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Versions: 00 01 02 03 04 05 06 07 08 09 10 11 RFC 5475

 Internet Draft                                               T. Zseby
 Document: <draft-ietf-psamp-sample-tech-11.txt>      Fraunhofer FOKUS
 Intended status: Proposed Standard                          M. Molina
 Expires: December 2008                                          DANTE
                                                           N. Duffield
                                                    AT&T Labs-Research
                                                          S. Niccolini
                                                       NEC Europe Ltd.
                                                            F. Raspall
                                                          July 9, 2008
    Sampling and Filtering Techniques for IP Packet Selection
 Status of this Memo
    By submitting this Internet-Draft, each author represents that
    any applicable patent or other IPR claims of which he or she is
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    This Internet-Draft will expire on December, 2008.
 Copyright Notice
    Copyright (C) The IETF Trust (2008).
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    This document describes Sampling and Filtering techniques for IP
    packet selection. It provides a categorization of schemes and
    defines what parameters are needed to describe the most common
    selection schemes. Furthermore it shows how techniques can be
    combined to build more elaborate packet Selectors. The document
    provides the basis for the definition of information models for
    configuring selection techniques in Metering Processes and for
    reporting the technique in use to a Collector.
 Conventions used in this document
    The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL
    "OPTIONAL" in this document are to be interpreted as described
    in RFC 2119 [RFC2119].
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 Table of Contents
    1.   Introduction................................................. 4
    2.   PSAMP Documents Overview..................................... 5
    3.   Terminology.................................................. 5
    3.1     Observation Points, Packet Streams and Packet Content..... 5
    3.2     Selection Process......................................... 6
    3.3     Reporting................................................. 8
    3.4     Metering Process ......................................... 8
    3.5     Exporting Process......................................... 8
    3.6     PSAMP Device.............................................. 9
    3.7     Collector................................................. 9
    3.8     Selection Methods......................................... 9
    4.   Categorization of Packet Selection Techniques............... 12
    5.   Sampling.................................................... 14
    5.1     Systematic Sampling...................................... 14
    5.2     Random Sampling.......................................... 15
    5.2.1   n-out-of-N Sampling...................................... 15
    5.2.2   Probabilistic Sampling................................... 16 Uniform Probabilistic Sampling........................... 16 Non-Uniform Probabilistic Sampling....................... 16 Non-Uniform Flow State Dependent Sampling................ 16 Configuration of non-uniform probabilistic and flow-
             state Sampling.......................................... 17
    6.   Filtering................................................... 17
    6.1     Property Match Filtering................................. 18
    6.2     Hash-based Filtering..................................... 20
    6.2.1   Application Examples for Coordinated Packet Selection ... 21 Trajectory Sampling...................................... 21 Passive One-way Measurements............................. 21 Generation of Pseudo-random Numbers...................... 22
    6.2.2   Desired Properties of Hash Functions..................... 22 Requirements for Packet Selection........................ 23 Requirements for Packet Digesting........................ 23
    6.2.3   Security Considerations for Hash Functions............... 24 Vulnerabilities of Hash-based selection without
             knowledge of selection outcomes......................... 25 Vulnerabilities of Hash-based selection using knowledge
             of selection outcomes................................... 26 Vulnerabilities to Replay Attacks........................ 27
    6.2.4   Choice of Hash-Function.................................. 27 Hash Functions for Packet Selection...................... 28 Hash Functions Suitable for Packet Digesting............. 30
    7.   Parameters for the Description of Selection Techniques...... 30
    7.1     Description of Sampling Techniques....................... 31
    7.2     Description of Filtering Techniques...................... 32
    8.   Composite Techniques........................................ 34
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    8.1     Cascaded Filtering->Sampling or Sampling->Filtering...... 35
    8.2     Stratified Sampling...................................... 35
    9.   Security Considerations..................................... 36
    10.  Acknowledgements............................................ 37
    11.  IANA Considerations......................................... 37
    12.  Normative References........................................ 37
    13.  Informative References...................................... 37
    14.  Authors' Addresses.......................................... 40
    15.  Contributors................................................ 41
    16.  Intellectual Property Statement............................. 41
    17.  Copyright Statement......................................... 42
    18.  Disclaimer.................................................. 42
    Appendix A: Hash Functions....................................... 42
    A.1 IP Shift-XOR (IPSX) Hash Function............................ 42
    A.2 BOB Hash Function............................................ 43
 1. Introduction
    There are two main drivers for the growth in measurement
    infrastructures and their underlying technology. First, network
    data rates are increasing, with a concomitant growth in
    measurement data. Secondly, the growth is compounded by the
    demand of measurement-based applications for increasingly fine
    grained traffic measurements. Devices such as routers, which
    perform the measurements, require increasingly sophisticated and
    resource intensive measurement capabilities, including the
    capture of packet headers or even parts of the payload, and
    classification for flow analysis. All these factors can lead to
    an overwhelming amount of measurement data, resulting in high
    demands on resources for measurement, storage, transfer and post
    The sustained capture of network traffic at line rate can be
    performed by specialized measurement hardware. However, the cost
    of the hardware and the measurement infrastructure required to
    accommodate the measurements preclude this as a ubiquitous
    approach. Instead some form of data reduction at the point of
    measurement is necessary.
    This can be achieved by an intelligent packet selection through
    Sampling or Filtering. Another way to reduce the amount of data
    is to use aggregation techniques (not addressed in this
    document). The motivation for Sampling is to select a
    representative subset of packets that allow accurate estimates
    of properties of the unsampled traffic to be formed. The
    motivation for Filtering is to remove all packets that are not
    of interest. Aggregation combines data and allows compact pre-
    defined views of the traffic. Examples of applications that
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    benefit from packet selection are given in [PSAMP-FW].
    Aggregation techniques are out of scope of this document.
 2. PSAMP Documents Overview
    This document is one out of a series of documents from the PSAMP
    [PSAMP-FW]:   "A Framework for Packet Selection and Reporting"
                   describes the PSAMP framework for network elements
                   to select subsets of packets by statistical and
                   other methods, and to export a stream of reports
                   on the selected packets to a Collector.
    [PSAMP-TECH]: "Sampling and Filtering Techniques for IP Packet
                   Selection" (this document) describes the set of
                   packet selection techniques supported by PSAMP.
    [PSAMP-PROTO]: "Packet Sampling (PSAMP) Protocol Specifications"
                   specifies the export of packet information from a
                   PSAMP Exporting Process to a PSAMP Collecting
    [PSAMP-INFO]: "Information Model for Packet Sampling Exports"
                   defines an information and data model for PSAMP.
 3. Terminology
    The PSAMP terminology defined here is fully consistent with all
    terms listed in [PSAMP-FW] but includes additional terms
    required for the description of packet selection methods. An
    architecture overview and possible configurations of PSAMP
    elements can be found in [PSAMP-FW]. PSAMP terminology also aims
    at consistency with terms used in [RFC3917]. The relationship
    between PSAMP and IPFIX terms is described in [PSAMP-FW].
    In the PSAMP documents all defined PSAMP terms are written
    capitalized. This document uses the same convention.
 3.1 Observation Points, Packet Streams and Packet Content
    * Observation Point
       An Observation Point is a location in the network where
       packets can be observed. Examples include:
         (i)  A line to which a probe is attached;
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         (ii) a shared medium, such as an Ethernet-based LAN;
         (iii) a single port of a router, or set of interfaces
               (physical or logical) of a router;
         (iv) an embedded measurement subsystem within an interface.
       Note that one Observation Point may be a superset of several
       other Observation Points.  For example one Observation Point
       can be an entire line card.  This would be the superset of the
       individual Observation Points at the line card's interfaces.
    * Observed Packet Stream
       The Observed Packet Stream is the set of all packets observed
       at the Observation Point.
    * Packet Stream
       A packet stream denotes a set of packets that flows past some
       specified point within the metering process. An example of a
       Packet Stream is the output of the selection process.
       Note that packets selected from a stream, e.g. by Sampling, do
       not necessarily possess a property by which they can be
       distinguished from packets that have not been selected. For
       this reason the term "stream" is favored over "flow", which is
       defined as set of packets with common properties [RFC3917].
    * Packet Content
       The packet content denotes the union of the packet header
       (which includes link layer, network layer and other
       encapsulation headers) and the packet payload. At some
       Observation Points the link header information may not be
 3.2 Selection Process
    * Selection Process
       A Selection Process takes the Observed Packet Stream as its
       input and selects a subset of that stream as its output.
    * Selection State
       A Selection Process may maintain state information for use by
       the Selection Process. At a given time, the Selection State
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       may depend on packets observed at and before that time, and
       other variables. Examples include:
         (i)  sequence numbers of packets at the input of Selectors;
         (ii) a timestamp of observation of the packet at the
               Observation Point;
         (iii) iterators for pseudo-random number generators;
         (iv) hash values calculated during selection;
         (v)  indicators of whether the packet was selected by a
               given Selector;
       Selection Processes may change portions of the Selection State
       as a result of processing a packet. Selection state for a
       packet is to reflect the state after processing the packet.
    * Selector
       A Selector defines the action of a Selection Process on a
       single packet of its input. If selected, the packet becomes an
       element of the output Packet Stream.
       The Selector can make use of the following information in
       determining whether a packet is selected:
         (i)  the packet's content;
         (ii) information derived from the packet's treatment at the
               Observation Point;
         (iii) any selection state that may be maintained by the
               Selection Process.
    * Composite Selector
       A Composite Selector is an ordered composition of Selectors,
       in which the output Packet Stream issuing from one Selector
       forms the input Packet Stream to the succeeding Selector.
