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6TiSCH Working Group                                           M. Tiloca
Internet-Draft                                                   RISE AB
Intended status: Standards Track                            S. Duquennoy
Expires: December 12, 2019                             Yanzi Networks AB
                                                                 G. Dini
                                                      University of Pisa
                                                           June 10, 2019


     Robust Scheduling against Selective Jamming in 6TiSCH Networks
                draft-tiloca-6tisch-robust-scheduling-02

Abstract

   This document defines a method to generate robust TSCH schedules in a
   6TiSCH (IPv6 over the TSCH mode of IEEE 802.15.4-2015) network, so as
   to protect network nodes against selective jamming attack.  Network
   nodes independently compute the new schedule at each slotframe, by
   altering the one originally available from 6top or alternative
   protocols, while preserving a consistent and collision-free
   communication pattern.  This method can be added on top of the
   minimal security framework for 6TiSCH.

Status of This Memo

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

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

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

   This Internet-Draft will expire on December 12, 2019.

Copyright Notice

   Copyright (c) 2019 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (https://trustee.ietf.org/license-info) in effect on the date of



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   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
   to this document.  Code Components extracted from this document must
   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
     1.1.  Terminology . . . . . . . . . . . . . . . . . . . . . . .   3
   2.  Properties of TSCH that Simplify Selective Jamming  . . . . .   4
   3.  Selective Jamming Attack  . . . . . . . . . . . . . . . . . .   5
     3.1.  Adversary Model . . . . . . . . . . . . . . . . . . . . .   5
     3.2.  Attack Example  . . . . . . . . . . . . . . . . . . . . .   6
   4.  Building Robust Schedules . . . . . . . . . . . . . . . . . .   7
   5.  Adaptation to the 6TiSCH Minimal Security Framework . . . . .   9
     5.1.  Error Handling  . . . . . . . . . . . . . . . . . . . . .  10
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .  10
     6.1.  Effectiveness of Schedule Shuffling . . . . . . . . . . .  11
     6.2.  Renewal of Key Material . . . . . . . . . . . . . . . . .  11
     6.3.  Static Timeslot Allocations . . . . . . . . . . . . . . .  11
     6.4.  Network Joining Through Randez-vous Cells . . . . . . . .  12
   7.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  12
     7.1.  Permutation Key Set . . . . . . . . . . . . . . . . . . .  12
     7.2.  Permutation Cipher  . . . . . . . . . . . . . . . . . . .  13
   8.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  13
     8.1.  Normative References  . . . . . . . . . . . . . . . . . .  13
     8.2.  Informative References  . . . . . . . . . . . . . . . . .  14
   Appendix A.  Test Vector  . . . . . . . . . . . . . . . . . . . .  14
     A.1.  Detailed Technique  . . . . . . . . . . . . . . . . . . .  15
       A.1.1.  Data Structures and Schedule Encoding . . . . . . . .  15
       A.1.2.  Pseudo-Random Number Generation . . . . . . . . . . .  15
       A.1.3.  Array Permutation . . . . . . . . . . . . . . . . . .  16
       A.1.4.  Schedule Permutation  . . . . . . . . . . . . . . . .  16
     A.2.  Test Configuration  . . . . . . . . . . . . . . . . . . .  17
     A.3.  Example Output  . . . . . . . . . . . . . . . . . . . . .  17
   Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . .  22
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  22

1.  Introduction

   Nodes in a 6TiSCH network communicate using the IEEE 802.15.4-2015
   standard and its Timeslotted Channel Hopping (TSCH) mode.  Some
   properties of TSCH make schedule units, i.e. cells, and their usage
   predictable, even if security services are used at the MAC layer.





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   This allows an external adversary to easily derive the communication
   pattern of a victim node.  After that, the adversary can perform a
   selective jamming attack, by covertly, efficiently, and effectively
   transmitting over the only exact cell(s) in the victim's schedule.
   For example, this enables the adversary to jeopardize a competitor's
   network, while still permitting their own network to operate
   correctly.

