



Internet Research Task Force (IRTF)                              F. Gont
Internet-Draft                                              SI6 Networks
Intended status: Informational                                   I. Arce
Expires: 14 June 2023                                          Quarkslab
                                                        11 December 2022


           On the Generation of Transient Numeric Identifiers
               draft-irtf-pearg-numeric-ids-generation-12

Abstract

   This document performs an analysis of the security and privacy
   implications of different types of "transient numeric identifiers"
   used in IETF protocols, and tries to categorize them based on their
   interoperability requirements and their associated failure severity
   when such requirements are not met.  Subsequently, it provides advice
   on possible algorithms that could be employed to satisfy the
   interoperability requirements of each identifier category, while
   minimizing the negative security and privacy implications, thus
   providing guidance to protocol designers and protocol implementers.
   Finally, it describes a number of algorithms that have been employed
   in real implementations to generate transient numeric identifiers,
   and analyzes their security and privacy properties.  This document is
   a product of the Privacy Enhancement and Assessment Research Group
   (PEARG) in the IRTF.

Status of This Memo

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   This Internet-Draft will expire on 14 June 2023.

Copyright Notice

   Copyright (c) 2022 IETF Trust and the persons identified as the
   document authors.  All rights reserved.



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   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents (https://trustee.ietf.org/
   license-info) in effect on the date of publication of this document.
   Please review these documents carefully, as they describe your rights
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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
   2.  Terminology . . . . . . . . . . . . . . . . . . . . . . . . .   4
   3.  Threat Model  . . . . . . . . . . . . . . . . . . . . . . . .   5
   4.  Issues with the Specification of Transient Numeric
           Identifiers . . . . . . . . . . . . . . . . . . . . . . .   6
   5.  Protocol Failure Severity . . . . . . . . . . . . . . . . . .   7
   6.  Categorizing Transient Numeric Identifiers  . . . . . . . . .   7
   7.  Common Algorithms for Transient Numeric Identifier
           Generation  . . . . . . . . . . . . . . . . . . . . . . .  10
     7.1.  Category #1: Uniqueness (soft failure)  . . . . . . . . .  10
     7.2.  Category #2: Uniqueness (hard failure)  . . . . . . . . .  14
     7.3.  Category #3: Uniqueness, stable within context (soft
           failure)  . . . . . . . . . . . . . . . . . . . . . . . .  15
     7.4.  Category #4: Uniqueness, monotonically increasing within
           context (hard failure)  . . . . . . . . . . . . . . . . .  17
   8.  Common Vulnerabilities Associated with Transient Numeric
           Identifiers . . . . . . . . . . . . . . . . . . . . . . .  23
     8.1.  Network Activity Correlation  . . . . . . . . . . . . . .  23
     8.2.  Information Leakage . . . . . . . . . . . . . . . . . . .  24
     8.3.  Fingerprinting  . . . . . . . . . . . . . . . . . . . . .  25
     8.4.  Exploitation of the Semantics of Transient Numeric
           Identifiers . . . . . . . . . . . . . . . . . . . . . . .  26
     8.5.  Exploitation of Collisions of Transient Numeric
           Identifiers . . . . . . . . . . . . . . . . . . . . . . .  27
     8.6.  Exploitation of Predictable Transient Numeric Identifiers
           for Injection Attacks . . . . . . . . . . . . . . . . . .  27
     8.7.  Cryptanalysis . . . . . . . . . . . . . . . . . . . . . .  28
   9.  Vulnerability Assessment of Transient Numeric Identifiers . .  28
     9.1.  Category #1: Uniqueness (soft failure)  . . . . . . . . .  28
     9.2.  Category #2: Uniqueness (hard failure)  . . . . . . . . .  29
     9.3.  Category #3: Uniqueness, stable within context (soft
           failure)  . . . . . . . . . . . . . . . . . . . . . . . .  29
     9.4.  Category #4: Uniqueness, monotonically increasing within
           context (hard failure)  . . . . . . . . . . . . . . . . .  30
   10. IANA Considerations . . . . . . . . . . . . . . . . . . . . .  32
   11. Security Considerations . . . . . . . . . . . . . . . . . . .  32
   12. Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  33
   13. References  . . . . . . . . . . . . . . . . . . . . . . . . .  33
     13.1.  Normative References . . . . . . . . . . . . . . . . . .  33
     13.2.  Informative References . . . . . . . . . . . . . . . . .  35



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   Appendix A.  Algorithms and Techniques with Known Issues  . . . .  41
     A.1.  Predictable Linear Identifiers Algorithm  . . . . . . . .  41
     A.2.  Random-Increments Algorithm . . . . . . . . . . . . . . .  43
     A.3.  Re-using Identifiers Across Different Contexts  . . . . .  44
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  44

1.  Introduction

   Networking protocols employ a variety of transient numeric
   identifiers for different protocol objects, such as IPv4 and IPv6
   Fragment Identifiers [RFC0791] [RFC8200], IPv6 Interface Identifiers
   (IIDs) [RFC4291], transport protocol ephemeral port numbers
   [RFC6056], TCP Initial Sequence Numbers (ISNs) [RFC0793], and DNS
   Query IDs [RFC1035].These identifiers usually have specific
   interoperability requirements (e.g. uniqueness during a specified
   period of time) that must be satisfied such that they do not result
   in negative interoperability implications, and an associated failure
   severity when such requirements are not met, ranging from soft to
   hard failures.

   For more than 30 years, a large number of implementations of IETF
   protocols have been subject to a variety of attacks, with effects
   ranging from Denial of Service (DoS) or data injection, to
   information leakages that could be exploited for pervasive monitoring
   [RFC7258].  The root cause of these issues has been, in many cases,
   the poor selection of transient numeric identifiers in such
   protocols, usually as a result of insufficient or misleading
   specifications.  While it is generally trivial to identify an
   algorithm that can satisfy the interoperability requirements of a
   given transient numeric identifier, empirical evidence exists that
   doing so without negatively affecting the security and/or privacy
   properties of the aforementioned protocols is prone to error
   [I-D.irtf-pearg-numeric-ids-history].

   For example, implementations have been subject to security and/or
   privacy issues resulting from:

   *  Predictable IPv4 or IPv6 Fragment Identifiers (see e.g.
      [Sanfilippo1998a], [RFC6274], and [RFC7739])

   *  Predictable IPv6 IIDs (see e.g.  [RFC7721], [RFC7707], and
      [RFC7217])

   *  Predictable transport protocol ephemeral port numbers (see e.g.
      [RFC6056] and [Silbersack2005])

   *  Predictable TCP Initial Sequence Numbers (ISNs) (see e.g.
      [Morris1985], [Bellovin1989], and [RFC6528])



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   *  Predictable initial timestamps in TCP timestamps Options (see e.g.
      [TCPT-uptime] and [RFC7323])

   *  Predictable DNS Query IDs (see e.g.  [Schuba1993] and [Klein2007])

   Recent history indicates that when new protocols are standardized or
   new protocol implementations are produced, the security and privacy
   properties of the associated transient numeric identifiers tend to be
   overlooked, and inappropriate algorithms to generate transient
   numeric identifiers are either suggested in the specifications or
   selected by implementers.  As a result, it should be evident that
   advice in this area is warranted.

   We note that the use of cryptographic techniques may readily mitigate
   some of the issues arising from predictable transient numeric
   identifiers.  For example, cryptographic integrity and authentication
   can readily mitigate data injection attacks even in the presence of
   predictable transient numeric identifiers (such as "sequence
   numbers").  However, use of flawed algorithms (such as global
   counters) for generating transient numeric identifiers could still
   result in information leakages even when cryptographic techniques are
   employed.

   This document contains a non-exhaustive survey of transient numeric
   identifiers employed in various IETF protocols, and aims to
   categorize such identifiers based on their interoperability
   requirements, and the associated failure severity when such
   requirements are not met.  Subsequently, it provides advice on
   possible algorithms that could be employed to satisfy the
   interoperability requirements of each category, while minimizing
   negative security and privacy implications.  Finally, it analyzes
   several algorithms that have been employed in real implementations to
   meet such requirements, and analyzes their security and privacy
   properties.

   This document represents the consensus of the Privacy Enhancement and
   Assessment Research Group (PEARG).

2.  Terminology

   Transient Numeric Identifier:
      A data object in a protocol specification that can be used to
      definitely distinguish a protocol object (a datagram, network
      interface, transport protocol endpoint, session, etc.) from all
      other objects of the same type, in a given context.  Transient
      numeric identifiers are usually defined as a series of bits, and
      represented using integer values.  These identifiers are typically
      dynamically selected, as opposed to statically-assigned numeric



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      identifiers (see e.g.  [IANA-PROT]).  We note that different
      transient numeric identifiers may have additional requirements or
      properties depending on their specific use in a protocol.  We use
      the term "transient numeric identifier" (or simply "numeric
      identifier" or "identifier" as short forms) as a generic term to
      refer to any data object in a protocol specification that
      satisfies the identification property stated above.

   Failure Severity:
      The interoperability consequences of a failure to comply with the
      interoperability requirements of a given identifier.  Severity
      considers the worst potential consequence of a failure, determined
      by the system damage and/or time lost to repair the failure.  In
      this document we define two types of failure severity: "soft
      failure" and "hard failure".

   Soft Failure:
      A soft failure is a recoverable condition in which a protocol does
      not operate in the prescribed manner but normal operation can be
      resumed automatically in a short period of time.  For example, a
      simple packet-loss event that is subsequently recovered with a
      packet-retransmission can be considered a soft failure.

   Hard Failure:
      A hard failure is a non-recoverable condition in which a protocol
      does not operate in the prescribed manner or it operates with
      excessive degradation of service.  For example, an established TCP
      connection that is aborted due to an error condition constitutes,
      from the point of view of the transport protocol, a hard failure,
      since it enters a state from which normal operation cannot be
      resumed.

3.  Threat Model

   Throughout this document, we do not consider on-path attacks.  That
   is, we assume an attacker does not have physical or logical access to
   the system(s) being attacked, and that the attacker can only observe
   traffic explicitly directed to the attacker.  Similarly, an attacker
   cannot observe traffic transferred between a sender and the
   receiver(s) of a target protocol, but may be able to interact with
   any of these entities, including by e.g. sending traffic to them to
   sample transient numeric identifiers employed by the target systems
   when communicating with the attacker.