    * Primitive Selector
       A Selector is primitive if it is not a Composite Selector.
    * Selection Sequence
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       From all the packets observed at an Observation Point, only a
       few packets are selected by one or more Selectors.  The
       Selection Sequence is a unique value per Observation Domain
       describing the Observation Point and the Selector IDs through
       which the packets are selected.
 3.3 Reporting
    * Packet Reports
       Packet Reports comprise a configurable subset of a packet's
       input to the Selection Process, including the packet's
       content, information relating to its treatment (for example,
       the output interface), and its associated selection state (for
       example, a hash of the packet's content)
    * Report Interpretation:
       Report Interpretation comprises subsidiary information,
       relating to one or more packets, that is used for
       interpretation of their packet reports. Examples include
       configuration parameters of the Selection Process.
    * Report Stream:
       The Report Stream is the output of a Metering Process,
       comprising two distinguished types of information: Packet
       Reports, and Report Interpretation.
 3.4 Metering Process
       A Metering Process selects packets from the Observed Packet
       Stream using a Selection Process, and produces as output a
       Report Stream concerning the selected packets. The PSAMP
       Metering Process can be viewed as analogous to the IPFIX
       metering process [RFC5101], which produces flow records as its
       output.  While the Metering Process definition in this
       document specifies the PSAMP definition, the PSAMP protocol
       specifications [PSAMP-PROTO] will use the IPFIX Metering
       Process definition, which also suits the PSAMP requirements.
       The relationship between PSAMP and IPFIX is described more in
       [PSAMP-INFO] and [PSAMP-PROTO].
 3.5 Exporting Process
    * Exporting Process:
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       An Exporting Process sends, in the form of Export Packet, the
       output of one or more Metering Processes to one or more
    * Export Packet:
       An Export Packet is a combination of Report Interpretation
       and/or one or more Packet Reports are bundled by the Exporting
       Process into an Export Packet for exporting to a Collector.
 3.6 PSAMP Device
    * PSAMP Device
       A PSAMP Device is a device hosting at least an Observation
       Point, a Metering Process (which includes a Selection Process)
       and an Exporting Process.  Typically, corresponding
       Observation Point(s), Metering Process(es) and Exporting
       Process(es) are co-located at this device, for example at a
 3.7 Collector
    * Collector
       A Collector receives a Report Stream exported by one or more
       Exporting Processes. In some cases, the host of the Metering
       and/or Exporting Processes may also serve as the Collector.
 3.8 Selection Methods
    * Filtering
       A filter is a Selector that selects a packet deterministically
       based on the Packet Content, or its treatment, or functions of
       these occurring in the Selection State.  Two examples are:
         (i) Property match filtering: a packet is selected if a
               specific field in the packet equals a predefined
         (ii) Hash-based selection: a hash function is applied to
               the Packet Content, and the packet is selected if the
               result falls in a specified range.
    * Sampling
       A selector that is not a filter is called a sampling
       operation.  This reflects the intuitive notion that if the
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       selection of a packet cannot be determined from its content
       alone, there must be some type of sampling taking place.
       Sampling operations can be divided into two subtypes:
          (i) Content-independent sampling, which does not use
               Packet Content in reaching sampling decisions.
               Examples include systematic sampling, and uniform
               pseudo-random sampling driven by a pseudo-random
               number whose generation is independent of Packet
               Content.  Note that in Content-independent Sampling it
               is not necessary to access the Packet Content in order
               to make the selection decision.
         (ii) Content-dependent sampling, in which the Packet
               Content is used in reaching selection decisions.  An
               application is pseudo-random selection according to a
               probability that depends on the contents of a packet
               field, e.g., sampling packets with a probability
               dependent on their TCP/UDP port numbers.  Note that
               this is not a Filter.
    * Hash Domain
       A subset of the Packet Content and the packet treatment,
       viewed as an N-bit string for some positive integer N.
    * Hash Range
       A set of M-bit strings for some positive integer M that define
       the range of values the result of the hash operation can take.
    * Hash Function
       A Hash Function defines a deterministic mapping from the Hash
       Domain into the Hash Range.
    * Hash Selection Range
       The Hash Selection Range is a subset of the Hash Range. The
       packet is selected if the action of the Hash Function on the
       Hash Domain for the packet yields a result in the Hash
       Selection Range.
    * Hash-based Selection
       Hash-based Selection is a Filtering specified by a Hash
       Domain, a Hash Function, and Hash Range and a Hash Selection
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    * Approximative Selection
       Selectors in any of the above categories may be approximated
       by operations in the same or another category for the purposes
       of implementation. For example, uniform pseudo-random Sampling
       may be approximated by Hash-based Selection, using a suitable
       Hash Function and Hash Domain. In this case, the closeness of
       the approximation depends on the choice of Hash Function and
       Hash Domain.
    * Population
       A Population is a Packet Stream, or a subset of a Packet
       Stream. A Population can be considered as a base set from
       which packets are selected. An example is all packets in the
       Observed Packet Stream that are observed within some specified
       time interval.
    * Population Size
       The Population Size is the number of all packets in the
    * Sample Size
       The number of packets selected from the Population by a
    * Configured Selection Fraction
       The Configured Selection Fraction is the ratio of the number
       of packets selected by a Selector from an input Population, to
       the Population Size, as based on the configured selection
    * Attained Selection Fraction
       The Attained Selection Fraction is the actual ratio of the
       number of packets selected by a Selector from an input
       Population, to the Population Size.
    For some sampling methods the Attained Selection Fraction can
    differ from the Configured Selection Fraction due to, for
    example, the inherent statistical variability in sampling
    decisions of probabilistic Sampling and Hash-based Selection.
    Nevertheless, for large Population Sizes and properly configured
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    Selectors, the Attained Selection Fraction usually approaches
    the Configured Selection Fraction.
 4. Categorization of Packet Selection Techniques
    Packet selection techniques generate a subset of packets from an
    Observed Packet Stream at an Observation Point. We distinguish
    between Sampling and Filtering.
    Sampling is targeted at the selection of a representative subset
    of packets. The subset is used to infer knowledge about the
    whole set of observed packets without processing them all. The
    selection can depend on packet position, and/or on packet
    content, and/or on (pseudo) random decisions.
    Filtering selects a subset with common properties. This is used
    if only a subset of packets is of interest. The properties can
    be directly derived from the packet content, or depend on the
    treatment given by the router to the packet. Filtering is a
    deterministic operation. It depends on packet content or router
    treatment. It never depends on packet position or on (pseudo)
    random decisions.
    Note that a common technique to select packets is to compute a
    Hash Function on some bits of the packet header and/or content
    and to select it if the Hash Value falls in the Hash Selection
    Range. Since hashing is a deterministic operation on the packet
    content, it is a Filtering technique according to our
    categorization. Nevertheless, Hash Functions are sometimes used
    to emulate random Sampling. Depending on the chosen input bits,
    the Hash Function and the Hash Selection Range, this technique
    can be used to emulate the random selection of packets with a
    given probability p. It is also a powerful technique to
    consistently select the same packet subset at multiple
    Observation Points [DuGr00]
    The following table gives an overview of the schemes described
    in this document and their categorization. An X in brackets (X)
    denotes schemes for which also content-independent variants
    exist. It easily can be seen that only schemes with both
    properties, content dependence and deterministic selection, are
    considered as filters.
           Selection Scheme   | Deterministic | Content- | Category
                              |  Selection    | dependent|
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       Systematic             |       X       |     _    | Sampling
       Count-based            |               |          |
       Systematic             |       X       |     -    | Sampling
       Time-based             |               |          |
       Random                 |       -       |     -    | Sampling
       n-out-of-N             |               |          |
       Random                 |       -       |     -    | Sampling
       Uniform probabilistic  |               |          |
       Random                 |       -       |    (X)   | Sampling
       Non-uniform probabil.  |               |          |
       Random                 |       -       |    (X)   | Sampling
       Non-uniform flow-state |               |          |
       Property Match         |       X       |    (X)   | Filtering
       Filtering              |               |          |
       Hash Function          |       X       |     X    | Filtering
    In the table x means that the characteristic applies to the
    selection scheme and (x) means that the characteristic only
    partly applies to the selection scheme. For instance property
    match filtering is typically based on packet content and
    therefore content dependent. But as explained in section 6.1 it
    may also depend on router state and then would be independent of
    the content.
    The categorization just introduced is mainly useful for the
    definition of an information model describing Primitive
    Selectors. More complex selection techniques can be described
    through the composition of cascaded Sampling and Filtering
    operations. For example, a packet selection that weights the
    selection probability on the basis of the packet length can be
    described as a cascade of a Filtering and a Sampling scheme.
    However, this descriptive approach is not intended to be rigid:
    if a common and consolidated selection practice turns out to be
    too complex to be described as a composition of the mentioned
    building blocks, an ad hoc description can be specified instead
    and added as a new scheme to the information model.
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 5. Sampling
    The deployment of Sampling techniques aims at the provisioning
    of information about a specific characteristic of the parent
    population at a lower cost than a full census would demand. In
    order to plan a suitable Sampling strategy it is therefore
    crucial to determine the needed type of information and the
    desired degree of accuracy in advance.