   This document describes a method to counteract such an attack.  At
   each slotframe, every node autonomously computes a TSCH schedule, as
   a pseudo-random permutation of the one originally available from 6top
   [RFC8480] or alternative protocols.

   The resulting schedule is provided to TSCH and used to communicate
   during the next slotframe.  In particular, the new communication
   pattern results unpredictable for an external adversary.  Besides,
   since all nodes compute the same pseudo-random permutation, the new
   communication pattern remains consistent and collision-free.

   The proposed solution is intended to operate on slotframes that are
   used for data transmission by current network nodes, and that are not
   used to join the network.  In fact, since the TSCH schedule is
   altered at each slotframe, the proposed method cannot be applied to
   slotframes that include a "minimal cell" [RFC8180] and possible other
   randez-vouz cells used for joining the 6TiSCH network.

   This document specifies also how this method can be added on top of
   the minimal security framework for 6TiSCH and its Constrained Join
   Protocol (CoJP) [I-D.ietf-6tisch-minimal-security].

1.1.  Terminology

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
   "OPTIONAL" in this document are to be interpreted as described in BCP
   14 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.

   Readers are expected to be familiar with terms and concepts defined
   in [I-D.ietf-6tisch-minimal-security], [I-D.ietf-6tisch-terminology]
   and [RFC8152].

   This document refers also to the following terminology.

   o  Permutation key.  A cryptographic key shared by network nodes and
      used to permute schedules.  Different keys are used to permute the
      utilization pattern of timeslots and of channelOffsets.




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2.  Properties of TSCH that Simplify Selective Jamming

   This section highlights a number of properties of the TSCH cell usage
   that greatly simplify the performance of the selective jamming attack
   described in Section 3.

   Given:

   o  N_S as the size of slotframes in timeslots;

   o  N_C as the number of available channelOffsets;

   o  The channel 'f' to communicate at timeslot 's' with ASN and
      channelOffset 'chOff' computed as f = F[(ASN + chOff) mod N_C];

   And assuming for simplicity that:

   o  N_S and N_C are coprime values;

   o  The channel hopping sequence is N_C in size and equal to {0, 1,
      ..., N_C - 1};

   Then, the following properties hold:

   o  Periodicity property.  The sequence of channels used for
      communication by a certain cell repeats with period (N_C x N_S)
      timeslots.

   o  Usage property.  Within a period, every cell uses all the
      available channels, each of which only once.

   o  Offset property.  All cells follow the same sequence of channels
      with a certain offset.

   o  Predictability property.  For each cell, the sequence of channels
      is predictable.  That is, by knowing the channel used by a cell in
      a given timeslot, it is possible to compute the remaining channel
      hopping sub-sequence.

      In fact, given a cell active on channel 'f' and timeslot 's' on
      slotframe 'T', and since ASN = (s + T x N_S), it holds that

      f = [(s + T x N_S + chOff) mod N_C]          (Equation 1)

      By solving this equation in 'chOff', one can predict the channels
      used by the cell in the next sloframes.  Note that, in order to do
      that, one does not need to know the absolute number 'T' of the
      slotframe (and thus the exact ASN) in which timeslot 's' uses a



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      certain channel 'f'.  In fact, one can re-number slotframes
      starting from any arbitrarily assumed "starting-slotframe".

3.  Selective Jamming Attack

   This section describes how an adversary can exploit the properties
   listed in Section 2, and determine the full schedule of a victim
   node, even if security services at the MAC layer are used.

   This allows the adversary to selectively jam only the exact cell(s)
   in the victim's schedule, while greatly limiting the exposure to
   detection.  At the same time, the attack is highly effective in
   jeopardizing victim's communications, and is highly energy-efficient,
   i.e., can be carried out on battery.