   For example, when analyzing vulnerabilities associated with TCP
   Initial Sequence Numbers (ISNs), we consider the attacker is unable
   to capture network traffic corresponding to a TCP connection between
   two other hosts.  However, we consider the attacker is able to



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   communicate with any of these hosts (e.g., establish a TCP connection
   with any of them), to e.g. sample the TCP ISNs employed by these
   systems when communicating with the attacker.

   Similarly, when considering host-tracking attacks based on IPv6
   interface identifiers, we consider an attacker may learn the IPv6
   address employed by a victim node if e.g. the address becomes exposed
   as a result of the victim node communicating with an attacker-
   operated server.  Subsequently, an attacker may perform host-tracking
   by probing a set of target addresses composed by a set of target
   prefixes and the IPv6 interface identifier originally learned by the
   attacker.  Alternatively, an attacker may perform host tracking if
   e.g. the victim node communicates with an attacker-operated server as
   it moves from one location to another, those exposing its configured
   addresses.  We note that none of these scenarios requires the
   attacker observe traffic not explicitly directed to the attacker.

4.  Issues with the Specification of Transient Numeric Identifiers

   While assessing protocol specifications regarding the use of
   transient numeric identifiers, we have found that most of the issues
   discussed in this document arise as a result of one of the following
   conditions:

   *  Protocol specifications that under-specify the requirements for
      their transient numeric identifiers

   *  Protocol specifications that over-specify their transient numeric
      identifiers

   *  Protocol implementations that simply fail to comply with the
      specified requirements

   A number of protocol specifications (too many of them) have simply
   overlooked the security and privacy implications of transient numeric
   identifiers [I-D.irtf-pearg-numeric-ids-history].  Examples of them
   are the specification of TCP ephemeral ports in [RFC0793], the
   specification of TCP sequence numbers in [RFC0793], or the
   specification of the DNS Query ID in [RFC1035].

   On the other hand, there are a number of protocol specifications that
   over-specify some of their associated transient numeric identifiers.
   For example, [RFC4291] essentially overloads the semantics of IPv6
   Interface Identifiers (IIDs) by embedding link-layer addresses in the
   IPv6 IIDs, when the interoperability requirement of uniqueness could
   be achieved in other ways that do not result in negative security and
   privacy implications [RFC7721].  Similarly, [RFC2460] suggested the
   use of a global counter for the generation of Fragment Identification



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   values, when the interoperability properties of uniqueness per {IPv6
   Source Address, IPv6 Destination Address} could be achieved with
   other algorithms that do not result in negative security and privacy
   implications [RFC7739].

   Finally, there are protocol implementations that simply fail to
   comply with existing protocol specifications.  For example, some
   popular operating systems (notably Microsoft Windows) still fail to
   implement transport protocol ephemeral port randomization, as
   recommended in [RFC6056].

5.  Protocol Failure Severity

   Section 2 defines the concept of "Failure Severity", along with two
   types of failure severities that we employ throughout this document:
   soft and hard.

   Our analysis of the severity of a failure is performed from the point
   of view of the protocol in question.  However, the corresponding
   severity on the upper protocol (or application) might not be the same
   as that of the protocol in question.  For example, a TCP connection
   that is aborted might or might not result in a hard failure of the
   upper application: if the upper application can establish a new TCP
   connection without any impact on the application, a hard failure at
   the TCP protocol may have no severity at the application level.  On
   the other hand, if a hard failure of a TCP connection results in
   excessive degradation of service at the application layer, it will
   also result in a hard failure at the application.

6.  Categorizing Transient Numeric Identifiers

   This section includes a non-exhaustive survey of transient numeric
   identifiers, which are representative of all the possible
   combinations of interoperability requirements and failure severities
   found in popular protocols from different layers.  Additionally, it
   proposes a number of categories that can accommodate these
   identifiers based on their interoperability requirements and their
   associated failure severity (soft or hard).

   NOTE:
      All other transient numeric identifiers that were analyzed as part
      of this effort could be accommodated into one of the existing
      categories from Table 1.








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    +==============+===============================+==================+
    |  Identifier  | Interoperability Requirements | Failure Severity |
    +==============+===============================+==================+
    | IPv6 Frag ID |   Uniqueness (for IP address  |  Soft/Hard (1)   |
    |              |             pair)             |                  |
    +--------------+-------------------------------+------------------+
    |   IPv6 IID   | Uniqueness (and stable within |     Soft (3)     |
    |              |        IPv6 prefix) (2)       |                  |
    +--------------+-------------------------------+------------------+
    |   TCP ISN    |  Monotonically-increasing (4) |     Hard (4)     |
    +--------------+-------------------------------+------------------+
    | TCP initial  |  Monotonically-increasing (5) |     Hard (5)     |
    |  timestamp   |                               |                  |
    +--------------+-------------------------------+------------------+
    |   TCP eph.   |   Uniqueness (for connection  |       Hard       |
    |     port     |              ID)              |                  |
    +--------------+-------------------------------+------------------+
    |  IPv6 Flow   |           Uniqueness          |     None (6)     |
    |    Label     |                               |                  |
    +--------------+-------------------------------+------------------+
    | DNS Query ID |           Uniqueness          |     None (7)     |
    +--------------+-------------------------------+------------------+

              Table 1: Survey of Transient Numeric Identifiers

   NOTE:

   (1)
      While a single collision of Fragment ID values would simply lead
      to a single packet drop (and hence a "soft" failure), repeated
      collisions at high data rates might result in self-propagating
      collisions of Fragment IDs, thus possibly leading to a hard
      failure [RFC4963].

   (2)
      While the interoperability requirements are simply that the
      Interface ID results in a unique IPv6 address, for operational
      reasons it is typically desirable that the resulting IPv6 address
      (and hence the corresponding Interface ID) be stable within each
      network [RFC7217] [RFC8064].

   (3)
      While IPv6 Interface IDs must result in unique IPv6 addresses,
      IPv6 Duplicate Address Detection (DAD) [RFC4862] allows for the
      detection of duplicate addresses, and hence such Interface ID
      collisions can be recovered.





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   (4)
      In theory, there are no interoperability requirements for TCP
      Initial Sequence Numbers (ISNs), since the TIME-WAIT state and
      TCP's "quiet time" concept take care of old segments from previous
      incarnations of a connection.  However, a widespread optimization
      allows for a new incarnation of a previous connection to be
      created if the ISN of the incoming SYN is larger than the last
      sequence number seen in that direction for the previous
      incarnation of the connection.  Thus, monotonically-increasing TCP
      ISNs allow for such optimization to work as expected [RFC6528],
      and can help avoid connection-establishment failures.

   (5)
      Strictly speaking, there are no interoperability requirements for
      the *initial* TCP timestamp employed by a TCP instance (i.e., the
      TS Value (TSval) in a segment with the SYN bit set).  However,
      some TCP implementations allow a new incarnation of a previous
      connection to be created if the TSval of the incoming SYN is
      larger than the last TSval seen in that direction for the previous
      incarnation of the connection (please see [RFC6191]).  Thus,
      monotonically-increasing TCP initial timestamps (across
      connections to the same endpoint) allow for such optimization to
      work as expected [RFC6191], and can help avoid connection-
      establishment failures.

   (6)
      The IPv6 Flow Label [RFC6437], along with the Source and
      Destination IPv6 addresses, is typically employed for load sharing
      [RFC7098].  Reuse of a Flow Label value for the same set {Source
      Address, Destination Address} would typically cause both flows to
      be multiplexed onto the same link.  However, as long as this does
      not occur deterministically, it will not result in any negative
      implications.

   (7)
      DNS Query IDs are employed, together with the Source Address,
      Destination Address, Source Port, and Destination Port, to match
      DNS requests and responses.  However, since an implementation
      knows which DNS requests were sent for that set of {Source
      Address, Destination Address, Source Port, and Destination Port,
      Query ID}, a collision of Query IDs would result, if anything, in
      a small performance penalty (the response would nevertheless be
      discarded when it is found that it does not answer the query sent
      in the corresponding DNS query).

   Based on the survey above, we can categorize identifiers as follows:





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   +=======+======================================+===================+
   | Cat # |               Category               |  Sample Proto IDs |
   +=======+======================================+===================+
   |   1   |      Uniqueness (soft failure)       | IPv6 Flow L., DNS |
   |       |                                      |      Query ID     |
   +-------+--------------------------------------+-------------------+
   |   2   |      Uniqueness (hard failure)       | IPv6 Frag ID, TCP |
   |       |                                      |   ephemeral port  |
   +-------+--------------------------------------+-------------------+
   |   3   |  Uniqueness, stable within context   |      IPv6 IID     |
   |       |            (soft failure)            |                   |
   +-------+--------------------------------------+-------------------+
   |   4   | Uniqueness, monotonically increasing |    TCP ISN, TCP   |
   |       |    within context (hard failure)     | initial timestamp |
   +-------+--------------------------------------+-------------------+

                      Table 2: Identifier Categories

   We note that Category #4 could be considered a generalized case of
   category #3, in which a monotonically increasing element is added to
   a stable (within context) element, such that the resulting
   identifiers are monotonically increasing within a specified context.
   That is, the same algorithm could be employed for both #3 and #4,
   given appropriate parameters.

7.  Common Algorithms for Transient Numeric Identifier Generation

   The following subsections describe some sample algorithms that can be
   employed for generating transient numeric identifiers for each of the
   categories above, while mitigating the vulnerabilities analyzed in
   Section 8 of this document.

   All of the variables employed in the algorithms of the following
   subsections are of "unsigned integer" type, except for the "retry"
   variable, that is of (signed) "integer" type.

7.1.  Category #1: Uniqueness (soft failure)

   The requirement of uniqueness with a soft failure severity can be
   complied with a Pseudo-Random Number Generator (PRNG).

   NOTE:
      Please see [RFC4086] regarding randomness requirements for
      security.







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   While most systems provide access to a PRNG, many of such PRNG
   implementations are not cryptographically secure, and therefore might
   be statistically biased or subject to adversarial influence.  For
   example, ISO C [C11] rand(3) implementations are not
   cryptographically secure.

   NOTE:
      Section 7.1 ("Uniform Deviates") of [Press1992] discusses the
      underlying issues affecting ISO C [C11] rand(3) implementations.