    First of all, it is important to know the type of metric that
    should be estimated. The metric of interest can range from
    simple packet counts [JePP92] up to the estimation of whole
    distributions of flow characteristics (e.g. packet
    Secondly, the required accuracy of the information and with
    this, the confidence that is aimed at, should be known in
    advance. For instance for usage-based accounting the required
    confidence for the estimation of packet counters can depend on
    the monetary value that corresponds to the transfer of one
    packet. That means that a higher confidence could be required
    for expensive packet flows (e.g. premium IP service) than for
    cheaper flows (e.g. best effort). The accuracy requirements for
    validating a previously agreed quality can also vary extremely
    with the customer demands. These requirements are usually
    determined by the service level agreement (SLA).
    The Sampling method and the parameters in use must be clearly
    communicated to all applications that use the measurement data.
    Only with this knowledge a correct interpretation of the
    measurement results can be ensured.
    Sampling methods can be characterized by the Sampling algorithm,
    the trigger type used for starting a Sampling interval and the
    length of the Sampling interval. These parameters are described
    here in detail. The Sampling algorithm describes the basic
    process for selection of samples. In accordance to [AmCa89] and
    [ClPB93] we define the following basic Sampling processes:
 5.1 Systematic Sampling
    Systematic Sampling describes the process of selecting the start
    points and the duration of the selection intervals according to
    a deterministic function. This can be for instance the periodic
    selection of every k-th element of a trace but also the
    selection of all packets that arrive at pre-defined points in
    time. Even if the selection process does not follow a periodic
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    function (e.g. if the time between the Sampling intervals varies
    over time) we consider this as systematic Sampling as long as
    the selection is deterministic.
    The use of systematic Sampling always involves the risk of
    biasing the results. If the systematics in the Sampling process
    resemble systematics in the observed stochastic process
    (occurrence of the characteristic of interest in the network),
    there is a high probability that the estimation will be biased.
    Systematics in the observed process might not be known in
    Here only equally spaced schemes are considered, where triggers
    for Sampling are periodic, either in time or in packet count.
    All packets occurring in a selection interval (either in time or
    packet count) beyond the trigger are selected.
    Systematic count-based
    In systematic count-based Sampling the start and stop triggers
    for the Sampling interval are defined in accordance to the
    spatial packet position (packet count).
    Systematic time-based
    In systematic time-based Sampling time-based start and stop
    triggers are used to define the Sampling intervals. All packets
    are selected that arrive at the Observation Point within the
    time-intervals defined by the start and stop triggers (i.e.
    arrival time of the packet is larger than the start time and
    smaller than the stop time).
    Both schemes are content-independent selection schemes. Content
    dependent deterministic Selectors are categorized as filter.
 5.2 Random Sampling
    Random Sampling selects the starting points of the Sampling
    intervals in accordance to a random process. The selection of
    elements are independent experiments. With this, unbiased
    estimations can be achieved. In contrast to systematic Sampling,
    random Sampling requires the generation of random numbers. One
    can differentiate two methods of random Sampling:
 5.2.1   n-out-of-N Sampling
    In n-out-of-N Sampling n elements are selected out of the parent
    population that consists of N elements. One example would be to
    generate n different random numbers in the range [1,N] and
    select all packets which have a packet position equal to one of
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    the random numbers. For this kind of Sampling the Sample Size n
    is fixed.
 5.2.2   Probabilistic Sampling
    In probabilistic Sampling the decision whether an element is
    selected or not is made in accordance to a pre-defined selection
    probability. An example would be to flip a coin for each packet
    and select all packets for which the coin showed the head. For
    this kind of Sampling the Sample Size can vary for different
    trials. The selection probability does not necessarily has to be
    the same for each packet. Therefore we distinguish between
    uniform probabilistic Sampling (with the same selection
    probability for all packets) and non-uniform probabilistic
    Sampling (where the selection probability can vary for different
    packets). Uniform Probabilistic Sampling
    For Uniform Probabilistic Sampling packets are selected
    independently with a uniform probability p. This Sampling can be
    count-driven, and is sometimes referred to as geometric random
    Sampling, since the difference in count between successive
    selected packets are independent random variables with a
    geometric distribution of mean 1/p. A time-driven analog,
    exponential random Sampling, has the time between triggers
    exponentially distributed.
    Both geometric and exponential random Sampling are examples of
    what is known as additive random Sampling, defined as Sampling
    where the intervals or counts between successive samples are
    independent identically distributed random variable. Non-Uniform Probabilistic Sampling
    This is a variant of Probabilistic Sampling in which the
    Sampling probabilities can depend on the selection process
    input. This can be used to weight Sampling probabilities in
    order e.g. to boost the chance of Sampling packets that are rare
    but are deemed important. Unbiased estimators for quantitative
    statistics are recovered by re-normalization of sample values;
    see [HT52]. Non-Uniform Flow State Dependent Sampling
    Another type of Sampling that can be classified as probabilistic
    Non-Uniform is closely related to the flow concept as defined in
    [RFC3917], and it is only used jointly with a flow monitoring
    function (IPFIX metering process). Packets are selected,
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    dependent on a selection state. The point, here, is that the
    selection state is determined also by the state of the flow the
    packet belongs to and/or by the state of the other flows
    currently being monitored by the associated flow monitoring
    function. An example for such an algorithm is the "sample and
    hold" method described in [EsVa01]:
    - If a packet accounts for a flow record that already exists in
       the IPFIX flow recording process, it is selected (i.e. the
       flow record is updated)
    - If a packet doesn't account to any existing flow record, it is
       selected with probability p. If it has been selected a new
       flow record has to be created.
    A further algorithm that fits into the category of non-uniform
    flow state dependent Sampling is described in [Moli03].
    This type of Sampling is content dependent because the
    identification of the flow the packet belongs to requires
    analyzing part of the packet content. If the packet is selected,
    then it is passed as an input to the IPFIX monitoring function
    (this is called "Local Export" in [PSAMP-FW]. Selecting the
    packet depending on the state of a flow cache is useful when
    memory resources of the flow monitoring function are scarce
    (i.e. there is no room to keep all the flows that have been
    scheduled for monitoring). Configuration of non-uniform probabilistic and flow-state
    Many different specific methods can be grouped under the terms
    non-uniform probabilistic and flow state Sampling. Dependent on
    the Sampling goal and the implemented scheme, a different number
    and type of input parameters is required to configure such
    Some concrete proposals for such methods exist from the research
    community (e.g. [EsVa01],[DuLT01],[Moli03]). Some of these
    proposals are still in an early stage and need further
    investigations to prove their usefulness and applicability. It
    is not our aim to indicate preference amongst these methods.
    Instead, we only describe here the basic methods and leave the
    specification of explicit schemes and their parameters up to
    vendors (e.g. as extension of the information model).
 6. Filtering
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    Filtering is the deterministic selection of packets based on the
    packet content, the treatment of the packet at the Observation
    Point, or deterministic functions of these occurring in the
    selection state. The packet is selected if these quantities fall
    into a specified range. The role of Filtering, as the word
    itself suggest, is to separate all the packets having a certain
    property from those not having it. A distinguishing
    characteristic from Sampling is that the selection decision does
    not depend on the packet position in time or in the space, or on
    a random process.
    We identify and describe in the following two Filtering
 6.1 Property Match Filtering
    With this Filtering method a packet is selected if specific
    fields within the packet and/or properties of the router state
    equal a predefined value. Possible filter fields are all IPFIX
    flow attributes specified in [RFC5102]. Further fields can be
    defined by proposing new information elements or defining vendor
    specific extensions.
    A packet is selected if Field=Value. Masks and ranges are only
    supported to the extent to which [RFC5102] allows them e.g. by
    providing explicit fields like the netmasks for source and
    destination addresses.
    AND operations are possible by concatenating filters, thus
    producing a composite selection operation.  In this case, the
    ordering in which the filtering happens is implicitly defined
    (outer filters come after inner filters).  However, as long as
    the concatenation is on filters only, the result of the cascaded
    filter is independent from the order, but the order may be
    important for implementation purposes, as the first filter will
    have to work at a higher rate.  In any case, an implementation
    is not constrained to respect the filter ordering, as long as
    the result is the same, and it may even implement the composite
    filtering in filtering in one single step.
    OR operations are not supported with this basic model.  More
    sophisticated filters (e.g. supporting bitmasks, ranges or OR
    operations etc.) can be realized as vendor specific schemes.
    All IPFIX flow attributes defined in [RFC5102] can be used for
    property match filtering. Further information elements can be
    easily defined. Typical header fields that should be supported
    for property match operations are the following:
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          (i) the IP header (excluding options in IPv4, stacked
               headers in IPv6)
         (ii) transport protocol header (e.g. TCP, UDP)
         (iii) encapsulation headers (e.g. the MPLS label stack, if
    When the PSAMP Device offers property match filtering, and, in
    its usual capacity other than in performing PSAMP functions,
    identifies or processes information from IP, transport protocol
    or encapsulation protocols, then the information should be made
    available for filtering.  For example, when a PSAMP Device
    routes based on destination IP address, that field should be
    made available for filtering.  Conversely, a PSAMP Device that
    does not route is not expected to be able to locate an IP
    address within a packet, or make it available for Filtering,
    although it may do so.
    Since packet encryption conceals the real values of encrypted
    fields, property match filtering must be configurable to ignore
    encrypted packets, when detected.
    The Selection Process may support filtering based on the
    properties of the router state:
         (i)  Ingress interface at which packet arrives equals a
               specified value
         (ii) Egress interface to which packet is routed to equals a
               specified value
         (iii) Packet violated Access Control List (ACL) on the
         (iv)  Failed Reverse Path Forwarding (RPF)
         (v)  Failed Resource Reservation (RSVP)
         (vi)  No route found for the packet
         (vii) Origin Border Gateway Protocol (BGP) Autonomous System
               (AS) [RFC4271] equals a specified value or lies within
               a given range
         (viii)Destination BGP AS equals a specified value or lies
               within a given range
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    Packets that match the Failed Reverse Path Forwarding (RPF)
    condition are packets for which ingress filtering failed as
    defined in [RFC3704].