   For simplicity, the following description also assumes that a victim
   node actually transmits/receives during all its allocated cells at
   each slotframe.

3.1.  Adversary Model

   This specification addresses an adversary with the following
   properties.

   o  The adversary is external, i.e. it does not control any node
      registered in the 6TiSCH network.

   o  The adversary wants to target precise network nodes and their
      traffic.  That is, it does not target the 6TiSCH network as a
      whole, and does not perform a wide-band constant jamming.

   o  The adversary is able to target multiple victim nodes at the same
      time.  This may require multiple jamming sources and/or multiple
      antennas per jamming source to carry out the attack.

   Furthermore, compared to wide-band constant jamming, the considered
   selective jamming attack deserves special attention to be addressed,
   due to the following reasons.

   o  It is much more energy efficient.

   o  It minimizes the adversary's exposure and hence the chances to be
      detected.

   o  It has the same effectiveness on the intended victim nodes.  That
      is, it achieves the same goal, while avoiding the unnecessarily
      exposure and costs of wide-band constant jamming.




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   It is worth noting that a wide-band constant jamming can achieve the
   same result more easily, in the extreme cases where the target
   slotframe is (nearly) fully used by a few nodes only, or the
   adversary has as many antennas as the number of available channels.
   However, this would still come at the cost of high exposure and
   higher energy consumption for the adversary.

3.2.  Attack Example

   The following example considers Figure 1, where N_S = 3, N_C = 4, and
   the channel hopping sequence is {0,1,2,3}. The shown schedule refers
   to a network node that uses three cells 'L_1', 'L_2' and 'L_3', with
   {0,3}, {1,1} and {2,0} as pairs {timeslot, channelOffset},
   respectively.

|==|===================================================================|
|Ch|                                ASN                                |
|  |===================================================================|
|Of| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |10 |11 |12 |13 |14 |15 |16 |
|==|===================================================================|
|0 |   |   |f=2|   |   |f=1|   |   |f=0|   |   |f=3|   |   |f=2|   |   |
|--|-------------------------------------------------------------------|
|1 |   |f=2|   |   |f=1|   |   |f=0|   |   |f=3|   |   |f=2|   |   |f=1|
|--|-------------------------------------------------------------------|
|2 |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
|--|-------------------------------------------------------------------|
|3 |f=3|   |   |f=2|   |   |f=1|   |   |f=0|   |   |f=3|   |   |f=2|   |
|==|===================================================================|
   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
   |s=0|s=1|s=2|s=0|s=1|s=2|s=0|s=1|s=2|s=0|s=1|s=2|s=0|s=1|s=2|s=0|s=1
   |           |           |           |           |           |
   |   T = 0   |   T = 1   |   T = 2   |   T = 3   |   T = 4   |  T = 5
               |
               \__ t = 0

           Figure 1: Attack Example with Slotframe Re-numbering

   1.  The adversary starts the attack at absolute slotframe T = 1,
       which is assumed as "starting-slotframe" and thus renamed as
       slotframe t = 0.  The renaming is possible due to the offset and
       predictability properties.

   2.  The adversary picks a channel 'f*' at random, and monitors it for
       N_C consecutive slotframes to determine the timeslots in which
       the victim node communicates on that channel.  Due to the usage
       property, the number of such timeslots is equal to the number of
       cells assigned to the victim node.




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       With reference to Figure 1, if, for example, f* = 1, the
       adversary determines that the victim node uses channel 'f*' in
       timeslots s = 1 and s = 2 of slotframe t = 0 and in timeslot s =
       0 of slotframe t = 1.  The adversary can then deduce that the
       victim node uses three different cells 'L_1', 'L_2' and 'L_3', in
       timeslots 0, 1 and 2, respectively.

   3.  The adversary determines the channels on which the victim node is
       going to transmit in the next slotframes, by exploiting the
       predictability property.