   On the other hand, a number of systems provide an interface to a
   Cryptographically Secure PRNG (CSPRNG) [RFC8937] [RFC4086], which
   guarantees high entropy, unpredictability, and good statistical
   distribution of the random values generated.  For example, GNU/
   Linux's CSPRNG implementation is available via the getentropy(3)
   interface [GETENTROPY], while OpenBSD's CSPRNG implementation is
   available via the arc4random(3) and arc4random_uniform(3) interfaces
   [ARC4RANDOM].  Where available, these CSPRNGs should be preferred
   over e.g.  POSIX [POSIX] random(3) or ISO C [C11] rand(3)
   implementations.

   In scenarios where a CSPRNG is not readily available to select
   transient numeric identifiers of Category #1, a security and privacy
   assessment of employing a regular PRNG should be performed,
   supporting the implementation decision.

   NOTE:
      [Aumasson2018], [Press1992], and [Knuth1983], discuss theoretical
      and practical aspects of pseudorandom numbers generation, and
      provide guidance on how to evaluate PRNGs.

   We note that since the premise is that collisions of transient
   numeric identifiers of this category only leads to soft failures, in
   many cases, the algorithm might not need to check the suitability of
   a selected identifier (i.e., the suitable_id() function, described
   below, could always return "true").

   In scenarios where e.g. simultaneous use of a given numeric ID is
   undesirable and the implementation detects such condition, an
   implementation may opt to select the next available identifier in the
   same sequence, or select another random number.  Section 7.1.1 is an
   implementation of the former strategy, while Section 7.1.2 is an
   implementation of the later.  Typically, the algorithm in
   Section 7.1.2 results in a more uniform distribution of the generated
   transient numeric identifiers.  However, for transient numeric
   identifiers where an implementation typically keeps local state about
   unsuitable/used identifiers, the algorithm in Section 7.1.2 may
   require many more iterations than the algorithm in Section 7.1.1 to



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   generate a suitable transient numeric identifier.  This will usually
   be affected by the current usage ratio of transient numeric
   identifiers (i.e., number of numeric identifiers considered suitable
   / total number of numeric identifiers) and other parameters.
   Therefore, in such cases many implementations tend to prefer the
   algorithm in Section 7.1.1 over the algorithm in Section 7.1.2.

7.1.1.  Simple Randomization Algorithm

       /* Transient Numeric ID selection function */

       id_range = max_id - min_id + 1;
       next_id = min_id + (random() % id_range);
       retry = id_range;

       do {
           if (suitable_id(next_id)) {
               return next_id;
           }

           if (next_id == max_id) {
               next_id = min_id;
           } else {
               next_id++;
           }

           retry--;

       } while (retry > 0);

       return ERROR;

   NOTE:
      random() is a PRNG that returns a pseudo-random unsigned integer
      number of appropriate size.  Beware that "adapting" the length of
      the output of random() with a modulo operator (e.g., C-language's
      "%") may change the distribution of the PRNG.  To preserve a
      uniform distribution, the rejection sampling technique
      [Romailler2020] can be used.












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      The function suitable_id() can check, when possible and desirable,
      whether a selected transient numeric identifier is suitable (e.g.
      it is not already in use).  Depending on how/where the numeric
      identifier is used, it may or may not be possible (or even
      desirable) to check whether the numeric identifier is in use (or
      whether it has been recently employed).  When an identifier is
      found to be unsuitable, this algorithm selects the next available
      numeric identifier in sequence.

  
      Even when this algorithm selects numeric IDs randomly, it is
      biased towards the first available numeric ID after a sequence of
      unavailable numeric IDs.  For example, if this algorithm is
      employed for transport protocol ephemeral port randomization
      [RFC6056] and the local list of unsuitable port numbers (e.g.,
      registered port numbers that should not be used for ephemeral
      ports) is significant, an attacker may actually have a
      significantly better chance of guessing a port number.

  
      All the variables (in this and all the algorithms discussed in
      this document) are unsigned integers.

   Assuming the randomness requirements for the PRNG are met (see
   [RFC4086]), this algorithm does not suffer from any of the issues
   discussed in Section 8.

7.1.2.  Another Simple Randomization Algorithm

   The following pseudo-code illustrates another algorithm for selecting
   a random transient numeric identifier which, in the event a selected
   identifier is found to be unsuitable (e.g., already in use), another
   identifier is randomly selected:


















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       /* Transient Numeric ID selection function */

       id_range = max_id - min_id + 1;
       retry = id_range;

       do {
           next_id = min_id + (random() % id_range);

           if (suitable_id(next_id)) {
               return next_id;
           }

           retry--;

       } while (retry > 0);

       return ERROR;


   This algorithm might be unable to select a transient numeric
   identifier (i.e., return "ERROR") even if there are suitable
   identifiers available, in cases where a large number of identifiers
   are found to be unsuitable (e.g. "in use").

   The same considerations from Section 7.1.1 with respect to the
   properties of random() and the adaptation of its output length apply
   to this algorithm.

   Assuming the randomness requirements for the PRNG are met (see
   [RFC4086]), this algorithm does not suffer from any of the issues
   discussed in Section 8.

7.2.  Category #2: Uniqueness (hard failure)

   One of the most trivial approaches for generating unique transient
   numeric identifier (with a hard failure severity) is to reduce the
   identifier reuse frequency by generating the numeric identifiers with
   a monotonically-increasing function (e.g. linear).  As a result, any
   of the algorithms described in Section 7.4 ("Category #4: Uniqueness,
   monotonically increasing within context (hard failure)") can be
   readily employed for complying with the requirements of this
   transient numeric identifier category.

   In cases where suitability (e.g. uniqueness) of the selected
   identifiers can be definitely assessed by the local system, any of
   the algorithms described in Section 7.1 ("Category #1: Uniqueness
   (soft failure)") can be readily employed for complying with the
   requirements of this numeric identifier category.



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   NOTE:
      In the case of e.g.  TCP ephemeral ports or TCP ISNs, a transient
      numeric identifier that might seem suitable from the perspective
      of the local system, might actually be unsuitable from the
      perspective of the remote system (e.g., because there is state
      associated with the selected identifier at the remote system).
      Therefore, in such cases it is not possible to employ the
      algorithms from Section 7.1 ("Category #1: Uniqueness (soft
      failure)").

7.3.  Category #3: Uniqueness, stable within context (soft failure)

   The goal of the following algorithm is to produce identifiers that
   are stable for a given context (identified by "CONTEXT"), but that
   change when the aforementioned context changes.

   In order to avoid storing in memory the transient numeric identifiers
   computed for each CONTEXT, the following algorithm employs a
   calculated technique (as opposed to keeping state in memory) to
   generate a stable transient numeric identifier for each given
   context.

       /* Transient Numeric ID selection function  */

       id_range = max_id - min_id + 1;

       retry = 0;

       do {
           offset = F(CONTEXT, retry, secret_key);
           next_id = min_id + (offset % id_range);

           if (suitable_id(next_id)) {
               return next_id;
           }

           retry++;

       } while (retry <= MAX_RETRIES);

       return ERROR;


   In this algorithm, the function F() provides a stateless and stable
   per-CONTEXT offset, where CONTEXT is the concatenation of all the
   elements that define the given context.

      For example, if this algorithm is expected to produce IPv6 IIDs



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      that are unique per network interface and SLAAC autoconfiguration
      prefix, the CONTEXT should be the concatenation of e.g. the
      network interface index and the SLAAC autoconfiguration prefix
      (please see [RFC7217] for an implementation of this algorithm for
      generation of stable IPv6 IIDs).

   F() is a pseudorandom function (PRF).  It must not be computable from
   the outside (without knowledge of the secret key).  F() must also be
   difficult to reverse, such that it resists attempts to obtain the
   secret_key, even when given samples of the output of F() and
   knowledge or control of the other input parameters.  F() should
   produce an output of at least as many bits as required for the
   transient numeric identifier.  SipHash-2-4 (128-bit key, 64-bit
   output) [SipHash] and BLAKE3 (256-bit key, arbitrary-length output)
   [BLAKE3] are two possible options for F().  Alternatively, F() could
   be implemented with a keyed-hash message authentication code (HMAC)
   [RFC2104].  HMAC-SHA-256 [FIPS-SHS] would be one possible option for
   such implementation alternative.  Note: Use of HMAC-MD5 [RFC1321] or
   HMAC-SHA1 [FIPS-SHS] are not recommended for F() [RFC6151] [RFC6194].

   The result of F() is no more secure than the secret key, and
   therefore 'secret_key' must be unknown to the attacker, and must be
   of a reasonable length. 'secret_key' must remain stable for a given
   CONTEXT, since otherwise the numeric identifiers generated by this
   algorithm would not have the desired stability properties (i.e.,
   stable for a given CONTEXT).  In most cases, 'secret_key' should be
   selected with a PRNG (see [RFC4086] for recommendations on choosing
   secrets) at an appropriate time, and stored in stable or volatile
   storage (as necessary) for future use.

   The result of F() is stored in the variable 'offset', which may take
   any value within the storage type range, since we are restricting the
   resulting identifier to be in the range [min_id, max_id] in a similar
   way as in the algorithm described in Section 7.1.1.

   suitable_id() checks whether the candidate identifier has suitable
   uniqueness properties.  Collisions (i.e., an identifier that is not
   unique) are recovered by incrementing the 'retry' variable and
   recomputing F(), up to a maximum of MAX_RETRIES times.  However,
   recovering from collisions will usually result in identifiers that
   fail to remain constant for the specified context.  This is normally
   acceptable when the probability of collisions is small, as in the
   case of e.g.  IPv6 IIDs resulting from SLAAC [RFC7217] [RFC8981].

   For obvious reasons, the transient numeric identifiers generated with
   this algorithm allow for network activity correlation and
   fingerprinting within "CONTEXT".  However, this is essentially a
   design goal of this category of transient numeric identifiers.