    Packets that match the Failed Resource Reservation condition are
    packets that do not fulfill the RSVP specification as defined in
    Router architectural considerations may preclude some
    information concerning the packet treatment being available at
    line rate for selection of packets.  For example, the Selection
    Process may not be implemented in the fast path that is able to
    access routing state at line rate.  However, when filtering
    follows sampling (or some other selection operation) in a
    Composite Selector, the rate of the Packet Stream output from
    the sampler and input to the filter may be sufficiently slow
    that the filter could select based on routing state.
 6.2 Hash-based Filtering
    A Hash Function h maps the Packet Content c, or some portion of
    it, onto a Hash Range R. The packet is selected if h(c) is an
    element of S, which is a subset of R called the Hash Selection
    Range. Thus Hash-based Selection is a particular case of
    Filtering. The object is selected if c is in inv(h(S)). But for
    desirable Hash Functions the inverse image inv(h(S)) will be
    extremely complex, and hence h would not be expressible as, say,
    a Property Match Filter or a simple combination of these.
    Hash-based selection is mainly used to realize a coordinated
    packet selection. That means that the same packets are selected
    at different Observation Points. This is useful for instance to
    observe the path (trajectory) that a packet took through the
    network or to apply packet selection to passive one-way
    A pre-requisite for the method to work and to ensure
    interoperability is that the same Hash Function with the same
    parameters (e.g. input vector) is used at the observation
    A consistent packet selection is also possible with property
    match filtering. Nevertheless, hash-based selection can be used
    to approximate a random selection. The desired statistical
    properties are discussed in section 6.2.2.
    In the following subsections we give some application examples
    for coordinated packet selection.
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 6.2.1   Application Examples for Coordinated Packet Selection Trajectory Sampling
    Trajectory Sampling is the consistent selection of a subset of
    packets at either all of a set of Observation Points or none of
    them. Trajectory Sampling is realized by Hash-based Selection if
    all Observation Points in the set use a common Hash Function,
    Hash Domain and selection range. The Hash Domain comprises all
    or part of the packet content that is invariant along the packet
    path. Fields such as Time-to-Live, which is decremented per hop,
    and header CRC, which is recalculated per hop, are thus excluded
    from the Hash Domain. The Hash Domain needs to be wider than
    just a flow key, if packets are to be selected quasi-randomly
    within flows.
    The trajectory (or path) followed by a packet is reconstructed
    from PSAMP reports on it that reach a Collector. Reports on a
    given packet originating from different observations points are
    associated by matching a label from the reports. The label may
    comprise that portion invariant packet content that is reported,
    or possibly some digest of the invariant packet content that is
    inserted into the packet report at the Observation Point. Such a
    digest may be constructed by applying a second Hash Function
    (distinct from that used for selection) to the invariant packet
    content. The reconstruction of trajectories, and methods for
    dealing with possible ambiguities due to label collisions
    (identical labels reported for different packets) and potential
    loss of reports in transmission, are dealt with in [DuGr00],
    [DuGG02] and [DuGr04].
    Applications of trajectory Sampling include (i) estimation of
    the network path matrix, i.e., the traffic intensities according
    to network path, broken down by flow key; (ii) detection of
    routing loops, as indicated by self-intersecting trajectories;
    (iii) passive performance measurement: prematurely terminating
    trajectories indicate packet loss, packet one way delay can be
    determined if reports include (synchronized) timestamps of
    packet arrival at the Observation Point; (iv) network attack
    tracing, of the actual paths taken by attack packets with
    spoofed source addresses. Passive One-way Measurements
    Coordinated packet selection can be applied for instance to one-
    way delay measurements in order to reduce the required
    resources. In one-way delay measurements packets are collected
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    at different Observation Points in the network. A packet digest
    is generated for each packet that helps to identify the packet.
    The packet digest and the arrival time of the packet at the
    observation point are reported to a process that calculates the
    delay. The delay is calculated by subtracting the arrival time
    of the same packet at the observation points (e.g. [ZsZC01]).
    With high data rates, capturing all packets can require a lot of
    resources for storage, transfer and processing. To reduce
    resource consumption packet selection methods can be applied.
    But for such selection techniques it has to be ensured that the
    same packets are collected at different observation points. Generation of Pseudo-random Numbers
    Although pseudo-random number generators with well understood
    properties have been developed, they may not be the method of
    choice in settings where computational resources are scarce. A
    convenient alternative is to use Hash Functions of packet
    content as a source of randomness. The hash (suitably re-
    normalized) is a pseudo-random variate in the interval [0,1].
    Other schemes may use packet fields in iterators for pseudo-
    random numbers. However, the statistical properties of an ideal
    packet selection law (such as independent Sampling for different
    packets, or independence on packet content) may not be exactly
    rendered by an implementation, but only approximately so.
    Use of packet content to generate pseudo-random variates shares
    with Non-uniform Probabilistic Sampling (see Section
    above) the property that selection decisions depend on Packet
    Content. However, there is a fundamental difference between the
    two. In the former case the content determines pseudo-random
    variates. In the latter case the content only determines the
    selection probabilities: selection could then proceed e.g., by
    use of random variates obtained by an independent pseudo-random
    number generator.
 6.2.2   Desired Properties of Hash Functions
    Here we formulate desired properties for hash functions. For
    this we have to distinguish whether a hash function is used for
    packet selection or just as a packet digest. The main purpose of
    this document is on packet selection. Nevertheless, we also
    provide some requirements for the use of hash functions as
    packet digest.
    First of all we need to define suitable input fields from the
    packet. In accordance to [DuGr00] input field should be
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    - invariant on the path
    - variable among packets
    Only if the input fields are the same at different observation
    points it is possible to recognize the packet. The input fields
    should be variable among packets in order to distribute the hash
    results over the Selection Range. Requirements for Packet Selection
    In accordance to considerations in [MoND05] and [Henk08] we
    define the following desired properties of hash functions used
    for packet selection:
    (i) Speed: The hash function has to be applied to each packet
    that traverses the observation point. Therefore it has to be
    fast in order to cope with the high packet rates. In the ideal
    case the hash operation should not influence the performance on
    the PSAMP device.
    (ii) Uniformity: The Hash Function h should have good mixing
    properties, in the sense that small changes in the input (e.g.
    the flipping of a single bit) cause large changes in the output
    (many bits change). Then any local clump of values of c is
    spread widely over R by h, and so the distribution of h(c) is
    fairly uniform even if the distribution of c is not. Then the
    Sampling Fraction is #S/#R, which can be tuned by choice of S.
    (iii) Unbiasedness: The selection decision should be as
    independent of packet attributes as possible. The set of
    selected packets should not be biased towards a specific type of
    (iv) Representativeness of sample: The sample should be as
    representative as possible for the observed traffic.
    (v) Non-linearity: The function should not be linear. This
    increases the mixing properties (uniformity criterion). In
    addition to this it decreases the predictability of the output
    and therefore the vulnerabilities against attacks.
    (vi) Robustness against vulnerabilities: The hash function
    should be robust against attacks. Potential vulnerabilities are
    described in section 6.2.3. Requirements for Packet Digesting
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    For digesting Packet Content for inclusion in a reported label,
    the most important property is a low collision frequency. A
    secondary requirement is the ability to accept variable length
    input, in order to allow inclusion of maximal amount of packet
    as input. Execution speed is of secondary importance, since the
    digest need only be formed from selected packets.
 6.2.3   Security Considerations for Hash Functions
    A concern for Hash-based Selection is whether some large set of
    related packets could be disproportionately sampled, i.e., that
    the Attained Sampling Fraction is significantly different from
    the Configured Sampling Fraction. This can happen either
    (i)  through unanticipated behavior in the Hash Function, or
    (ii) because the packets had been deliberately crafted to have
       this property.
    The first point underlines the importance of using a Hash
    Function with good mixing properties. For this the statistical
    properties of candidate Hash Functions need to be evaluated.
    Since the hash output depends on the traffic mix, the evaluation
    should be done preferably on up-to-date packet traces from the
    network in which the hash-based selection will be deployed.
    However, hash functions which perform well on typical traffic
    may not be sufficiently strong to withstand attacks specifically
    targeted against them. Such potential attacks have been
    described in [GoRe07].
    The following we point out different potential attack scenarios.
    We encourage the use of standardized hash functions. Therefore
    we assume that the hash function itself is public and hence
    known to an attacker.
    Nevertheless, we also assume the possibility of using a private
    input parameter for the hash function that is kept secret. Such
    an input parameter can for instance be attached to the hash
    input before the hash operation is applied. With this at least
    parts of the hash operation remains secret.
    For the attack scenarios we assume that an attacker uses its
    knowledge of the hash function to craft packets which are then
    dispatched, either as the attack itself, or to elicit further
    information which can be used to refine the attack.
    Two scenarios are considered. In the first scenario, the
    attacker has no knowledge about whether the crafted packets are
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    selected or not. In the second scenario the attacker uses some
    knowledge of sampling outcomes. The means by which this might be
    acquired is discussed below. Some additional attacks that
    involve tampering with export packets in transit, as opposed to
    attacking the PSAMP device, are discussed in [GoRe07]. Vulnerabilities of Hash-based selection without knowledge
       of selection outcomes
    (i) The hash function does not use a private parameter.