       That is, by instantiating Equation 1 for cell L_1, timeslot s = 0
       and slotframe t = 1, one gets [1 = (3 + chOff_1) mod 4], which
       has solution for chOff_1 = 2.  Hence, the function to predict the
       channel 'f_1' to be used by cell 'L_1' in a slotframe 't', t >=
       1, is f_1 = [(2 + 3 x t) mod 4], which produces the correct
       periodic sequence of channels {1, 0, 3, 2}. Similarly, one can
       instantiate Equation 1 for cells 'L_2' and 'L_3', so producing
       the respective periodic sequence of channels {1,0,3,2} and
       {1,0,3,2}.

   4.  The adversary has discovered the full schedule of the victim node
       and can proceed with the actual selective jamming attack.  That
       is, according to the found schedule, the adversary transmits over
       the exact cells used by the victim node for transmission/
       reception, while staying quiet and saving energy otherwise.  This
       results in a highly effective, highly efficient and hard to
       detect attack against communications of network nodes.

4.  Building Robust Schedules

   This section defines a method to protect network nodes against the
   selective jamming attack described in Section 3.  The proposed method
   alters the communication pattern of all network nodes at every
   slotframe, in a way unpredictable for the adversary.

   At each slotframe 'T', network nodes autonomously compute the
   communication pattern for the next slotframe 'T+1' as a pseudo-random
   permutation of the one originally available.  In order to ensure that
   the new communication pattern remains consistent and collision-free,
   all nodes compute the same permutation of the original one.  In
   particular, at every slotframe, each node separately and
   independently permutes its timeslot utilization pattern (optionally)
   as well as its channelOffset utilization pattern.

   To perform the required permutations, all network nodes rely on a
   same secure pseudo-random number generator (SPRNG) as shown in
   Figure 2, where E(x,y) denotes a cipher which encrypts a plaintext



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   'y' by means of a key 'x'.  Network nodes MUST support the AES-CCM-
   16-64-128 algorithm.

   unsigned random(unsigned K, unsigned z) {
       unsigned val = E(K,z);
       return val;
   }

              Figure 2: Secure Pseudo-Random Number Generator

   All network nodes share the same following pieces of information.

   o  K_s, a permutation key used to permute the timeslot utilization
      pattern, and used as input to the random() function in Figure 2.
      K_s is provided upon joining the network, and MAY be provided as
      described in Section 5.

   o  K_c, a permutation key used to permute the channelOffset
      utilization pattern, and used as input to the random() function in
      Figure 2.  K_c is provided upon joining the network, and MAY be
      provided as described in Section 5.

   o  z_s, a counter used to permute the timeslot utilization pattern,
      and used as input to the random() function in Figure 2.  At the
      beginning of each slotframe, z_s is equal to [(N_S - 1) x
      floor(ASN* / N_S)], where ASN* is the ASN value of the first
      timeslot of that slotframe.  Then, z_s grows by (N_S - 1) from the
      beginning of a slotframe to the beginning of the next one.

   o  z_c, a counter used to permute the channelOffset utilization
      pattern, and used as input to the random() function in Figure 2.
      At the beginning of each slotframe, z_c is equal to [(N_C - 1) x
      floor(ASN* / N_S)], where ASN* is the ASN value of the first
      timeslot of that slotframe.  Then, z_c grows by (N_C - 1) from the
      beginning of a slotframe to the beginning of the next one.

   Then, at every slotframe, each network node takes the following
   steps, and generates its own permuted communication schedule to be
   used at the following slotframe.  The actual permutation of cells
   relies on the well-known Fisher-Yates algorithm, that requires to
   generate (n - 1) pseudo-random numbers in order to pseudo-randomly
   shuffle a vector of n elements.

   1.  First, a pseudo-random permutation is performed on the timeslot
       dimension of the slotframe.  This requires (N_S - 1) invocations
       of random(K,z), consistently with the Fisher-Yates algorithm.  In
       particular, K = K_s, while z_s is passed as second argument and
       is incremented by 1 after each invocation.  The result of this



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       step is a permuted timeslot utilization pattern, while the
       channelOffset utilization pattern is not permuted yet.