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7.4.  Category #4: Uniqueness, monotonically increasing within context
      (hard failure)

7.4.1.  Per-context Counter Algorithm

   One possible way of selecting unique monotonically-increasing
   identifiers (per context) is to employ a per-context counter.  Such
   an algorithm could be described as follows:

       /* Transient Numeric ID selection function */

       id_range = max_id - min_id + 1;
       retry = id_range;
       id_inc = increment() % id_range;

       if( (next_id = lookup_counter(CONTEXT)) == ERROR){
            next_id = min_id + random() % id_range;
       }

       do {
           if ( (max_id - next_id) >= id_inc){
               next_id = next_id + id_inc;
           }
           else {
               next_id = min_id + id_inc - (max_id - next_id);
           }

           if (suitable_id(next_id)){
               store_counter(CONTEXT, next_id);
               return next_id;
           }

           retry = retry - id_inc;

       } while (retry > 0);

       return ERROR;

   NOTES:
      increment() returns a small integer that is employed to increment
      the current counter value to obtain the next transient numeric
      identifier.  This value must be much smaller than the number of
      possible values for the numeric IDs (i.e., "id_range").  Most
      implementations of this algorithm employ a constant increment of
      1.  Using a value other than 1 can help mitigate some information
      leakages (please see below), at the expense of a possible increase
      in the numeric ID reuse frequency.




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      The code above makes sure that the increment employed in the
      algorithm (id_inc) is always smaller than the number of possible
      values for the numeric IDs (i.e., "max_id - min_d + 1").  However,
      as noted above, this value must also be much smaller than the
      number of possible values for the numeric IDs.

  
      lookup_counter() is a function that returns the current counter
      for a given context, or an error condition if that counter does
      not exist.

  
      store_counter() is a function that saves a counter value for a
      given context.

  
      suitable_id() is a function that checks whether the resulting
      identifier is acceptable (e.g., whether it is not already in use,
      etc.).

   Essentially, whenever a new identifier is to be selected, the
   algorithm checks whether a counter for the corresponding context
   exists.  If does, the value of such counter is incremented to obtain
   the new transient numeric identifier, and the counter is updated.  If
   no counter exists for such context, a new counter is created and
   initialized to a random value, and used as the selected transient
   numeric identifier.  This algorithm produces a per-context counter,
   which results in one monotonically-increasing function for each
   context.  Since each counter is initialized to a random value, the
   resulting values are unpredictable by an off-path attacker.

   The choice of id_inc has implications on both the security and
   privacy properties of the resulting identifiers, but also on the
   corresponding interoperability properties.  On one hand, minimizing
   the increments generally minimizes the identifier reuse frequency,
   albeit at increased predictability.  On the other hand, if the
   increments are randomized, predictability of the resulting
   identifiers is reduced, and the information leakage produced by
   global constant increments is mitigated.  However, using larger
   increments than necessary can result in higher numeric ID reuse
   frequency.

   This algorithm has the following drawbacks:

   *  It requires an implementation to store each per-CONTEXT counter in
      memory.  If, as a result of resource management, the counter for a
      given context must be removed, the last transient numeric
      identifier value used for that context will be lost.  Thus, if



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      subsequently an identifier needs to be generated for the same
      context, the corresponding counter will need to be recreated and
      reinitialized to a random value, thus possibly leading to reuse/
      collision of numeric identifiers.

   *  Keeping one counter for each possible "context" may in some cases
      be considered too onerous in terms of memory requirements.

   Otherwise, the identifiers produced by this algorithm do not suffer
   from the other issues discussed in Section 8.

7.4.2.  Simple PRF-Based Algorithm

   The goal of this algorithm is to produce monotonically-increasing
   transient numeric identifiers (for each given context), with a
   randomized initial value.  For example, if the identifiers being
   generated must be monotonically-increasing for each {IP Source
   Address, IP Destination Address} set, then each possible combination
   of {IP Source Address, IP Destination Address} should have a separate
   monotonically-increasing sequence, that starts at a different random
   value.

   Instead of maintaining a per-context counter (as in the algorithm
   from Section 7.4.1), the following algorithm employs a calculated
   technique to maintain a random offset for each possible context.


























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       /* Initialization code */
       counter = 0;

       /* Transient Numeric ID selection function  */

       id_range = max_id - min_id + 1;
       id_inc = increment() % id_range;
       offset = F(CONTEXT, secret_key);
       retry = id_range;

       do {
           next_id = min_id + (offset + counter) % id_range;
           counter = counter + id_inc;

           if (suitable_id(next_id)) {
               return next_id;
           }

           retry = retry - id_inc;

       } while (retry > 0);

       return ERROR;


   In the algorithm above, the function F() provides a (stateless)
   unpredictable offset for each given context (as identified by
   'CONTEXT').

   F() is a PRF, with the same properties as those specified for F() in
   Section 7.3.

   CONTEXT is the concatenation of all the elements that define a given
   context.  For example, if this algorithm is expected to produce
   identifiers that are monotonically-increasing for each set (Source IP
   Address, Destination IP Address), CONTEXT should be the concatenation
   of these two IP addresses.

   The function F() provides a "per-CONTEXT" fixed offset within the
   numeric identifier "space".  Both the 'offset' and 'counter'
   variables may take any value within the storage type range since we
   are restricting the resulting identifier to be in the range [min_id,
   max_id] in a similar way as in the algorithm described in
   Section 7.1.1.  This allows us to simply increment the 'counter'
   variable and rely on the unsigned integer to wrap around.






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   The result of F() is no more secure than the secret key, and
   therefore 'secret_key' must be unknown to the attacker, and must be
   of a reasonable length. 'secret_key' must remain stable for a given
   CONTEXT, since otherwise the numeric identifiers generated by this
   algorithm would not have the desired stability properties (i.e.,
   monotonically-increasing for a given CONTEXT).  In most cases,
   'secret_key' should be selected with a PRNG (see [RFC4086] for
   recommendations on choosing secrets) at an appropriate time, and
   stored in stable or volatile storage (as necessary) for future use.

   It should be noted that, since this algorithm uses a global counter
   ("counter") for selecting identifiers (i.e., all counters share the
   same increments space), this algorithm results in an information
   leakage (as described in Section 8.2).  For example, if this
   algorithm were used for selecting TCP ephemeral ports, and an
   attacker could force a client to periodically establish a new TCP
   connection to an attacker-controlled system (or through an attacker-
   observable routing path), the attacker could subtract consecutive
   source port values to obtain the number of outgoing TCP connections
   established globally by the victim host within that time period (up
   to wrap-around issues and five-tuple collisions, of course).  This
   information leakage could be partially mitigated by employing small
   random values for the increments (i.e., increment() function),
   instead of having increment() return the constant "1".

   We nevertheless note that an improved mitigation of this information
   leakage could be more successfully achieved by employing the
   algorithm from Section 7.4.3, instead.

7.4.3.  Double-PRF Algorithm

   A trade-off between maintaining a single global 'counter' variable
   and maintaining 2**N 'counter' variables (where N is the width of the
   result of F()), could be achieved as follows.  The system would keep
   an array of TABLE_LENGTH values, which would provide a separation of
   the increment space into multiple buckets.  This improvement could be
   incorporated into the algorithm from Section 7.4.2 as follows:














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       /* Initialization code */

       for(i = 0; i < TABLE_LENGTH; i++) {
           table[i] = random();
       }

       /* Transient Numeric ID selection function */

       id_range = max_id - min_id + 1;
       id_inc = increment() % id_range;
       offset = F(CONTEXT, secret_key1);
       index = G(CONTEXT, secret_key2) % TABLE_LENGTH;
       retry = id_range;

       do {
           next_id = min_id + (offset + table[index]) % id_range;
           table[index] = table[index] + id_inc;

           if (suitable_id(next_id)) {
               return next_id;
           }

          retry = retry - id_inc;

       } while (retry > 0);

       return ERROR;


   'table[]' could be initialized with random values, as indicated by
   the initialization code in the pseudo-code above.

   Both F() and G() are PRFs, with the same properties as those required
   for F() in Section 7.3.

   The results of F() and G() are no more secure than their respective
   secret keys ('secret_key1' and 'secret_key2', respectively), and
   therefore both secret keys must be unknown to the attacker, and must
   be of a reasonable length.  Both secret keys must remain stable for
   the given CONTEXT, since otherwise the transient numeric identifiers
   generated by this algorithm would not have the desired stability
   properties (i.e., monotonically-increasing for a given CONTEXT).  In
   most cases, both secret keys should be selected with a PRNG (see
   [RFC4086] for recommendations on choosing secrets) at an appropriate
   time, and stored in stable or volatile storage (as necessary) for
   future use.





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   The 'table[]' array assures that successive transient numeric
   identifiers for a given context will be monotonically-increasing.
   Since the increments space is separated into TABLE_LENGTH different
   spaces, the identifier reuse frequency will be (probabilistically)
   lower than that of the algorithm in Section 7.4.2.  That is, the
   generation of an identifier for one given context will not
   necessarily result in increments in the identifier sequence of other
   contexts.  It is interesting to note that the size of 'table[]' does
   not limit the number of different identifier sequences, but rather
   separates the *increment space* into TABLE_LENGTH different spaces.
   The selected transient numeric identifier sequence will be obtained
   by adding the corresponding entry from 'table[]' to the value in the
   'offset' variable, which selects the actual identifier sequence space
   (as in the algorithm from Section 7.4.2).

   An attacker can perform traffic analysis for any "increment space"
   (i.e., context) into which the attacker has "visibility" -- namely,
   the attacker can force a system to generate identifiers for
   G(CONTEXT, secret_key2), where the result of G() identifies the
   target "increment space".  However, the attacker's ability to perform
   traffic analysis is very reduced when compared to the simple PRF-
   based identifiers (described in Section 7.4.2) and the predictable
   linear identifiers (described in Appendix A.1).  Additionally, an
   implementation can further limit the attacker's ability to perform
   traffic analysis by further separating the increment space (that is,
   using a larger value for TABLE_LENGTH) and/or by randomizing the
   increments (i.e., increment() returning a small random number as
   opposed to the constant "1").

   Otherwise, this algorithm does not suffer from the issues discussed
   in Section 8.

8.  Common Vulnerabilities Associated with Transient Numeric Identifiers

8.1.  Network Activity Correlation

   An identifier that is predictable within a given context allows for
   network activity correlation within that context.

   For example, a stable IPv6 Interface Identifier allows for network
   activity to be correlated within the context in which the Interface
   Identifier is stable [RFC7721].  A stable-per-network IPv6 Interface
   Identifier (as in [RFC7217]) allows for network activity correlation
   within a network, whereas a constant IPv6 Interface Identifier (that
   remains constant across networks) allows not only network activity
   correlation within the same network, but also across networks ("host
   tracking").