    If no private input parameter is used, potential attackers can
    easily calculate which packets result in which hash values.
    If the selection range is public, an attacker can craft packets
    whose selection properties are known in advance. If the
    selection range is private, an attacker cannot determine whether
    a crafted packet is selected. However by computing the hash on
    different trial crafted packets, and selecting those yielding a
    given hash value, the attacker can construct an arbitrarily
    large set of distinct packets with a common selection
    properties, i.e., packets that will be either all selected or
    all not selected. This can be done whatever the strength of the
    hash function.
    (ii) The hash function is not cryptographically strong.
    If the hash function is not cryptographically strong, it may be
    possible to construct sequences of distinct packets with the
    common selection property even if a private parameter is used.
    An example is the standard CRC-32 hash function used with a
    private modulus (but without a private string post-pended to the
    input). It has weak mixing properties for low order bits.
    Consequently, simply by incrementing the hash input, one obtains
    distinct packets whose hashes mostly fall in a narrow range, and
    hence are likely commonly selected; see [GoRe07]
    Suitable parameterization of the hash function can make such
    attacks more difficult. For example, post-pending a private
    string to the input before hashing with CRC-32 will give
    stronger mixing properties over all bits of the input. However,
    with a hash function, such as CRC-32, that is not
    cryptographically strong, the possibility of discovering a
    method to construct packet sets with the common selected
    property cannot be ruled out, even when a private modulus or
    post-pended string is used.
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       selection outcomes
    Knowledge of the selection outcomes of crafted packets can be
    used by an attacker to more easily construct sets of packets
    which are disproportionately sampled and/or are commonly
    selected. For this the attacker does not need any a priori
    knowledge about the hash function or selection range.
    There are several ways an attacker might acquire this knowledge
    about the selection outcome:
    (i) Billing Reports: if samples are used for billing purposes,
    then the selection outcomes of packets may be able to be
    inferred by correlating a crafted packet stream with the billing
    reports that it generates. However, the rate at knowledge of
    selection outcomes can be acquired depends on the temporal and
    spatial granularity of the billing reports, being slower the
    more aggregated the reports are.
    (ii) Feedback from an Intrusion Detection System: e.g., a
    botmaster adversary learns if his packets were detected by the
    intrusion detection system by seeing if one of his bots is
    blocked by the network.
    (iii) Observation of the Report Stream: export packets sent
    across a public network may be eavesdropped on by an adversary.
    Encryption of the export packets provides only a partial
    defense, since it may be possible to infer the selection
    outcomes of packets by correlating a crafted packet stream with
    the occurrence (not the content) of packets in the export stream
    that it generates. The rate at which such knowledge could be
    acquired is limited by the temporal resolution at which reports
    can be associated with packets, e.g. due to processing and
    propagation variability, and difficulty in distinguishing report
    on attack packets from those of background traffic, if present.
    The association between packets and their reports on which this
    depends could be removed by padding export packets to a constant
    length and sending them at a constant rate.
    We now turn to attacks that can exploit knowledge of selection
    outcomes. Firstly, with a non-cryptographic hash function,
    knowledge of selection outcomes for a trial stream may be used
    to further craft a packet set with the common selection
    property. This has been demonstrated for the modular hash f(x) =
    a x + b mod k, for private parameters a, b, and k. With sampling
    rate p, knowledge of the sampling outcomes of roughly 2/p is
    sufficient for the attack to succeed, independent of the values
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    of a, b and k. With knowledge of the selection outcomes of a
    larger number of packets, the parameters a b and k can be
    determined; see [GoRe07].
    A cryptographic hash function employing a private parameter and
    operating in one of the pseudo-random function modes specified
    above is not vulnerable to these attacks, even if the selection
    range is known. Vulnerabilities to Replay Attacks
    Since hash-based selection is deterministic, any packet or set
    of packets with known selection properties can be replayed into
    a network and experience the same selection outcomes provide the
    hash function and its parameters are not changed. Repetition of
    a single packet may be noticeable to other measurement methods
    if employed (e.g. collection of flow statistics), whereas a set
    of distinct packets that appears statistically similar to
    regular traffic may be less noticeable.
    Replay attacks may be mitigated by repeated changing of hash
    function parameters. This also prevents attacks that exploit
    knowledge of sampling outcomes, at least if the parameters are
    changed at least as fast as the knowledge can be acquired by an
    attacker. In order to preserve the ability to perform Trajectory
    Sampling, parameter changed would have to be simultaneous (or
    approximately so) across all observation point.
 6.2.4   Choice of Hash-Function
    The specific choice of hash function represents a trade-off
    between complexity and ease of implementation. Ideally, a
    cryptographically strong hash function employing a private
    parameter and operating in pseudo-random function mode as
    specified above would be used, yielding a good emulation a
    random packet selection at a target sampling rate, and giving
    maximal robustness against the attacks described in the previous
    section. Unfortunately there is currently no single hash
    function that fulfills all the requirements.
    As detailed in section 6.2.3, only cryptographic hash functions
    employing a private parameter operating in pseudo-random
    function mode are sufficiently strong to withstand the range of
    conceivable attacks. For example, fixed or variable length
    inputs could be hashed using a block cipher (like AES) in
    cipher-block-chaining mode.  Fixed length inputs could also be
    hashed using an iterated cryptographic hash function (like MD5
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    or SHA1), with a private initial vector.  For variable length
    inputs, iterated cryptographic hash function (like MD5 or SHA1)
    should employ private string post-pended to the data in addition
    to a private initial vector. For more details, see the "append-
    cascade" construction of [BeCK96]. We encourage the use of such
    cryptographically strong hash function wherever possible.
    However, a problem with using such function is the low
    performance. As shown for instance in [Henk08], the computation
    time for MD5 and SHA are about 7-10 times higher compared to
    non-cryptographic functions. The difference increases for small
    hash input lengths.
    Therefore it is not assumed that all PSAMP devices will be
    capable of applying a cryptographically strong hash function to
    every packet at line rate. For this reason, the hash functions
    listed in this section will be of a weaker variety. Future
    protocol extensions that employ stronger hash functions are
    highly welcome.
    Comparisons of hash-functions for packet selection and packet
    digesting with regard to various criteria can be found in
    [MoND05] and [Henk08]. Hash Functions for Packet Selection
    If hash-based packet selection is applied, the BOB function MUST
    be used for packet selection operations in order to be compliant
    with PSAMP. The specification of BOB is given in the appendix.
    Both the parameter (the init value) and the selection range
    should be kept private. The initial vector of the hash function
    MUST be configurable out of band to prevent security breaches
    like exposure of the initial vector content.
    Other functions, such as CRC-32 and IPSX MAY be used.  The IPSX
    function is described in the appendix, the CRC-32 function is
    described in [RFC1141]. If CRC-32 is used, the input should
    first be post-pended with a private string that acts as a
    parameter, and the modulus of the CRC should also be kept
    IPSX is simple to implement and was correspondingly about an
    order of magnitude faster to execute per packet than BOB or CRC-
    32 [MoND05].
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    All three hash functions evaluated showed relatively poor
    uniformity with 16 byte input that was drawn from only invariant
    fields in the IP and TCP/UDP headers (i.e. header fields that do
    not change from hop to hop). IPSX is inherently limited to 16
    BOB and CRC-32 exhibits noticeably better uniformity when 4 or
    more bytes from the payload are also included in the input
    [MoND05].  Also with other criteria BOB performed quite well
    Although the characteristics have been checked for different
    traffic traces, results cannot be generalized to arbitrary
    traffic. Since hash-based selection is a deterministic function
    on the packet content, it can always be biased towards packets
    with specific attributes. Furthermore, it should be noted that
    all Hash Functions were evaluated only for IPv4.
    None of these hash functions is recommended for cryptographic
    purposes. Please also note that the use of a private parameter
    only slightly reduces the vulnerabilities against attacks. As
    shown in section 6.2.3. functions that are not cryptographically
    strong (e.g., BOB and CRC) cannot prevent attackers from
    crafting packets that are disproportionally selected even if a
    private parameter is used and the selection range is kept
    As described in section 6.2.2 the input bytes for the Hash
    Function need to be invariant along the path the packet is
    traveling. Only with this it is ensured that the same packets
    are selected at different observation points. Furthermore they
    should have a high variability between different packets to
    generate a high variation in the Hash Range. An evaluation of
    the variability of different packet header fields can be found
    in [DuGr00], [HeSZ08] and [Henk08].
    If a hash-based selection with the BOB function is used with
    IPv4 traffic, the following input bytes MUST be used.
    - IP identification field
    - Flags field
    - Fragment offset
    - Source IP address
    - Destination IP address
    - A configurable number of bytes from the IP payload, starting
       at a configurable offset.
    Due to the lack of suitable IPv6 packet traces, all candidate
    Hash Functions in [DuGr00], [MoND05] and [Henk08] were evaluated
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    only for IPv4. Due to the IPv6 header fields and address
    structure it is expected that there is less randomness in IPv6
    packet headers than in IPv4 headers. Nevertheless, the
    randomness of IPv6 traffic has not yet been evaluated
    sufficiently to get any evidence. In addition to this, IPv6
    traffic profiles may change significantly in future when IPv6 is
    used by a broader community.
    If a hash-based selection with the BOB function is used with
    IPv6 traffic, the following input bytes MUST be used.
    - Payload length (2 bytes)
    - Byte number 10,11,14,15,16 of the IPv6 source address
    - Byte number 10,11,14,15,16 of the IPv6 destination address
    - A configurable number of bytes from the IP payload, starting
       at a configurable offset. It is recommended to use at least 4
       bytes from the IP payload.