   2.  Second, a pseudo-random permutation is performed on the
       channelOffset dimension of the slotframe.  This requires (N_C -
       1) invocations of random(K,z), consistently with the Fisher-Yates
       algorithm.  In particular, K = K_c, while z_c is passed as second
       argument and is incremented by 1 after each invocation.  The
       result of this step is a fully shuffled communication pattern.

   The resulting schedule is then provided to TSCH and considered for
   sending/receiving traffic during the next slotframe.

   As further discussed in Section 6.3, it is possible to skip step 1
   above, and hence permute only the channelOffset utilization pattern,
   while keeping a static timeslot utilization pattern.

   Note for implementation: the process described above can be
   practically implemented by using two vectors, i.e. one for shuffling
   the timeslot utilization pattern and one for shuffling the
   channelOffset utilization pattern.

5.  Adaptation to the 6TiSCH Minimal Security Framework

   The security mechanism described in this specification can be added
   on top of the minimal security framework for 6TiSCH
   [I-D.ietf-6tisch-minimal-security].

   That is, the two permutation keys K_s and K_c can be provided to a
   pledge when performing the Constrained Join Protocol (CoJP) defined
   in Section 8 of [I-D.ietf-6tisch-minimal-security].

   To this end, the Configuration CBOR object [RFC7049] used as payload
   of the Join Response Message and defined in Section 8.4.2 of
   [I-D.ietf-6tisch-minimal-security] is extended with two new CoJP
   parameters defined in this specification, namely 'permutation key
   set' and 'permutation cipher'.  The resulting payload of the Join
   Response message is as follows.

   Configuration = {
      ? 2   : [ +Link_Layer_Key ],     ; link-layer key set
      ? 3   : Short_Identifier,        ; short identifier
      ? 4   : bstr,                    ; JRC address
      ? 6   : [ *bstr ],               ; blacklist
      ? 7   : uint,                    ; join rate
      ? TBD : [ +Permutation_Key ],    ; permutation key set
      ? TBD : Permutation_Cipher       ; permutation cipher
   }



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   The parameter 'permutation key set' is an array encompassing one or
   two permutation keys encoded as byte strings.  That is, the encoding
   of each individual permutation key is as follows.

   Permutation_Key = (
         key_value          : bstr
   (

   If the 6TiSCH network uses the security mechanism described in this
   specification, the parameter 'permutation key set' MUST be included
   in the CoJP Join Response message and the pledge MUST interpret it as
   follows.

   o  In case only one permutation key is present, it is used as K_c to
      permute the channelOffset utilization pattern, as per Section 4.

   o  In case two permutation keys are present, the first one is used as
      K_s to permute the timeslot utilization pattern, while the second
      one is used as K_c to permute the channelOffset utilization
      pattern, as per Section 4.  The two keys MUST have the same
      length.

   The parameter 'permutation cipher' indicates the encryption algorithm
   used for the secure pseudo-random number generator as per Figure 2 in
   Section 4.  The value is one of the encryption algorithms defined for
   COSE [RFC8152], and is taken from Tables 9, 10 and 11 of [RFC8152].
   In case the parameter is omitted, the default value of AES-CCM-
   16-64-128 (COSE algorithm encoding: 10) MUST be assumed.

5.1.  Error Handling

   In case 'permutation key set' includes two permutation keys with
   different length or more than two permutation keys, the pledge
   considers 'permutation key set' not valid and MUST signal the error
   as specified in Section 8.3.1 of [I-D.ietf-6tisch-minimal-security].

   The pledge MUST validate that keys included in 'permutation key set'
   are appropriate for the encryption algorithm specified in
   'permutation cipher' or assumed as default.  In case of failed
   validation, the pledge MUST signal the error as specified in
   Section 8.3.1 of [I-D.ietf-6tisch-minimal-security].