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   Similarly, an implementation that generates TCP ISNs with a global
   counter could allow for fingerprinting and network activity
   correlation across networks, since an attacker could passively infer
   the identity of the victim based on the TCP ISNs employed for
   subsequent communication instances.  Similarly, an implementation
   that generates predictable IPv6 Fragment Identification values could
   be subject to fingerprinting attacks (see e.g.  [Bellovin2002]).

8.2.  Information Leakage

   Transient numeric identifiers that result in specific patterns can
   produce an information leakage to other communicating entities.  For
   example, it is common to generate transient numeric identifiers with
   an algorithm such as:

                   ID = offset(CONTEXT) + mono(CONTEXT);

   This generic expression generates identifiers by adding a
   monotonically-increasing function (e.g. linear) to a randomized
   offset. offset() is constant within a given context, whereas mono()
   produces a monotonically-increasing sequence for the given context.
   Identifiers generated with this expression will generally be
   predictable within CONTEXT.



   The predictability of mono(), irrespective of the predictability of
   offset(), can leak information that may be of use to attackers.  For
   example, a node that selects ephemeral port numbers as in:

                 ephemeral_port = offset(Dest_IP) + mono()

   that is, with a per-destination offset, but a global mono() function
   (e.g., a global counter), will leak information about total number of
   outgoing connections that have been issued by the vulnerable
   implementation.


   Similarly, a node that generates Fragment Identification values as
   in:

            Frag_ID = offset(IP_src_addr, IP_dst_addr) + mono()

   will leak out information about the total number of fragmented
   packets that have been transmitted by the vulnerable implementation.
   The vulnerabilities described in





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   [Sanfilippo1998a], [Sanfilippo1998b], and [Sanfilippo1999] are all
   associated with the use of a global mono() function (i.e., with a
   global and constant "context") -- particularly when it is a linear
   function (constant increments of 1).

   Predicting transient numeric identifiers can be of help for other
   types of attacks.  For example, predictable TCP ISNs can open the
   door to trivial connection-reset and data injection attacks (see
   Section 8.6).

8.3.  Fingerprinting

   Fingerprinting is the capability of an attacker to identify or re-
   identify a visiting user, user agent or device via configuration
   settings or other observable characteristics.  Observable protocol
   objects and characteristics can be employed to identify/re-identify a
   variety of entities, ranging from the underlying hardware or
   Operating System (vendor, type and version), to the user itself (i.e.
   his/her identity).  [EFF] illustrates web browser-based
   fingerprinting, but similar techniques can be applied at other layers
   and protocols, whether alternatively or in conjunction with it.

   Transient numeric identifiers are one of the observable protocol
   components that could be leveraged for fingerprinting purposes.  That
   is, an attacker could sample transient numeric identifiers to infer
   the algorithm (and its associated parameters, if any) for generating
   such identifiers, possibly revealing the underlying Operating System
   (OS) vendor, type, and version.  This information could possibly be
   further leveraged in conjunction with other fingerprinting techniques
   and sources.

   Evasion of protocol-stack fingerprinting can prove to be a very
   difficult task: most systems make use of a wide variety of protocols,
   each of which have a large number of parameters that can be set to
   arbitrary values or generated with a variety of algorithms with
   multiple parameters.















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   NOTE:
      General protocol-based fingerprinting is discussed in [RFC6973],
      along with guidelines to mitigate the associated vulnerability.
      [Fyodor1998] and [Fyodor2006] are classic references on Operating
      System detection via TCP/IP stack fingerprinting.  Nmap [nmap] is
      probably the most popular tool for remote OS identification via
      active TCP/IP stack fingerprinting. p0f [Zalewski2012], on the
      other hand, is a tool for performing remote OS detection via
      passive TCP/IP stack fingerprinting.  Finally, [TBIT] is a TCP
      fingerprinting tool that aims at characterizing the behaviour of a
      remote TCP peer based on active probes, and which has been widely
      used in the research community.

   Algorithms that, from the perspective of an observer (e.g., the
   legitimate communicating peer), result in specific values or
   patterns, will allow for at least some level of fingerprinting.  For
   example, the algorithm from Section 7.3 will typically allow
   fingerprinting within the context where the resulting identifiers are
   stable.  Similarly, the algorithms from Section 7.4 will result in a
   monotonically-increasing sequences within a given context, thus
   allowing for at least some level of fingerprinting (when the other
   communicating entity can correlate different sampled identifiers as
   belonging to the same monotonically-increasing sequence).

   Thus, where possible, algorithms from Section 7.1 should be preferred
   over algorithms that result in specific values or patterns.

8.4.  Exploitation of the Semantics of Transient Numeric Identifiers

   Identifiers that are not semantically opaque tend to be more
   predictable than semantically-opaque identifiers.  For example, a MAC
   address contains an OUI (Organizationally-Unique Identifier) which
   may identify the vendor that manufactured the corresponding network
   interface card.  This can be leveraged by an attacker trying to
   "guess" MAC addresses, who has some knowledge about the possible
   Network Interface Card (NIC) vendor.

   [RFC7707] discusses a number of techniques to reduce the search space
   when performing IPv6 address-scanning attacks by leveraging the
   semantics of the IIDs produced by traditional SLAAC algorithms
   (eventually replaced by [RFC7217]) that embed MAC addresses in the
   IID of IPv6 addresses.









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8.5.  Exploitation of Collisions of Transient Numeric Identifiers

   In many cases, the collision of transient network identifiers can
   have a hard failure severity (or result in a hard failure severity if
   an attacker can cause multiple collisions deterministically, one
   after another).  For example, predictable Fragment Identification
   values open the door to Denial of Service (DoS) attacks (see e.g.
   [RFC5722].).

8.6.  Exploitation of Predictable Transient Numeric Identifiers for
      Injection Attacks

   Some protocols rely on "sequence numbers" for the validation of
   incoming packets.  For example, TCP employs sequence numbers for
   reassembling TCP segments, while IPv4 and IPv6 employ Fragment
   Identification values for reassembling IPv4 and IPv6 fragments
   (respectively).  Lacking built-in cryptographic mechanisms for
   validating packets, these protocols are therefore vulnerable to on-
   path data (see e.g.  [Joncheray1995]) and/or control-information (see
   e.g.  [RFC4953] and [RFC5927]) injection attacks.  The extent to
   which these protocols may resist off-path (i.e. "blind") injection
   attacks depends on whether the associated "sequence numbers" are
   predictable, and effort required to successfully predict a valid
   "sequence number" (see e.g.  [RFC4953] and [RFC5927]).

   We note that the use of unpredictable "sequence numbers" is a
   completely-ineffective mitigation for on-path injection attacks, and
   also a mostly-ineffective mitigation for off-path (i.e. "blind")
   injection attacks.  However, many legacy protocols (such as TCP) do
   not natively incorporate cryptographic mitigations, but rather only
   as optional features (see e.g.  [RFC5925]), if at all available.
   Additionally, ad-hoc use of cryptographic mitigations might not be
   sufficient to relieve a protocol implementation of generating
   appropriate transient numeric identifiers.  For example, use of the
   Transport Layer Security (TLS) protocol [RFC8446] with TCP will
   protect the application protocol, but will not help to mitigate e.g.
   TCP-based connection-reset attacks (see e.g.  [RFC4953]).  Similarly,
   use of SEcure Neighbor Discovery (SEND) [RFC3971] will still imply
   reliance on the successful reassembly of IPv6 fragments in those
   cases where SEND packets do not fit into the link Maximum
   Transmission Unit (MTU) (see [RFC6980]).










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8.7.  Cryptanalysis

   A number of algorithms discussed in this document (such as those
   described in Section 7.4.2 and Section 7.4.3) rely on PRFs.
   Implementations that employ weak PRFs or keys of inappropriate size
   can be subject to cryptanalysis, where an attacker can obtain the
   secret key employed for the PRF, predict numeric identifiers, etc.

   Furthermore, an implementation that overloads the semantics of the
   secret key can result in more trivial cryptanalysis, possibly
   resulting in the leakage of the value employed for the secret key.

   NOTE:
      [IPID-DEV] describes two vulnerable transient numeric ID
      generators that employ cryptographically-weak hash functions.
      Additionally, one of such implementations employs 32-bits of a
      kernel address as the secret key for a hash function, and
      therefore successful cryptanalysis leaks the aforementioned kernel
      address, allowing for Kernel Address Space Layout Randomization
      (KASLR) [KASLR] bypass.

9.  Vulnerability Assessment of Transient Numeric Identifiers

   The following subsections analyze possible vulnerabilities associated
   with the algorithms described in Section 7.

9.1.  Category #1: Uniqueness (soft failure)

   Possible vulnerabilities associated with the algorithms from
   Section 7.1 include:

   *  Use of flawed PRNGs (please see e.g.  [Zalewski2001],
      [Zalewski2002], [Klein2007] and [CVEs]).

   *  Inadvertently affecting the distribution of an otherwise suitable
      PRNG (please see e.g.  [Romailler2020]).

   Where available, CSPRNGs should be preferred over regular PRNGs such
   as e.g.  POSIX random(3) implementations.  In scenarios where a
   CSPRNG is not readily available, a security and privacy assessment of
   employing a regular PRNG should be performed, supporting the
   implementation decision.

   NOTE:
      Please see [RFC4086] regarding randomness requirements for
      security.  [Aumasson2018], [Press1992], and [Knuth1983], discuss
      theoretical and practical aspects of random numbers generation,
      and provide guidance on how to evaluate PRNGs.



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   When employing a PRNG, many implementations "adapt" the length of its
   output with a modulo operator (e.g., C language's "%"), possibly
   changing the distribution of the output of the PRNG.

   For example, consider an implementation that employs the following
   code:

                          id = random() % 50000;

   This example implementation means to obtain a transient numeric
   identifier in the range 0-49999.  If random() produces e.g. a
   pseudorandom number of 16 bits (with uniform distribution), the
   selected transient numeric identifier will have a non-uniform
   distribution with the numbers in the range 0-15535 having double-
   frequency than the numbers in the range 15536-49999.


   NOTE:
      For example, in our sample code both an output of 10 and output of
      50010 from the random() function will result in an 'id' value of
      10.

