H is used for all hashing processes in that run.

In the TESLA scheme, hash algorithms are used as pseudo-random functions to construct the one-way key chain. Here, the utilized hash algorithm is communicated by the server and is non-negotiable.

Note:

Any hash algorithm is prone to be compromised in the future. A successful attack on a hash algorithm would enable any NTS client to derive the server seed from its own cookie. Therefore, the server MUST have separate seed values for its different supported hash algorithms. This way, knowledge gained from an attack on a hash algorithm H can at least only be used to compromise such clients who use hash algorithm H as well.

9.2. MAC Calculation

For the calculation of the MAC, client and server use a Keyed-Hash Message Authentication Code (HMAC) approach [RFC2104]. The HMAC is generated with the hash algorithm specified by the client (see Section 9.1).

10. IANA Considerations

11. Security Considerations

11.1. Privacy

tbd

11.2. Initial Verification of the Server Certificates

The client has to verify the validity of the certificates during the certification message exchange (Section 6.1.2). Since it generally has no reliable time during this initial communication phase, it is impossible to verify the period of validity of the certificates. Therefore, the client MUST use one of the following approaches:

• The validity of the certificates is preconditioned. Usually this will be the case in corporate networks.
• The client ensures that the certificates are not revoked. To this end, the client uses the Online Certificate Status Protocol (OCSP) defined in [RFC6277].
• The client requests a different service to get an initial time stamp in order to be able to verify the certificates' periods of validity. To this end, it can, e.g., use a secure shell connection to a reliable host. Another alternative is to request a time stamp from a Time Stamping Authority (TSA) by means of the Time-Stamp Protocol (TSP) defined in [RFC3161].

11.3. Revocation of Server Certificates

According to Section 8, it is the client's responsibility to initiate a new association with the server after the server's certificate expires. To this end, the client reads the expiration date of the certificate during the certificate message exchange (Section 6.1.2). Furthermore, certificates may also be revoked prior to the normal expiration date. To increase security the client MAY periodically verify the state of the server's certificate via OCSP.

11.4. Mitigating Denial-of-Service for broadcast packets

TESLA authentication buffers packets for delayed authentication. This makes the protocol vulnerable to flooding attacks, causing the client to buffer excessive numbers of packets. To add stronger DoS protection to the protocol, the client and the server use the "not re-using keys" scheme of TESLA as pointed out in Section 3.7.2 of RFC 4082 [RFC4082]. In this scheme the server never uses a key for the MAC generation more than once. Therefore, the client can discard any packet that contains a disclosed key it already knows, thus preventing memory flooding attacks.

Note that an alternative approach to enhance TESLA's resistance against DoS attacks involves the addition of a group MAC to each packet. This requires the exchange of an additional shared key common to the whole group. This adds additional complexity to the protocol and hence is currently not considered in this document.

11.5. Delay Attack

In a packet delay attack, an adversary with the ability to act as a MITM delays time synchronization packets between client and server asymmetrically [RFC7384]. This prevents the client from accurately measuring the network delay, and hence its time offset to the server [Mizrahi]. The delay attack does not modify the content of the exchanged synchronization packets. Therefore, cryptographic means do not provide a feasible way to mitigate this attack. However, several non-cryptographic precautions can be taken in order to detect this attack.

1. Usage of multiple time servers: this enables the client to detect the attack, provided that the adversary is unable to delay the synchronization packets between the majority of servers. This approach is commonly used in NTP to exclude incorrect time servers [RFC5905].
2. Multiple communication paths: The client and server utilize different paths for packet exchange as described in the I-D [I-D.shpiner-multi-path-synchronization]. The client can detect the attack, provided that the adversary is unable to manipulate the majority of the available paths [Shpiner]. Note that this approach is not yet available, neither for NTP nor for PTP.
3. Usage of an encrypted connection: the client exchanges all packets with the time server over an encrypted connection (e.g. IPsec). This measure does not mitigate the delay attack, but it makes it more difficult for the adversary to identify the time synchronization packets.
4. For unicast-type messages: Introduction of a threshold value for the delay time of the synchronization packets. The client can discard a time server if the packet delay time of this time server is larger than the threshold value.