6.  Security Considerations

   With reference to Section 3.9 of [RFC7554], this specification
   achieves an additional "Secure Communication" objective, namely it
   defines a mechanism to build and enforce a TSCH schedule which is




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   robust against selective jamming attack, while at the same time
   consistent and collision-free.

   Furthermore, the same security considerations from the minimal
   security framework for 6TiSCH [I-D.ietf-6tisch-minimal-security] hold
   for this document.  The rest of this section discusses a number of
   additional security considerations.

6.1.  Effectiveness of Schedule Shuffling

   The countermeasure defined in Section 4 practically makes each node's
   schedule look random to an external observer.  Hence, it prevents the
   adversary from performing the attack described in Section 3.

   Then, a still available strategy for the adversary is to jam a number
   of cells selected at random, possibly on a per-slotframe basis.  This
   considerably reduces the attack effectiveness in successfully
   jeopardizing victims' communications.

   At the same time, nodes using different cells than the intended
   victims' would experience an overall slightly higher fraction of
   corrupted messages.  In fact, the communications of such accidental
   victims might be corrupted by the adversary, when they occur during a
   jammed timeslot and exactly over the channelOffset chosen at random.

6.2.  Renewal of Key Material

   It is RECOMMENDED that the two permutation keys K_s and K_c are
   revoked and renewed every time a node leaves the network.  This
   prevents a leaving node to keep the permutation keys, which may be
   exploited to selectively jam communications in the network.

   This rekeying operation is supposed to be performed anyway upon every
   change of network membership, in order to preserve backward and
   forward security.  In particular, new IEEE 802.15.4 link-layer keys
   are expected to be distributed before a new pledge can join the
   network, or after one or more nodes have left the network.

   The specific approach to renew the two permutation keys, possibly
   together with other security material, is out of the scope of this
   specification.

6.3.  Static Timeslot Allocations

   As mentioned in Section 4 and Section 5, it is possible to permute
   only the channelOffset utilization pattern, while preserving the
   originally scheduled timeslot utilization pattern.  This can be
   desirable, or even unavoidable in some scenarios, in order to



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   guarantee end-to-end latencies in multi-hop networks, as per
   accordingly designed schedules.

   However, preserving a static timeslot utilization pattern would
   considerably increase the attack surface for a random jammer
   adversary.  That is, the adversary would immediately learn the
   timeslot utilization pattern of a victim node, and would have a
   chance to successfully jam a victim's cell equal to (1 / N_C).

6.4.  Network Joining Through Randez-vous Cells

   As described in [I-D.ietf-6tisch-minimal-security], a pledge joins a
   6TiSCH network through a Join Proxy (JP), according to the
   Constrained Join Protocol (CoJP) and based on the information
   conveyed in broadcast Enhanced Beacons (EBs).  In particular, the
   pledge will communicate with the JP over randez-vous cells indicated
   in the EBs.

   In practice, such cells are commonly part of a separate slotframe,
   which includes one scheduled "minimal cell" [RFC8180], typically used
   also for broadcasting EBs.  Such slotframe, i.e. Slotframe 0, usually
   differs from the slotframe(s) used for both EBs and data
   transmission.

   In order to keep the join process feasible and deterministic, the
   solution described in this specification is not applied to Slotframe
   0 or any other slotframes that include randez-vous cells for joining.
   As a consequence, an adversary remains able to selectively jam the
   "minimal cell" (or any randez-vous cell used for joining), so
   potentially jeopardizing the CoJP and preventing pledges to join the
   network altogether.

7.  IANA Considerations

   This document has the following actions for IANA.

7.1.  Permutation Key Set

   IANA is asked to enter the following value into the "Constrained Join
   Protocol Parameters Registry" defined in
   [I-D.ietf-6tisch-minimal-security] and within the "IPv6 over the TSCH
   mode of IEEE 802.15.4e (6TISCH) parameters" registry.