    The payload itself is not changing during the path. Even if some
    routers process some extension headers they are not going to
    strip them from the packet. Therefore the payload length is
    invariant along the path. Furthermore it usually differs for
    different packets. The IPv6 address has 16 bytes. The first part
    is the network part and it contains low variation. The second
    part is the host part and contains higher variation. Therefore
    the second part of the address is used. Nevertheless, the
    uniformity has not been checked for IPv6 traffic. Hash Functions Suitable for Packet Digesting
    For this purpose also the BOB function SHOULD be used. Other
    functions (such as CRC-32) MAY be used. Among the functions
    capable of operating with variable length input BOB and CRC-32
    have the fastest execution, BOB being slightly faster. IPSX is
    not recommended for digesting because it has a significantly
    higher collision rate and takes only a fixed length input.
 7. Parameters for the Description of Selection Techniques
    This section gives an overview of different alternative
    selection schemes and their required parameters. In order to be
    compliant with PSAMP at least one of proposed schemes MUST be
    The decision whether to select a packet or not is based on a
    function which is performed when the packet arrives at the
    selection process. Packet selection schemes differ in the input
    parameters for the selection process and the functions they
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    require to do the packet selection. The following table gives an
         Scheme       |   input parameters     |     functions
        systematic    |    packet position     |  packet counter
        count-based   |    Sampling pattern    |
        systematic    |      arrival time      |  clock or timer
        time-based    |     Sampling pattern   |
        random        |  packet position       |  packet counter,
        n-out-of-N    |  Sampling pattern      |  random numbers
                      | (random number list)   |
        uniform       |        Sampling        |  random function
        probabilistic |      probability       |
        non-uniform   |e.g. packet position,   | selection function,
        probabilistic |  packet content(parts) |  probability calc.
        non-uniform   |e.g. flow state,        | selection function,
        flow-state    |  packet content(parts) |  probability calc.
        property      | packet content(parts)  |  filter function or
        match         | or router state        |  state discovery
        hash-based    |  packet content(parts) |  Hash Function
 7.1 Description of Sampling Techniques
    In this section we define what elements are needed to describe
    the most common Sampling techniques. Here the selection function
    is pre-defined and given by the Selector ID.
    Sampler Description:
    Unique ID for the packet sampler.
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    For Sampling processes the SELECTOR TYPE defines what Sampling
    algorithm is used.
    Values: Systematic Count-based | Systematic Time-based | Random
    n-out-of-N | Uniform Probabilistic | Non-uniform Probabilistic |
    Non-uniform Flow-state
    For Sampling processes the SELECTOR PARAMETERS define the input
    parameters for the process. Interval length in systematic
    Sampling means, that all packets that arrive in this interval
    are selected. The spacing parameter defines the spacing in time
    or number of packets between the end of one Sampling interval
    and the start of the next succeeding interval.
    Case n out of N:
       - Population size N, Sample size n
    Case Systematic Time Based:
       - Interval length (in usec), Spacing (in usec)
    Case Systematic Count Based:
       - Interval length(in packets), Spacing (in packets)
    Case Uniform Probabilistic (with equal probability per packet):
       - Sampling probability p
    Case Non-uniform Probabilistic:
       - Calculation function for Sampling probability p (see also
    Case flow state:
       - Information reported for flow state sampling are not
          defined in this document (see also section
 7.2 Description of Filtering Techniques
    In this section we define what elements are needed to describe
    the most common Filtering techniques. The structure closely
    parallels the one presented for the Sampling techniques.
    Filter Description:
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    Unique ID for the packet filter. The ID can be calculated under
    consideration of the SELECTION SEQUENCE and a local ID.
    For Filtering processes the SELECTOR TYPE defines what Filtering
    type is used.
    Values: Matching | Hashing | Router_state
    For Filtering processes the SELECTOR PARAMETERS define formally
    the common property of the packet being filtered. For the
    filters of type Matching and Hashing the definitions have a lot
    of points in common.
    Case Matching
       - Information Element (from [RFC5102])
       - Value (type in accordance to [RFC5102])
    In case of multiple match criteria, multiple "case matching"
    have to be bound by a logical AND.
    Case Hashing:
       - Hash Domain (Input bits from packet)
            - <Header type = IPv4>
            - <Input bit specification, header part>
            - <Header type =  IPv6>
            - <Input bit specification, header part>
            - <payload byte number N>
            - <Input bit specification, payload part>
       - Hash Function
            - Hash function name
            - Length of input key (eliminate 0x bytes)
            - Output value (length M and bitmask)
            - Hash Selection Range, as a list of non overlapping
              intervals [start value, end value] where value is in
            - Additional parameters dependent on specific Hash
              Function (e.g. hash input bits (seed))
    Notes to input bits for Case Hashing:
       - Input bits can be from header part only, from the payload
          part only or from both.
       - The bit specification, for the header part, can be
          specified for IPv4 or IPv6 only, or both
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       - In case of IPv4, the bit specification is a sequence of 20
          Hexadecimal numbers [00,FF] specifying a 20 bytes bitmask
          to be applied to the header.
       - In case of IPv6, it is a sequence of 40 Hexadecimal numbers
          [00,FF] specifying a 40 bytes bitmask to be applied to the
       - The bit specification, for the payload part, is a sequence
          of Hexadecimal numbers [00,FF] specifying the bitmask to be
          applied to the first N bytes of the payload, as specified
          by the previous field. In case the Hexadecimal number
          sequence is longer than N, only the first N numbers are
       - In case the payload is shorter than N, the Hash Function
          cannot be applied. Other options, like padding with zeros,
          may be considered in the future.
       - A Hash Function cannot be defined on the options field of
          the IPv4 header, neither on stacked headers of IPv6.
       - The Hash Selection Range defines a range of hash-values
          (out of all possible results of the Hash-Operation). If the
          hash result for a specific packet falls in this range, the
          packet is selected. If the value is outside the range, the
          packet is not selected. E.g. if the selection interval
          specification is [1:3], [6:9] all packets are selected for
          which the hash result is 1,2,3,6,7,8, or 9. In all other
          cases the packet is not selected.
    Case Router State:
       - Ingress interface at which the packet arrives equals a
          specified value
       - Egress interface to which the packet is routed equals a
          specified value
       - Packet violated Access Control List (ACL) on the router
       - Reverse Path Forwarding (RPF) failed for the packet
       - Resource Reservation is insufficient for the packet
       - No route found for the packet
       - Origin AS equals a specified value or lies within a given
       - Destination AS equals a specified value or lies within a
          given range
    Note to Case Router State:
       - All Router state entries can be linked by AND operators
 8. Composite Techniques
    Composite schemes are realized by combining the selector IDs
    into a Selection Sequence. The Selection Sequence contains all
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    selector IDs that are applied to the packet stream subsequently.
    Some examples of composite schemes are reported below.
 8.1 Cascaded Filtering->Sampling or Sampling->Filtering
    If a filter precedes a Sampling process the role of Filtering is
    to create a set of "parent populations" from a single stream
    that can then be fed independently to different Sampling
    functions, with different parameters tuned for the population
    itself (e.g. if streams of different intensity result from
    Filtering, it may be good to have different Sampling rates). If
    Filtering follows a Sampling process, the same Sampling Fraction
    and type is applied to the whole stream, independently of the
    relative size of the streams resulting from the Filtering
    function. Moreover, also packets not destined to be selected in
    the Filtering operation will "load" the Sampling function. So,
    in principle, Filtering before Sampling allows a more accurate
    tuning of the Sampling procedure, but if filters are too complex
    to work at full line rate (e.g. because they have to access
    router state information), Sampling before Filtering may be a
 8.2 Stratified Sampling
    Stratified Sampling is one example for using a composite
    technique. The basic idea behind stratified Sampling is to
    increase the estimation accuracy by using a-priori information
    about correlations of the investigated characteristic with some
    other characteristic that is easier to obtain. The a-priori
    information is used to perform an intelligent grouping of the
    elements of the parent population. In this manner, a higher
    estimation accuracy can be achieved with the same Sample Size or
    the Sample Size can be reduced without reducing the estimation
    Stratified Sampling divides the Sampling process into multiple
    steps. First, the elements of the parent population are grouped
    into subsets in accordance to a given characteristic. This
    grouping can be done in multiple steps. Then samples are taken
    from each subset.
    The stronger the correlation between the characteristic used to
    divide the parent population (stratification variable) and the
    characteristic of interest (for which an estimate is sought
    after), the easier is the consecutive Sampling process and the
    higher is the stratification gain. For instance, if the dividing
    characteristic were equal to the investigated characteristic,
    each element of the sub-group would be a perfect representative
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    of that characteristic. In this case it would be sufficient to
    take one arbitrary element out of each subgroup to get the
    actual distribution of the characteristic in the parent
    population. Therefore stratified Sampling can reduce the costs
    for the Sampling process (i.e. the number of samples needed to
    achieve a given level of confidence).
    For stratified Sampling one has to specify classification rules
    for grouping the elements into subgroups and the Sampling scheme
    that is used within the subgroups. The classification rules can
    be expressed by multiple filters. For the Sampling scheme within
    the subgroups the parameters have to be specified as described
    above. The use of stratified Sampling methods for measurement
    purposes is described for instance in [ClPB93] and [Zseb03].