   This effect is reduced if the PRNG produces an output that is much
   longer than the length implied by the modulo operation.  We note that
   to preserve a uniform distribution, the rejection sampling technique
   [Romailler2020] can be used.

   Use of algorithms other than PRNGs for generating identifiers of this
   category is discouraged.

9.2.  Category #2: Uniqueness (hard failure)

   As noted in Section 7.2, this category can employ the same algorithms
   as Category #4, since a monotonically-increasing sequence tends to
   minimize the transient numeric identifier reuse frequency.
   Therefore, the vulnerability analysis in Section 9.4 also applies to
   this category.

   Additionally, as noted in Section 7.2, some transient numeric
   identifiers of this category might be able to use the algorithms from
   Section 7.1, in which case the same considerations as in Section 9.1
   would apply.

9.3.  Category #3: Uniqueness, stable within context (soft failure)

   Possible vulnerabilities associated with the algorithms from
   Section 7.3 are:




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   1.  Use of weak PRFs, or inappropriate secret keys (whether
       inappropriate selection or inappropriate size) could allow for
       cryptanalysis, which could eventually be exploited by an attacker
       to predict future transient numeric identifiers.

   2.  Since the algorithm generates a unique and stable identifier
       within a specified context, it may allow for network activity
       correlation and fingerprinting within the specified context.

9.4.  Category #4: Uniqueness, monotonically increasing within context
      (hard failure)

   The algorithm described in Section 7.4.1 for generating identifiers
   of Category #4 will result in an identifiable pattern (i.e. a
   monotonically-increasing sequence) for the transient numeric
   identifiers generated for each CONTEXT, and thus will allow for
   fingerprinting and network activity correlation within each CONTEXT.

   On the other hand, a simple way to generalize and analyze the
   algorithms described in Section 7.4.2 and Section 7.4.3 for
   generating identifiers of Category #4, is as follows:

       /* Transient Numeric ID selection function */

       id_range = max_id - min_id + 1;
       retry = id_range;
       id_inc = increment() % id_range;

       do {
           update_mono(CONTEXT, id_inc);
           next_id = min_id + (offset(CONTEXT) + \
                               mono(CONTEXT)) % id_range;

           if (suitable_id(next_id)) {
               return next_id;
           }

           retry = retry - id_inc;

       } while (retry > 0);

       return ERROR;









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   NOTE:
      increment() returns a small integer that is employed to generate a
      monotonically-increasing function.  Most implementations employ a
      constant value for "increment()" (usually 1).  The value returned
      by increment() must be much smaller than the value computed for
      "id_range".

  
      update_mono(CONTEXT, id_inc) increments the counter corresponding
      to CONTEXT by "id_inc".

  
      mono(CONTEXT) reads the counter corresponding to CONTEXT.

   Essentially, an identifier (next_id) is generated by adding a
   monotonically-increasing function (mono()) to an offset value,
   unknown to the attacker and stable for given context (CONTEXT).

   The following aspects of the algorithm should be considered:

   *  For the most part, it is the offset() function that results in
      identifiers that are unpredictable by an off-patch attacker.
      While the resulting sequence is known to be monotonically-
      increasing, the use of a randomized offset value makes the
      resulting values unknown to the attacker.

   *  The most straightforward "stateless" implementation of offset() is
      with a PRF that takes the values that identify the context and a
      "secret_key" (not shown in the figure above) as arguments.

   *  One possible implementation of mono() would be to have mono()
      internally employ a single counter (as in the algorithm from
      Section 7.4.2), or map the increments for different contexts into
      a number of counters/buckets, such that the number of counters
      that need to be maintained in memory is reduced (as in the
      algorithm from algorithm in Section 7.4.3).

   *  In all cases, a monotonically increasing function is implemented
      by incrementing the previous value of a counter by increment()
      units.  In the most trivial case, increment() could return the
      constant "1".  But increment() could also be implemented to return
      small random integers such that the increments are unpredictable
      (see Appendix A of [RFC7739]).  This represents a trade-off
      between the unpredictability of the resulting transient numeric
      IDs and the transient numeric ID reuse frequency.

   Considering the generic algorithm illustrated above, we can identify
   the following possible vulnerabilities:



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   *  Since the algorithms for this category are similar to those of
      Section 9.3, with the addition of a monotonically-increasing
      function, all the issues discussed in Section 9.3 ("Category #3:
      Uniqueness, stable within context (soft failure)") also apply to
      this case.

   *  mono() can be correlated to the number of identifiers generated
      for a given context (CONTEXT).  Thus, if mono() spans more than
      the necessary context, the "increments" could be leaked to other
      parties, thus disclosing information about the number of
      identifiers that have been generated by the algorithm for all
      contexts.  This is information disclosure becomes more evident
      when an implementation employs a constant increment of 1.  For
      example, an implementation where mono() is actually a single
      global counter, will unnecessarily leak information the number of
      identifiers that have been generated by the algorithm (globally,
      for all contexts).  [Fyodor2003] is one example of how such
      information leakages can be exploited.  We note that limiting the
      span of the increments space will require a larger number of
      counters to be stored in memory (i.e., a larger value for the
      TABLE_LENGTH parameter of the algorithm in Section 7.4.3).

   *  Transient numeric identifiers generated with the algorithms
      described in Section 7.4.2 and Section 7.4.3 will normally allow
      for fingerprinting within CONTEXT since, for such context, the
      resulting identifiers will have an identifiable pattern (i.e. a
      monotonically-increasing sequence).

10.  IANA Considerations

   This document has no IANA actions.

11.  Security Considerations

   The entire document is about the security and privacy implications of
   transient numeric identifiers.
   [I-D.gont-numeric-ids-sec-considerations] recommends that protocol
   specifications specify the interoperability requirements of their
   transient numeric identifiers, perform a vulnerability assessment of
   their transient numeric identifiers, and suggest an algorithm for
   generating each of their transient numeric identifiers.  This
   document analyzes possible algorithms (and their implications) that
   could be employed to comply with the interoperability properties of
   most common categories of transient numeric identifiers, while
   minimizing the associated negative security and privacy implications.






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12.  Acknowledgements

   The authors would like to thank (in alphabetical order) Bernard
   Aboba, Jean-Philippe Aumasson, Steven Bellovin, Luis Leon Cardenas
   Graide, Spencer Dawkins, Theo de Raadt, Guillermo Gont, Joseph
   Lorenzo Hall, Gre Norcie, Colin Perkins, Vincent Roca, Shivan Sahib,
   Rich Salz, Martin Thomson, and Michael Tuexen, for providing valuable
   comments on earlier versions of this document.

   The authors would like to thank Shivan Sahib and Christopher Wood,
   for their guidance during the publication process of this document.

   The authors would like to thank Jean-Philippe Aumasson and Mathew D.
   Green (John Hopkins University) for kindly answering a number of
   questions.

   The authors would like to thank Diego Armando Maradona for his magic
   and inspiration.

13.  References

13.1.  Normative References

   [RFC0793]  Postel, J., "Transmission Control Protocol", RFC 793,
              DOI 10.17487/RFC0793, September 1981,
              <https://www.rfc-editor.org/info/rfc793>.

   [RFC6528]  Gont, F. and S. Bellovin, "Defending against Sequence
              Number Attacks", RFC 6528, DOI 10.17487/RFC6528, February
              2012, <https://www.rfc-editor.org/info/rfc6528>.

   [RFC6056]  Larsen, M. and F. Gont, "Recommendations for Transport-
              Protocol Port Randomization", BCP 156, RFC 6056,
              DOI 10.17487/RFC6056, January 2011,
              <https://www.rfc-editor.org/info/rfc6056>.

   [RFC5925]  Touch, J., Mankin, A., and R. Bonica, "The TCP
              Authentication Option", RFC 5925, DOI 10.17487/RFC5925,
              June 2010, <https://www.rfc-editor.org/info/rfc5925>.

   [RFC0791]  Postel, J., "Internet Protocol", STD 5, RFC 791,
              DOI 10.17487/RFC0791, September 1981,
              <https://www.rfc-editor.org/info/rfc791>.

   [RFC2460]  Deering, S. and R. Hinden, "Internet Protocol, Version 6
              (IPv6) Specification", RFC 2460, DOI 10.17487/RFC2460,
              December 1998, <https://www.rfc-editor.org/info/rfc2460>.




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   [RFC8200]  Deering, S. and R. Hinden, "Internet Protocol, Version 6
              (IPv6) Specification", STD 86, RFC 8200,
              DOI 10.17487/RFC8200, July 2017,
              <https://www.rfc-editor.org/info/rfc8200>.

   [RFC4086]  Eastlake 3rd, D., Schiller, J., and S. Crocker,
              "Randomness Requirements for Security", BCP 106, RFC 4086,
              DOI 10.17487/RFC4086, June 2005,
              <https://www.rfc-editor.org/info/rfc4086>.

   [RFC4291]  Hinden, R. and S. Deering, "IP Version 6 Addressing
              Architecture", RFC 4291, DOI 10.17487/RFC4291, February
              2006, <https://www.rfc-editor.org/info/rfc4291>.

   [RFC8981]  Gont, F., Krishnan, S., Narten, T., and R. Draves,
              "Temporary Address Extensions for Stateless Address
              Autoconfiguration in IPv6", RFC 8981,
              DOI 10.17487/RFC8981, February 2021,
              <https://www.rfc-editor.org/info/rfc8981>.

   [RFC4862]  Thomson, S., Narten, T., and T. Jinmei, "IPv6 Stateless
              Address Autoconfiguration", RFC 4862,
              DOI 10.17487/RFC4862, September 2007,
              <https://www.rfc-editor.org/info/rfc4862>.

   [RFC5722]  Krishnan, S., "Handling of Overlapping IPv6 Fragments",
              RFC 5722, DOI 10.17487/RFC5722, December 2009,
              <https://www.rfc-editor.org/info/rfc5722>.

   [RFC7217]  Gont, F., "A Method for Generating Semantically Opaque
              Interface Identifiers with IPv6 Stateless Address
              Autoconfiguration (SLAAC)", RFC 7217,
              DOI 10.17487/RFC7217, April 2014,
              <https://www.rfc-editor.org/info/rfc7217>.