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   +-------------+-------+-------+------------------------+------------+
   |        Name | Label |  CBOR | Description            | Reference  |
   |             |       |  type |                        |            |
   +-------------+-------+-------|------------------------+------------|
   | permutation | TBD   | array | Identifies the array   | [[this     |
   |     key set |       |       | including one or two   | document]] |
   |             |       |       | permutation keys to    |            |
   |             |       |       | alter cell utilization |            |
   +-------------|-------+-------+------------------------+------------|

7.2.  Permutation Cipher

   IANA is asked to enter the following value into the "Constrained Join
   Protocol Parameters Registry" defined in
   [I-D.ietf-6tisch-minimal-security] and within the "IPv6 over the TSCH
   mode of IEEE 802.15.4e (6TISCH) parameters" registry.

  +-------------+-------+---------+-----------------------+------------+
  |        Name | Label |    CBOR | Description           | Reference  |
  |             |       |    type |                       |            |
  +-------------+-------+---------|-----------------------+------------|
  | permutation | TBD   | integer | Identifies the cipher | [[this     |
  |      cipher |       |         | used for generating   | document]] |
  |             |       |         | pseudo-random numbers |            |
  |             |       |         | to alter cell         |            |
  |             |       |         | utilization           |            |
  +-------------|-------+---------+-----------------------+------------|

8.  References

8.1.  Normative References

   [I-D.ietf-6tisch-minimal-security]
              Vucinic, M., Simon, J., Pister, K., and M. Richardson,
              "Minimal Security Framework for 6TiSCH", draft-ietf-
              6tisch-minimal-security-10 (work in progress), April 2019.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <https://www.rfc-editor.org/info/rfc2119>.

   [RFC7049]  Bormann, C. and P. Hoffman, "Concise Binary Object
              Representation (CBOR)", RFC 7049, DOI 10.17487/RFC7049,
              October 2013, <https://www.rfc-editor.org/info/rfc7049>.






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   [RFC8152]  Schaad, J., "CBOR Object Signing and Encryption (COSE)",
              RFC 8152, DOI 10.17487/RFC8152, July 2017,
              <https://www.rfc-editor.org/info/rfc8152>.

   [RFC8174]  Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
              2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
              May 2017, <https://www.rfc-editor.org/info/rfc8174>.

8.2.  Informative References

   [I-D.ietf-6tisch-terminology]
              Palattella, M., Thubert, P., Watteyne, T., and Q. Wang,
              "Terms Used in IPv6 over the TSCH mode of IEEE 802.15.4e",
              draft-ietf-6tisch-terminology-10 (work in progress), March
              2018.

   [RFC7554]  Watteyne, T., Ed., Palattella, M., and L. Grieco, "Using
              IEEE 802.15.4e Time-Slotted Channel Hopping (TSCH) in the
              Internet of Things (IoT): Problem Statement", RFC 7554,
              DOI 10.17487/RFC7554, May 2015,
              <https://www.rfc-editor.org/info/rfc7554>.

   [RFC8180]  Vilajosana, X., Ed., Pister, K., and T. Watteyne, "Minimal
              IPv6 over the TSCH Mode of IEEE 802.15.4e (6TiSCH)
              Configuration", BCP 210, RFC 8180, DOI 10.17487/RFC8180,
              May 2017, <https://www.rfc-editor.org/info/rfc8180>.

   [RFC8480]  Wang, Q., Ed., Vilajosana, X., and T. Watteyne, "6TiSCH
              Operation Sublayer (6top) Protocol (6P)", RFC 8480,
              DOI 10.17487/RFC8480, November 2018,
              <https://www.rfc-editor.org/info/rfc8480>.

   [Test-Implementation]
              "Test Implementation in C with OpenSSL", May 2019,
              <https://gitlab.com/crimson84/draft-tiloca-6tisch-robust-
              scheduling/tree/master/test>.