 9. Security Considerations
    Security considerations concerning the choice of sampling hash
    function have been discussed in Section 6.2.2. That section
    discussed a number of potential attacks to craft packet streams
    which are disproportionately detected and/or discover the hash
    function parameters, the vulnerabilities of different hash
    functions to these attacks, and practices to minimize these
    In addition to this a user can gains knowledge about the start
    and stop triggers in time-based systematic sampling e.g. by
    sending test packets. This knowledge might allow users to modify
    their send schedule in a way that their packets are
    disproportionately selected or not selected [GoRe07].
    For random sampling cryptographically-strong random number
    generator should be used in order to prevent that an advisory
    can predict the selection decision [GoRe07].
    Further security threats can occur when sampling parameters are
    configured or communicated to other entities. The configuration
    and reporting of sampling parameters are out of scope of this
    document. Therefore the security threats that originate from
    this kind of communication cannot be assessed with the
    information given in this document.
    Some of these threats can probably be addressed by keeping
    configuration information confidential and by authenticating
    entities that configure sampling. Nevertheless a full analysis
    and assessment of threats for configuration and reporting has to
    be done if configuration or reporting methods are proposed.
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 10. Acknowledgements
    We would like to thank the PSAMP group, especially Benoit Claise
    and Stewart Bryant, for fruitful discussions and for
    proofreading the document. We thank Sharon Goldberg for her
    input on security issues concerning hash-based selection.
 11. IANA Considerations
    This document has no actions for IANA.
 12. Normative References
    [RFC2119]   Bradner, S., Key words for use in RFCs to Indicate
                 Requirement Levels, BCP 14, RFC 2119, March 1997
 13. Informative References
    [AmCa89]    Paul D. Amer, Lillian N. Cassel, "Management of
                 Sampled Real-Time Network Measurements", 14th
                 Conference on Local Computer Networks, October
                 1989, Minneapolis, pages 62-68, IEEE, 1989.
    [BeCK96]    M. Bellare, R. Canetti and H. Krawczyk,
                 "Pseudorandom Functions Revisited: The Cascade
                 Construction and its Concrete Security", Symposium
                 on Foundations of Computer Science, 1996.
    [ClPB93]    K.C. Claffy, George C. Polyzos, Hans-Werner Braun,
                 "Application of Sampling Methodologies to Network
                 Traffic Characterization", Proceedings of ACM
                 SIGCOMM'93, San Francisco, CA, USA, September 13 -
                 17, 1993.
    [DuGG02]    N.G. Duffield, A. Gerber, M. Grossglauser,
                 "Trajectory Engine: A Backend for Trajectory
                 Sampling", IEEE Network Operations and Management
                 Symposium 2002, Florence, Italy, April 15-19, 2002.
    [DuGr00]    N.G. Duffield, M. Grossglauser, "Trajectory
                 Sampling for Direct Traffic Observation",
                 Proceedings of ACM SIGCOMM 2000, Stockholm, Sweden,
                 August 28 - September 1, 2000.
    [DuGr04]    N. G. Duffield and M. Grossglauser "Trajectory
                 Sampling with Unreliable Reporting", Proc IEEE
                 Infocom 2004, Hong Kong, March 2004.
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    [DuLT01]    N.G. Duffield, C. Lund, and M. Thorup, "Charging
                 from Sampled Network Usage", ACM Internet
                 Measurement Workshop IMW 2001, San Francisco, USA,
                 November 1-2, 2001.
    [EsVa01]    C. Estan and G. Varghese, "New Directions in
                 Traffic Measurement and Accounting", ACM SIGCOMM
                 Internet Measurement Workshop 2001, San Francisco
                 (CA) Nov. 2001.
    [GoRe07]    S. Goldberg, J. Rexford, "Security Vulnerabilities
                 and Solutions for Packet Sampling", IEEE Sarnoff
                 Symposium, Princeton, NJ, May 2007.
    [HT52]      D.G. Horvitz and D.J. Thompson, "A Generalization
                 of Sampling without replacement from a Finite
                 Universe" J. Amer. Statist. Assoc. Vol. 47, pp.
                 663-685, 1952.
    [Henk08]    Christian Henke, Evaluation of Hash Functions for
                 Multipoint Sampling in IP Networks, Diploma Thesis,
                 TU Berlin, April 2008.
    [HeSZ08]    Christian Henke, Carsten Schmoll, Tanja Zseby,
                 Evaluation of Header Field Entropy for Hash-Based
                 Packet Selection, Proceedings of Passive and Active
                 Measurement Conference PAM 2008, Cleveland, Ohio,
                 USA, April 2008.
    [RFC5102]   J. Quittek, S. Bryant, B. Claise, P. Aitken, J.
                 Meyer, "Information Model for IP Flow Information
                 Export", RFC 5102, January 2008.
    [RFC5101]   B. Claise (Editor) "Specification of the IPFIX
                 Protocol for the Exchange of IP Traffic Flow
                 Information", RFC 5101, January 2008.
    [Jenk97]    B. Jenkins, "Algorithm Alley", Dr. Dobb's Journal,
                 September 1997.
    [JePP92]    Jonathan Jedwab, Peter Phaal, Bob Pinna, "Traffic
                 Estimation for the Largest Sources on a Network,
                 Using Packet Sampling with Limited Storage", HP
                 technical report, Managemenr, Mathematics and
                 Security Department, HP Laboratories, Bristol,
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                 March 1992,
    [Moli03]    M.Molina, "A scalable and efficient methodology for
                 flow monitoring in the Internet", International
                 Teletraffic Congress (ITC-18), Berlin, Sep. 2003
    [MoND05]    M. Molina, S.Niccolini, N.G.Duffield "A Comparative
                 Experimental Study of Hash Functions Applied to
                 Packet Sampling" International Teletraffic Congress
                 (ITC-19), Beijing, August 2005.
    [PSAMP-FW]  Nick Duffield (Ed.), "A Framework for Packet
                 Selection and Reporting", RFC XXXX [currently
                 Internet Draft draft-ietf-psamp-framework-11, work
                 in progress, May 2007].
    [PSAMP-INFO] T. Dietz, F. Dressler, G. Carle, B. Claise,
                 "Information Model for Packet Sampling Exports",
                 RFC XXXX. [Currently Internet Draft, draft-ietf-
                 psamp-info-06, June 2007]
    [PSAMP-PROTO] B. Claise (Ed.), "Packet Sampling (PSAMP) Protocol
                 Specifications", RFC XXXX. [Currently Internet
                 Draft draft-ietf-psamp-protocol-07.txt, work in
                 progress, October 2006].
    [RFC1141]   T. Mallory, A. Kullberg, "Incremental Updating of
                 the Internet Checksum", RFC 1141, January 1990
                 (updated by RFC1624).
    [RFC1624]   A. Rijsinghani, Computation of the Internet
                 Checksum via Incremental Update, RFC1624, May 1994
    [RFC2205]   R. Braden (Ed.), L. Zhang, S. Berson, S. Herzog, S.
                 Jamin, Resource ReSerVation Protocol (RSVP) -
                 Version 1 Functional Specification, RFC2205,
                 September 1997
    [RFC3704]   F. Baker, P. Savola, Ingress Filtering for
                 Multihomed Networks, RFC3704, March 2004
    [RFC3917]   J. Quittek, T. Zseby, B. Claise, S. Zander,
                 "Requirements for IP Flow Information Export", RFC
                 3917, October 2004.
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    [RFC4271]   Y. Rekhter, T. Li, S. Hares, "A Border Gateway
                 Protocol 4 (BGP-4)", RFC 4271, January 2006.
    [Zseb03]    T. Zseby, "Stratification Strategies for Sampling-
                 based Non-intrusive Measurement of One-way Delay",
                 Proceedings of Passive and Active Measurement
                 Workshop (PAM 2003), La Jolla, CA, USA, pp. 171-
                 179, April 2003.
    [ZsZC01]    Tanja Zseby, Sebastian Zander, Georg Carle.
                 Evaluation of Building Blocks for Passive One-way-
                 delay Measurements. Proceedings of Passive and
                 Active Measurement Workshop (PAM 2001), Amsterdam,
                 The Netherlands, April 23-24, 2001.
 14. Authors' Addresses
    Tanja Zseby
    Fraunhofer Institute for Open Communication Systems
    Kaiserin-Augusta-Allee 31
    10589 Berlin
    Phone: +49-30-34 63 7153
    Email: tanja.zseby@fokus.fraunhofer.de
    Maurizio Molina
    City House
    126-130 Hills Road
    Cambridge CB21PQ
    United Kingdom
    Phone: +44 1223 371 300
    Email: maurizio.molina@dante.org.uk
    Nick Duffield
    AT&T Labs - Research
    Room B-139
    180 Park Ave
    Florham Park NJ 07932, USA
    Phone: +1 973-360-8726
    Email: duffield@research.att.com
    Saverio Niccolini
    Network Laboratories, NEC Europe Ltd.
    Kurfuerstenanlage 36
    69115 Heidelberg
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    Phone: +49-6221-9051118
    Email:  saverio.niccolini@netlab.nec.de
    Fredric Raspall
    Dept. of Telematics
    Av. del Canal Olimpic, s/n
    Edifici C4
    E-08860 Castelldefels, Barcelona
    Email: fredi@entel.upc.es
 15. Contributors
    Sharon Goldberg contributed to the security considerations
    for hash-based selection.
    Sharon Goldberg
    Department of Electrical Engineering
    Princeton University
    F210-K EQuad
    Princeton, NJ 08544, USA
    Email: goldbe@princeton.edu
 16. Intellectual Property Statement
    The IETF has been notified of intellectual property rights
    claimed in regard to some or all of the specification contained
    in this document. For more information consult the online list
    of claimed rights.