   [RFC8064]  Gont, F., Cooper, A., Thaler, D., and W. Liu,
              "Recommendation on Stable IPv6 Interface Identifiers",
              RFC 8064, DOI 10.17487/RFC8064, February 2017,
              <https://www.rfc-editor.org/info/rfc8064>.

   [RFC6437]  Amante, S., Carpenter, B., Jiang, S., and J. Rajahalme,
              "IPv6 Flow Label Specification", RFC 6437,
              DOI 10.17487/RFC6437, November 2011,
              <https://www.rfc-editor.org/info/rfc6437>.

   [RFC6191]  Gont, F., "Reducing the TIME-WAIT State Using TCP
              Timestamps", BCP 159, RFC 6191, DOI 10.17487/RFC6191,
              April 2011, <https://www.rfc-editor.org/info/rfc6191>.



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   [RFC7323]  Borman, D., Braden, B., Jacobson, V., and R.
              Scheffenegger, Ed., "TCP Extensions for High Performance",
              RFC 7323, DOI 10.17487/RFC7323, September 2014,
              <https://www.rfc-editor.org/info/rfc7323>.

   [RFC1321]  Rivest, R., "The MD5 Message-Digest Algorithm", RFC 1321,
              DOI 10.17487/RFC1321, April 1992,
              <https://www.rfc-editor.org/info/rfc1321>.

   [RFC6151]  Turner, S. and L. Chen, "Updated Security Considerations
              for the MD5 Message-Digest and the HMAC-MD5 Algorithms",
              RFC 6151, DOI 10.17487/RFC6151, March 2011,
              <https://www.rfc-editor.org/info/rfc6151>.

   [RFC1035]  Mockapetris, P., "Domain names - implementation and
              specification", STD 13, RFC 1035, DOI 10.17487/RFC1035,
              November 1987, <https://www.rfc-editor.org/info/rfc1035>.

13.2.  Informative References

   [KASLR]    PaX Team, "Address Space Layout Randomization",
              <https://pax.grsecurity.net/docs/aslr.txt>.

   [IANA-PROT]
              IANA, "Protocol Registries",
              <https://www.iana.org/protocols>.

   [RFC6973]  Cooper, A., Tschofenig, H., Aboba, B., Peterson, J.,
              Morris, J., Hansen, M., and R. Smith, "Privacy
              Considerations for Internet Protocols", RFC 6973,
              DOI 10.17487/RFC6973, July 2013,
              <https://www.rfc-editor.org/info/rfc6973>.

   [Fyodor1998]
              Fyodor, "Remote OS Detection via TCP/IP Stack
              Fingerprinting",  Phrack Magazine, Volume 9, Issue 54,
              1998, <http://www.phrack.org/archives/issues/54/9.txt>.

   [Fyodor2006]
              Lyon, G., "Chapter 8. Remote OS Detection", 2006,
              <https://nmap.org/book/osdetect.html>.

   [nmap]     nmap, "Nmap: Free Security Scanner For Network Exploration
              and Audit", 2020, <https://www.insecure.org/nmap>.

   [EFF]      EFF, "Cover your tracks: See how trackers view your
              browser", 2020, <https://coveryourtracks.eff.org/>.




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   [Schuba1993]
              Schuba, C., "ADDRESSING WEAKNESSES IN THE DOMAIN NAME
              SYSTEM PROTOCOL", 1993,
              <http://ftp.cerias.purdue.edu/pub/papers/christoph-schuba/
              schuba-DNS-msthesis.pdf>.

   [TBIT]     TBIT, "TBIT, the TCP Behavior Inference Tool", 2001,
              <https://www.icir.org/tbit/>.

   [C11]      ISO/IEC, "Information technology - Programming languages -
              C",  ISO/IEC 9899:2011, 2011.

   [POSIX]    IEEE, "IEEE Standard for Information Technology --
              Portable Operating System Interface (POSIX)",  IEEE Std
              1003.1-2017, 2017.

   [ARC4RANDOM]
              OpenBSD, "arc4random(3)", Library Functions Manual, 2022,
              <https://man.openbsd.org/arc4random>.

   [GETENTROPY]
              Linux, "getentropy(3)", Linux Programmer's Manual, 2022,
              <https://man7.org/linux/man-pages/man3/getentropy.3.html>.

   [CVEs]     NVD, "Vulnerability Advisories for Pseudo Random Number
              Generators", 2022,
              <https://www.gont.com.ar/miscellanea/prng-cves/>.

   [Zalewski2012]
              Zalewski, M., "p0f v3 (version 3.09b)", 2012,
              <https://lcamtuf.coredump.cx/p0f.shtml>.

   [RFC2104]  Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-
              Hashing for Message Authentication", RFC 2104,
              DOI 10.17487/RFC2104, February 1997,
              <https://www.rfc-editor.org/info/rfc2104>.

   [RFC7098]  Carpenter, B., Jiang, S., and W. Tarreau, "Using the IPv6
              Flow Label for Load Balancing in Server Farms", RFC 7098,
              DOI 10.17487/RFC7098, January 2014,
              <https://www.rfc-editor.org/info/rfc7098>.

   [RFC7258]  Farrell, S. and H. Tschofenig, "Pervasive Monitoring Is an
              Attack", BCP 188, RFC 7258, DOI 10.17487/RFC7258, May
              2014, <https://www.rfc-editor.org/info/rfc7258>.






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   [CPNI-TCP] Gont, F., "Security Assessment of the Transmission Control
              Protocol (TCP)",  United Kingdom's Centre for the
              Protection of National Infrastructure (CPNI) Technical
              Report, 2009, <https://www.gont.com.ar/papers/tn-03-09-
              security-assessment-TCP.pdf>.

   [Zalewski2001]
              Zalewski, M., "Strange Attractors and TCP/IP Sequence
              Number Analysis", 2001,
              <https://lcamtuf.coredump.cx/oldtcp/tcpseq.html>.

   [Zalewski2002]
              Zalewski, M., "Strange Attractors and TCP/IP Sequence
              Number Analysis - One Year Later", 2001,
              <https://lcamtuf.coredump.cx/newtcp/>.

   [Joncheray1995]
              Joncheray, L., "A Simple Active Attack Against TCP", Proc.
              Fifth Usenix UNIX Security Symposium, 1995, <https://www.u
              senix.org/legacy/publications/library/proceedings/
              security95/full_papers/joncheray.pdf>.

   [Morris1985]
              Morris, R., "A Weakness in the 4.2BSD UNIX TCP/IP
              Software", CSTR 117, AT&T Bell Laboratories, Murray Hill,
              NJ, 1985,
              <https://pdos.csail.mit.edu/~rtm/papers/117.pdf>.

   [Shimomura1995]
              Shimomura, T., "Technical details of the attack described
              by Markoff in NYT", Message posted in USENET's
              comp.security.misc newsgroup Message-ID:
              <3g5gkl$5j1@ariel.sdsc.edu>, 1995,
              <https://www.gont.com.ar/docs/post-shimomura-usenet.txt>.

   [RFC5927]  Gont, F., "ICMP Attacks against TCP", RFC 5927,
              DOI 10.17487/RFC5927, July 2010,
              <https://www.rfc-editor.org/info/rfc5927>.

   [RFC4953]  Touch, J., "Defending TCP Against Spoofing Attacks",
              RFC 4953, DOI 10.17487/RFC4953, July 2007,
              <https://www.rfc-editor.org/info/rfc4953>.

   [RFC8446]  Rescorla, E., "The Transport Layer Security (TLS) Protocol
              Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018,
              <https://www.rfc-editor.org/info/rfc8446>.





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   [RFC3971]  Arkko, J., Ed., Kempf, J., Zill, B., and P. Nikander,
              "SEcure Neighbor Discovery (SEND)", RFC 3971,
              DOI 10.17487/RFC3971, March 2005,
              <https://www.rfc-editor.org/info/rfc3971>.

   [RFC6980]  Gont, F., "Security Implications of IPv6 Fragmentation
              with IPv6 Neighbor Discovery", RFC 6980,
              DOI 10.17487/RFC6980, August 2013,
              <https://www.rfc-editor.org/info/rfc6980>.

   [RFC7739]  Gont, F., "Security Implications of Predictable Fragment
              Identification Values", RFC 7739, DOI 10.17487/RFC7739,
              February 2016, <https://www.rfc-editor.org/info/rfc7739>.

   [RFC4963]  Heffner, J., Mathis, M., and B. Chandler, "IPv4 Reassembly
              Errors at High Data Rates", RFC 4963,
              DOI 10.17487/RFC4963, July 2007,
              <https://www.rfc-editor.org/info/rfc4963>.

   [RFC6274]  Gont, F., "Security Assessment of the Internet Protocol
              Version 4", RFC 6274, DOI 10.17487/RFC6274, July 2011,
              <https://www.rfc-editor.org/info/rfc6274>.

   [Press1992]
              Press, W. H., Teukolsky, S. A., Vetterling, W. T., and B.
              P. Flannery, "Numerical Recipes in C: The Art of
              Scientific Computing", 2nd ed. ISBN 0-521-43108-5.
              Cambridge University Press, 1992.

   [Romailler2020]
              Romailler, Y., "THE DEFINITIVE GUIDE TO "MODULO BIAS AND
              HOW TO AVOID IT"!", Kudelski Security Research, 2020,
              <https://research.kudelskisecurity.com/2020/07/28/the-
              definitive-guide-to-modulo-bias-and-how-to-avoid-it/>.

   [Aumasson2018]
              Aumasson, J.P., "Serious Cryptography: A Practical
              Introduction to Modern Encryption", ISBN-10:
              1-59327-826-8, No Starch Press, Inc., 2018.

   [Knuth1983]
              Knuth, D., "The Art of Computer Programming", volume 2
              (Seminumerical Algorithms), 2nd ed. Reading,
              Massachusetts: Addison-Wesley Publishing Company, 1981.







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   [Bellovin1989]
              Bellovin, S., "Security Problems in the TCP/IP Protocol
              Suite", Computer Communications Review, vol. 19, no. 2,
              pp. 32-48, 1989,
              <https://www.cs.columbia.edu/~smb/papers/ipext.pdf>.

   [Bellovin2002]
              Bellovin, S. M., "A Technique for Counting NATted Hosts",
              IMW'02 Nov. 6-8, 2002, Marseille, France, 2002,
              <https://www.cs.columbia.edu/~smb/papers/fnat.pdf>.