Additional provision against delay attacks has to be taken for broadcast-type messages. This mode relies on the TESLA scheme which is based on the requirement that a client and the broadcast server are loosely time synchronized. Therefore, a broadcast client has to establish time synchronization with its broadcast server before it starts utilizing broadcast messages for time synchronization. To this end, it initially establishes a unicast association with its broadcast server until time synchronization and calibration of the packet delay time is achieved. After that it establishes a broadcast association with the broadcast server and utilizes TESLA to verify integrity and authenticity of any received broadcast packets.

An adversary who is able to delay broadcast packets can cause a time adjustment at the receiving broadcast clients. If the adversary delays broadcast packets continuously, then the time adjustment will accumulate until the loose time synchronization requirement is violated, which breaks the TESLA scheme. To mitigate this vulnerability the security condition in TESLA has to be supplemented by an additional check in which the client, upon receipt of a broadcast message, verifies the status of the corresponding key via a unicast message exchange with the broadcast server (see Appendix B.4 for a detailed description of this check). Note that a broadcast client should also apply the above-mentioned precautions as far as possible.

12. Acknowledgements

The authors would like to thank Russ Housley, Steven Bellovin, David Mills and Kurt Roeckx for discussions and comments on the design of NTS. Also, thanks go to Harlan Stenn for his technical review and specific text contributions to this document.

13. References

13.1. Normative References

13.2. Informative References

Appendix A. TICTOC Security Requirements

The following table compares the NTS specifications against the TICTOC security requirements [RFC7384].

*) See discussion in Section 11.5.

Appendix B. Using TESLA for Broadcast-Type Messages

For broadcast-type messages , NTS adopts the TESLA protocol with some customizations. This appendix provides details on the generation and usage of the one-way key chain collected and assembled from [RFC4082]. Note that NTS uses the "not re-using keys" scheme of TESLA as described in Section 3.7.2. of [RFC4082].

B.1. Server Preparation

Server setup:

1. The server determines a reasonable upper bound B on the network delay between itself and an arbitrary client, measured in milliseconds.
2. It determines the number n+1 of keys in the one-way key chain. This yields the number n of keys that are usable to authenticate broadcast packets. This number n is therefore also the number of time intervals during which the server can send authenticated broadcast messages before it has to calculate a new key chain.
3. It divides time into n uniform intervals I_1, I_2, ..., I_n. Each of these time intervals has length L, measured in milliseconds. In order to fulfill the requirement 3.7.2. of RFC 4082, the time interval L has to be shorter than the time interval between the broadcast messages.
4. The server generates a random key K_n.
5. Using a one-way function F, the server generates a one-way chain of n+1 keys K_0, K_1, ..., K_{n} according to

   K_i = F(K_{i+1}).

6. Using another one-way function F', it generates a sequence of n+1 MAC keys K'_0, K'_1, ..., K'_{n-1} according to

   K'_i = F'(K_i).

7. Each MAC key K'_i is assigned to the time interval I_i.
8. The server determines the key disclosure delay d, which is the number of intervals between using a key and disclosing it. Note that although security is provided for all choices d>0, the choice still makes a difference:
   • If d is chosen too short, the client might discard packets because it fails to verify that the key used for its MAC has not yet been disclosed.
   • If d is chosen too long, the received packets have to be buffered for an unnecessarily long time before they can be verified by the client and be subsequently utilized for time synchronization.

   The server SHOULD calculate d according to

   d = ceil( 2*B / L) + 1,

   where ceil yields the smallest integer greater than or equal to its argument.

< - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
                      Generation of Keys

          F              F               F                 F
 K_0  <-------- K_1  <--------  ...  <-------- K_{n-1} <------- K_n
  |              |                              |                |
  |              |                              |                |
  | F'           | F'                           | F'             | F'
  |              |                              |                |
  v              v                              v                v
 K'_0           K'_1            ...           K'_{n-1}         K'_n
          [______________|____       ____|_________________|_______]
                I_1             ...            I_{n-1}          I_n

                  Course of Time/Usage of Keys
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ->

A schematic explanation of the TESLA protocol's one-way key chain

B.2. Client Preparation

A client needs the following information in order to participate in a TESLA broadcast:

• One key K_i from the one-way key chain, which has to be authenticated as belonging to the server. Typically, this will be K_0.
• The disclosure schedule of the keys. This consists of:
  • the length n of the one-way key chain,
  • the length L of the time intervals I_1, I_2, ..., I_n,
  • the starting time T_i of an interval I_i. Typically this is the starting time T_1 of the first interval;
  • the disclosure delay d.
• The one-way function F used to recursively derive the keys in the one-way key chain,
• The second one-way function F' used to derive the MAC keys K'_0, K'_1, ... , K'_n from the keys in the one-way chain.
• An upper bound D_t on how far its own clock is "behind" that of the server.

Note that if D_t is greater than (d - 1) * L, then some authentic packets might be discarded. If D_t is greater than d * L, then all authentic packets will be discarded. In the latter case, the client should not participate in the broadcast, since there will be no benefit in doing so.

B.3. Sending Authenticated Broadcast Packets

During each time interval I_i, the server sends one authenticated broadcast packet P_i. This packet consists of:

• a message M_i,
• the index i (in case a packet arrives late),
• a MAC authenticating the message M_i, with K'_i used as key,
• the key K_{i-d}, which is included for disclosure.

B.4. Authentication of Received Packets

When a client receives a packet P_i as described above, it first checks that it has not already received a packet with the same disclosed key. This is done to avoid replay/flooding attacks. A packet that fails this test is discarded.

Next, the client begins to check the packet's timeliness by ensuring that according to the disclosure schedule and with respect to the upper bound D_t determined above, the server cannot have disclosed the key K_i yet. Specifically, it needs to check that the server's clock cannot read a time that is in time interval I_{i+d} or later. Since it works under the assumption that the server's clock is not more than D_t "ahead" of the client's clock, the client can calculate an upper bound t_i for the server's clock at the time when P_i arrived. This upper bound t_i is calculated according to

t_i = R + D_t,

where R is the client's clock at the arrival of P_i. This implies that at the time of arrival of P_i, the server could have been in interval I_x at most, with[RFC4082]). If it is falsified, it is discarded.

x = floor((t_i - T_1) / L) + 1,

where floor gives the greatest integer less than or equal to its argument. The client now needs to verify that

x < i+d

is valid (see also Section 3.5 of

If the check above is successful, the client performs another more rigorous check: it sends a key check request to the server (in the form of a client_keycheck message), asking explicitly if K_i has already been disclosed. It remembers the time stamp t_check of the sending time of that request as well as the nonce it used correlated with the interval number i. If it receives an answer from the server stating that K_i has not yet been disclosed and it is able to verify the HMAC on that response, then it deduces that K_i was undisclosed at t_check and therefore also at R. In this case, the client accepts P_i as timely.

Next the client verifies that a newly disclosed key K_{i-d} belongs to the one-way key chain. To this end, it applies the one-way function F to K_{i-d} until it can verify the identity with an earlier disclosed key (see Clause 3.5 in RFC 4082, item 3).

Next the client verifies that the transmitted time value s_i belongs to the time interval I_i, by checking

T_i =< s_i, and

s_i < T_{i+1}.

If it is falsified, the packet MUST be discarded and the client MUST reinitialize its broadcast module by performing a unicast time synchronization as well as a new broadcast parameter exchange (because a falsification of this check yields that the packet was not generated according to protocol, which suggests an attack).

If a packet P_i passes all the tests listed above, it is stored for later authentication. Also, if at this time there is a package with index i-d already buffered, then the client uses the disclosed key K_{i-d} to derive K'_{i-d} and uses that to check the MAC included in package P_{i-d}. Upon success, it regards M_{i-d} as authenticated.

Appendix C. Random Number Generation

At various points of the protocol, the generation of random numbers is required. The employed methods of generation need to be cryptographically secure. See [RFC4086] for guidelines concerning this topic.

Authors' Addresses