    The IETF takes no position regarding the validity or scope of
    any Intellectual Property Rights or other rights that might be
    claimed to pertain to the implementation or use of the
    technology described in this document or the extent to which any
    license under such rights might or might not be available; nor
    does it represent that it has made any independent effort to
    identify any such rights.  Information on the procedures with
    respect to rights in RFC documents can be found in BCP 78 and
    BCP 79.
    Copies of IPR disclosures made to the IETF Secretariat and any
    assurances of licenses to be made available, or the result of an
    attempt made to obtain a general license or permission for the
    use of such proprietary rights by implementers or users of this
    specification can be obtained from the IETF on-line IPR
    repository at http://www.ietf.org/ipr.
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    The IETF invites any interested party to bring to its attention
    any copyrights, patents or patent applications, or other
    proprietary rights that may cover technology that may be
    required to implement this standard. Please address the
    information to the IETF at ietf-ipr@ietf.org.
 17. Copyright Statement
    Copyright (C) The IETF Trust (2008).
    This document is subject to the rights, licenses and
    restrictions contained in BCP 78, and except as set forth
    therein, the authors retain all their rights.
 18. Disclaimer
    This document and the information contained herein are provided
 Appendix A: Hash Functions
 A.1 IP Shift-XOR (IPSX) Hash Function
    The IPSX Hash Function is tailored for acting on IP version 4
    packets. It exploits the structure of IP packet and in
    particular the variability expected to be exhibited within
    different fields of the IP packet in order to furnish a hash
    value with little apparent correlation with individual packet
    fields. Fields from the IPv4 and TCP/UDP headers are used as
    input. The IPSX Hash Function uses a small number of simple
    Input parameters: None
    Built-in parameters: None
    Output: The output of the IPSX is a 16 bit number
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    The functioning can be divided into two parts: input selection,
    which forms are composite input from various portions of the IP
    packet, followed by computation of the hash on the composite.
    Input Selection:
    The raw input is drawn from the first 20 bytes of the IP packet
    header and the first 8 bytes of the IP payload. If IP options
    are not used, the IP header has 20 bytes, and hence the two
    portions adjoin and comprise the first 28 bytes of the IP
    packet. We now use the raw input as 4 32-bit subportions of
    these 28 bytes. We specify the input by bit offsets from the
    start of IP header or payload.
    f1 = bits 32 to 63 of the IP header, comprising the IP
         identification field, flags, and fragment offset.
    f2 = bits 96 to 127 of the IP header, the source IP address.
    f3 = bits 128 to 159 of the IP header, the destination IP
    f4 = bits 32 to 63 of the IP payload. For a TCP packet, f4
         comprises the TCP sequence number followed by the message
         length. For a UDP packet f4 comprises the UDP checksum.
    Hash Computation:
    The hash is computed from f1, f2, f3 and f4 by a combination of
    XOR (^), right shift (>>) and left shift (<<) operations. The
    intermediate quantities h1, v1, v2 are 32-bit numbers.
           1.    v1 = f1 ^ f2;
           2.    v2 = f3 ^ f4;
           3.    h1 = v1 << 8;
           4.    h1 ^= v1 >> 4;
           5.    h1 ^= v1 >> 12;
           6.    h1 ^= v1 >> 16;
           7.    h1 ^= v2 << 6;
           8.    h1 ^= v2 << 10;
           9.    h1 ^= v2 << 14;
           10.   h1 ^= v2 >> 7;
    The output of the hash is the least significant 16 bits of h1.
 A.2 BOB Hash Function
    The BOB Hash Function is a Hash Function designed for having
    each bit of the input affecting every bit of the return value
    and using both 1-bit and 2-bit deltas to achieve the so called
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    avalanche effect [Jenk97]. This function was originally built
    for hash table lookup with fast software implementation.
    Input Parameters:
    The input parameters of such a function are:
    - the length of the input string (key) to be hashed, in bytes.
    The elementary input blocks of Bob hash are the single bytes,
    therefore no padding is needed.
    - an init value (an arbitrary 32-bit number).
    Built in parameters:
    The Bob Hash uses the following built-in parameter:
    - the golden ratio (an arbitrary 32-bit number used in the hash
    function computation: its purpose is to avoid mapping all zeros
    to all zeros);
    Note: the mix sub-function (see mix (a,b,c) macro in the
    reference code in 3.2.4) has a number of parameters governing
    the shifts in the registers. The one presented is not the only
    possible choice.
    It is an open point whether these may be considered additional
    built-in parameters to specify at function configuration.
    The output of the BOB function is a 32-bit number. It should be
    - A 32 bit mask to apply to the output
    - The selection range as a list of non overlapping intervals
    [start value, end value] where value is in [0,2^32]
    The hash value is obtained computing first an initialization of
    an internal state (composed of 3 32-bit numbers, called a, b, c
    in the reference code below), then, for each input byte of the
    key the internal state is combined by addition and mixed using
    the mix sub-function. Finally, the internal state mixed one last
    time and the third number of the state (c) is chosen as the
    return value.
    typedef unsigned long int  ub4;   /* unsigned 4-byte quantities
    typedef unsigned      char ub1;   /* unsigned 1-byte quantities
    #define hashsize(n) ((ub4)1<<(n))
    #define hashmask(n) (hashsize(n)-1)
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    /* ------------------------------------------------------
      mix -- mix 3 32-bit values reversibly.
      For every delta with one or two bits set, and the deltas of
    all three high bits or all three low bits, whether the original
    value of a,b,c is almost all zero or is uniformly distributed,
      * If mix() is run forward or backward, at least 32 bits in
    a,b,c have at least 1/4 probability of changing.
      * If mix() is run forward, every bit of c will change between
    1/3 and 2/3 of the time.  (Well, 22/100 and 78/100 for some 2-
    bit deltas.) mix() was built out of 36 single-cycle latency
    instructions in a structure that could supported 2x parallelism,
    like so:
            a -= b;
            a -= c; x = (c>>13);
            b -= c; a ^= x;
            b -= a; x = (a<<8);
            c -= a; b ^= x;
            c -= b; x = (b>>13);
    Unfortunately, superscalar Pentiums and Sparcs can't take
    advantage of that parallelism.  They've also turned some of
    those single-cycle latency instructions into multi-cycle latency
      #define mix(a,b,c)  \
      { \
        a -= b; a -= c; a ^= (c>>13); \
        b -= c; b -= a; b ^= (a<<8); \
        c -= a; c -= b; c ^= (b>>13); \
        a -= b; a -= c; a ^= (c>>12);  \
        b -= c; b -= a; b ^= (a<<16); \
        c -= a; c -= b; c ^= (b>>5); \
        a -= b; a -= c; a ^= (c>>3);  \
        b -= c; b -= a; b ^= (a<<10); \
        c -= a; c -= b; c ^= (b>>15); \
      /* -----------------------------------------------------------
    hash() -- hash a variable-length key into a 32-bit value
    k       : the key (the unaligned variable-length array of bytes)
    len     : the length of the key, counting by bytes
    initval : can be any 4-byte value
    Returns a 32-bit value.  Every bit of the key affects every bit
    of the return value.  Every 1-bit and 2-bit delta achieves
    avalanche. About 6*len+35 instructions.
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    The best hash table sizes are powers of 2.  There is no need to
    do mod a prime (mod is sooo slow!).  If you need less than 32
    bits, use a bitmask.  For example, if you need only 10 bits, do
    h = (h & hashmask(10));
    In which case, the hash table should have hashsize(10) elements.
    If you are hashing n strings (ub1 **)k, do it like this:
    for (i=0, h=0; i<n; ++i) h = hash( k[i], len[i], h);
    By Bob Jenkins, 1996.  bob_jenkins@burtleburtle.net.  You may
    use this code any way you wish, private, educational, or
    commercial.  It's free. See
    Use for hash table lookup, or anything where one collision in
    2^^32 is acceptable.  Do NOT use for cryptographic purposes.
     ----------------------------------------------------------- */
      ub4 bob_hash(k, length, initval)
      register ub1 *k;        /* the key */
      register ub4  length;   /* the length of the key */
      register ub4  initval;  /* an arbitrary value */
         register ub4 a,b,c,len;
         /* Set up the internal state */
         len = length;
         a = b = 0x9e3779b9; /*the golden ratio; an arbitrary value
         c = initval;         /* another arbitrary value */
    /*------------------------------------ handle most of the key */
         while (len >= 12)
            a += (k[0] +((ub4)k[1]<<8) +((ub4)k[2]<<16)
            b += (k[4] +((ub4)k[5]<<8) +((ub4)k[6]<<16)
            c += (k[8] +((ub4)k[9]<<8)
            k += 12; len -= 12;
         /*---------------------------- handle the last 11 bytes */
         c += length;
         switch(len)       /* all the case statements fall through*/
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 Internet Draft  Techniques for IP Packet Selection   July 2008
         case 11: c+=((ub4)k[10]<<24);
         case 10: c+=((ub4)k[9]<<16);
         case 9 : c+=((ub4)k[8]<<8);
            /* the first byte of c is reserved for the length */
         case 8 : b+=((ub4)k[7]<<24);
         case 7 : b+=((ub4)k[6]<<16);
         case 6 : b+=((ub4)k[5]<<8);
         case 5 : b+=k[4];
         case 4 : a+=((ub4)k[3]<<24);
         case 3 : a+=((ub4)k[2]<<16);
         case 2 : a+=((ub4)k[1]<<8);
         case 1 : a+=k[0];
           /* case 0: nothing left to add */
         /*-------------------------------- report the result */
         return c;
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