   [Fyodor2003]
              Fyodor, "Idle scanning and related IP ID games", 2003,
              <https://nmap.org/presentations/CanSecWest03/CD_Content/
              idlescan_paper/idlescan.html>.

   [Sanfilippo1998a]
              Sanfilippo, S., "about the ip header id", Post to Bugtraq
              mailing-list, Mon Dec 14 1998,
              <http://seclists.org/bugtraq/1998/Dec/48>.

   [Sanfilippo1998b]
              Sanfilippo, S., "Idle scan", Post to Bugtraq mailing-list,
              1998, <https://github.com/antirez/hping/raw/master/docs/
              SPOOFED_SCAN.txt>.

   [Sanfilippo1999]
              Sanfilippo, S., "more ip id", Post to Bugtraq mailing-
              list, 1999,
              <https://github.com/antirez/hping/raw/master/docs/MORE-
              FUN-WITH-IPID>.

   [Silbersack2005]
              Silbersack, M.J., "Improving TCP/IP security through
              randomization without sacrificing interoperability",
              EuroBSDCon 2005 Conference, 2005,
              <https://citeseerx.ist.psu.edu/viewdoc/
              download?doi=10.1.1.91.4542&rep=rep1&type=pdf>.

   [Klein2007]
              Klein, A., "OpenBSD DNS Cache Poisoning and Multiple O/S
              Predictable IP ID Vulnerability", 2007,
              <https://dl.packetstormsecurity.net/papers/attack/OpenBSD_
              DNS_Cache_Poisoning_and_Multiple_OS_Predictable_IP_ID_Vuln
              erability.pdf>.






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   [IPID-DEV] Klein, A. and B. Pinkas, "From IP ID to Device ID and
              KASLR Bypass (Extended Version)", June 2019,
              <https://arxiv.org/pdf/1906.10478.pdf>.

   [I-D.irtf-pearg-numeric-ids-history]
              Gont, F. and I. Arce, "Unfortunate History of Transient
              Numeric Identifiers", Work in Progress, Internet-Draft,
              draft-irtf-pearg-numeric-ids-history-10, 11 July 2022,
              <https://www.ietf.org/archive/id/draft-irtf-pearg-numeric-
              ids-history-10.txt>.

   [I-D.gont-numeric-ids-sec-considerations]
              Gont, F. and I. Arce, "Security Considerations for
              Transient Numeric Identifiers Employed in Network
              Protocols", Work in Progress, Internet-Draft, draft-gont-
              numeric-ids-sec-considerations-08, 10 December 2022,
              <https://datatracker.ietf.org/api/v1/doc/document/draft-
              gont-numeric-ids-sec-considerations/>.

   [RFC7721]  Cooper, A., Gont, F., and D. Thaler, "Security and Privacy
              Considerations for IPv6 Address Generation Mechanisms",
              RFC 7721, DOI 10.17487/RFC7721, March 2016,
              <https://www.rfc-editor.org/info/rfc7721>.

   [RFC7707]  Gont, F. and T. Chown, "Network Reconnaissance in IPv6
              Networks", RFC 7707, DOI 10.17487/RFC7707, March 2016,
              <https://www.rfc-editor.org/info/rfc7707>.

   [RFC8937]  Cremers, C., Garratt, L., Smyshlyaev, S., Sullivan, N.,
              and C. Wood, "Randomness Improvements for Security
              Protocols", RFC 8937, DOI 10.17487/RFC8937, October 2020,
              <https://www.rfc-editor.org/info/rfc8937>.

   [TCPT-uptime]
              McDanel, B., "TCP Timestamping - Obtaining System Uptime
              Remotely", 14 March 2001,
              <https://securiteam.com/securitynews/5np0c153pi/>.

   [SipHash]  Aumasson, J. P. and D. J. Bernstein, "SipHash: a fast
              short-input PRF", 2012,
              <https://github.com/veorq/SipHash>.

   [BLAKE3]   O'Connor, J., Aumasson, J. P., Neves, S., and Z. Wilcox-
              O'Hearn, "BLAKE3: one function, fast everywhere", 2020,
              <https://blake3.io/>.






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   [FIPS-SHS] NIST, "Secure Hash Standard (SHS)",  Federal Information
              Processing Standards Publication 180-4, August 2015,
              <https://nvlpubs.nist.gov/nistpubs/FIPS/
              NIST.FIPS.180-4.pdf>.

   [RFC6194]  Polk, T., Chen, L., Turner, S., and P. Hoffman, "Security
              Considerations for the SHA-0 and SHA-1 Message-Digest
              Algorithms", RFC 6194, DOI 10.17487/RFC6194, March 2011,
              <https://www.rfc-editor.org/info/rfc6194>.

Appendix A.  Algorithms and Techniques with Known Issues

   The following subsections discuss algorithms and techniques with
   known negative security and privacy implications.

   NOTE:
      As discussed in Section 1, the use of cryptographic techniques
      might allow for the safe use of some of these algorithms and
      techniques.  However, this should be evaluated on a case by case
      basis.

A.1.  Predictable Linear Identifiers Algorithm

   One of the most trivial ways to achieve uniqueness with a low
   identifier reuse frequency is to produce a linear sequence.  This
   type of algorithm has been employed in the past to generate
   identifiers of Categories #1, #2, and #4 (please see Section 6 for an
   analysis of these categories).

   For example, the following algorithm has been employed (see e.g.
   [Morris1985], [Shimomura1995], [Silbersack2005] and [CPNI-TCP]) in a
   number of operating systems for selecting IP fragment IDs, TCP
   ephemeral ports, etc.:


















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       /* Initialization code */

       next_id = min_id;
       id_inc= 1;


       /* Transient Numeric ID selection function */

       id_range = max_id - min_id + 1;
       retry = id_range;

       do {
           if (next_id == max_id) {
               next_id = min_id;
           }
           else {
               next_id = next_id + id_inc;
           }

           if (suitable_id(next_id)) {
               return next_id;
           }

           retry--;

       } while (retry > 0);

       return ERROR;

   NOTE:
      suitable_id() is a function that checks whether the resulting
      identifier is acceptable (e.g., whether it's in use, etc.).

   For obvious reasons, this algorithm results in predictable sequences.
   Since a global counter is used to generate the transient numeric
   identifiers ("next_id" in the example above), an entity that learns
   one numeric identifier can infer past numeric identifiers and predict
   future values to be generated by the same algorithm.  Since the value
   employed for the increments is known (such as "1" in this case), an
   attacker can sample two values, and learn the number of identifiers
   that have been were generated in-between the two sampled values.
   Furthermore, if the counter is initialized e.g. when the system its
   bootstrapped to some known value, the algorithm will leak additional
   information, such as the number of transmitted fragmented datagrams
   in the case of an IP ID generator [Sanfilippo1998a], or the system
   uptime in the case of TCP timestamps [TCPT-uptime].





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A.2.  Random-Increments Algorithm

   This algorithm offers a middle ground between the algorithms that
   generate randomized transient numeric identifiers (such as those
   described in Section 7.1.1 and Section 7.1.2), and those that
   generate identifiers with a predictable monotonically-increasing
   function (see Appendix A.1).

       /* Initialization code */

       next_id = random();        /* Initialization value */
       id_rinc = 500;             /* Determines the trade-off */


       /* Transient Numeric ID selection function */

       id_range = max_id - min_id + 1;
       retry = id_range;


       do {
           /* Random increment */
           id_inc = (random() % id_rinc) + 1;

           if ( (max_id - next_id) >= id_inc){
               next_id = next_id + id_inc;
           }
           else {
               next_id = min_id + id_inc - (max_id - next_id);
           }

           if (suitable_id(next_id)) {
              return next_id;
           }

           retry = retry - id_inc;

       } while (retry > 0);

       return ERROR;


   This algorithm aims at producing a global monotonically-increasing
   sequence of transient numeric identifiers, while avoiding the use of
   fixed increments, which would lead to trivially predictable
   sequences.  The value "id_inc" allows for direct control of the
   trade-off between unpredictability and identifier reuse frequency.
   The smaller the value of "id_inc", the more similar this algorithm is



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   to a predicable, global linear ID generation algorithm (as the one in
   Appendix A.1).  The larger the value of "id_inc", the more similar
   this algorithm is to the algorithm described in Section 7.1.1 of this
   document.

   When the identifiers wrap, there is a risk of collisions of transient
   numeric identifiers (i.e., identifier reuse).  Therefore, "id_inc"
   should be selected according to the following criteria:

   *  It should maximize the wrapping time of the identifier space.

   *  It should minimize identifier reuse frequency.

   *  It should maximize unpredictability.

   Clearly, these are competing goals, and the decision of which value
   of "id_inc" to use is a trade-off.  Therefore, the value of "id_inc"
   is at times a configurable parameter so that system administrators
   can make the trade-off for themselves.  We note that the alternative
   algorithms discussed throughout this document offer better
   interoperability, security and privacy properties than this
   algorithm, and hence implementation of this algorithm is discouraged.

A.3.  Re-using Identifiers Across Different Contexts

   Employing the same identifier across contexts in which stability is
   not required (i.e. overloading the semantics of transient numeric
   identifier) usually has negative security and privacy implications.

   For example, in order to generate transient numeric identifiers of
   Category #2 or Category #3, an implementation or specification might
   be tempted to employ a source for the numeric identifiers which is
   known to provide unique values, but that may also be predictable or
   leak information related to the entity generating the identifier.
   This technique has been employed in the past for e.g. generating IPv6
   IIDs by re-using the MAC address of the underlying network interface.
   However, as noted in [RFC7721] and [RFC7707], embedding link-layer
   addresses in IPv6 IIDs not only results in predictable values, but
   also leaks information about the manufacturer of the underlying
   network interface card, allows for network activity correlation, and
   makes address-based scanning attacks feasible.

Authors' Addresses








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   Fernando Gont
   SI6 Networks
   Segurola y Habana 4310 7mo piso
   Ciudad Autonoma de Buenos Aires
   Buenos Aires
   Argentina
   Email: fgont@si6networks.com
   URI:   https://www.si6networks.com


   Ivan Arce
   Quarkslab
   Segurola y Habana 4310 7mo piso
   Ciudad Autonoma de Buenos Aires
   Buenos Aires
   Argentina
   Email: iarce@quarkslab.com
   URI:   https://www.quarkslab.com

































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