Appendix A.  Test Vector

   This appendix provides a test vector for an example where the method
   proposed in this document is used to generate robust TSCH schedules.

   The example focuses on one network node and considers the schedule in
   Figure 1 as the original schedule to permute at each slotframe.

   The results shown in this example have been produced using the
   implementation available at [Test-Implementation].




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A.1.  Detailed Technique

   In this example, the permutation of the timeslot utilization pattern
   and of the channelOffset utilization pattern occurs as follows.

A.1.1.  Data Structures and Schedule Encoding

   Each network node maintains two vectors X_s and X_c, each composed of
   N_S unsigned integer values.  At the beginning of each slotframe, X_s
   and X_c indicate the node's original schedule.  In particular:

   o  X_s indicates the usage of timeslots in the slotframe.  That is,
      the element X_s[i] refers to the i-th timeslot of the slotframe.

   o  X_c indicates the usage of channelOffsets at each timeslot in the
      slotframe.  That is, X_c[i] refers to the channelOffset value used
      in the i-th timeslot of the slotframe.

   Then, the two vectors encode the schedule information as follows:

   o  If the i-th timeslot is not used, X_s[i] = 0 and X_c[i] = N_C.

   o  If the i-th timeslot is used to transmit with channelOffset 'c',
      X_s[i] = 1 and X_c[i] = c.

   o  If the i-th timeslot is used to receive with channelOffset 'c',
      X_s[i] = 2 and X_c[i] = c.

   Note that optimized implementations can achieve the same goal with
   permutation vectors of smaller size.

A.1.2.  Pseudo-Random Number Generation

   When invoking E() within the random() function in Figure 2:

   o  The second parameter has 5 bytes in size like the ASN, and is
      provided as plaintext to the permutation cipher.

   o  A copy of the second parameter is left-padded with 8 octects with
      value 0x00.  The result is provided as 13-byte nonce to the
      permutation cipher, i.e. AES-CCM-16-64-128 in this example.

   o  No additional authenticated data are provided to the permutation
      cipher.

   The unsigned value returned by E() and random() is the computed
   ciphertext left-padded with 3 octects with value 0x00.  That is, the
   returned value is 8 bytes in size.



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A.1.3.  Array Permutation

   To produce the required permutations, this example considers the
   Fisher-Yates modern version in Figure 3, which requires (n - 1) swaps
   to shuffle an array of n elements.

     // Shuffle an array 'a' of 'n' elements (indices 0, ... , n - 1)
     for i from (n - 1) down to 1 do {
        j = random integer such that 0 <= j <= i;
        exchange a[j] and a[i];
     }

                     Figure 3: Fisher-Yates algorithm

   At each step of the loop, 'j' is computed as r % (i + 1), where '%'
   is the modulo operator, and 'r' is the value returned by the function
   random() in Figure 2, as described in Appendix A.1.2.

A.1.4.  Schedule Permutation

   At each slotframe, the original schedule is considered as starting
   point to produce the permuted schedule for the following slotframe.

   In particular, the permuted schedule for the following slotframe is
   computed according to the following steps.

   1.  The same pseudo-random permutation is performed on both vectors
       X_s and X_c, by using the Fisher-Yates algorithm in Figure 3.
       This requires (N_S - 1) invocations of random(K,z).  In
       particular, K = K_s, while z_s is passed as second argument and
       is incremented by 1 after each invocation.  As a result, X_s
       specifies the permuted timeslot utilization pattern, whereas X_c
       specifies a consistent while temporary channelOffset utilization
       pattern.

   2.  A vector Y of size N_C is produced, as a permutation of {0, 1,
       ..., N_C - 1} performed by using the Fisher-Yates algorithm in
       Figure 3.  This requires (N_C - 1) invocations of random(K,z).
       In particular, K = K_c, while z_c is passed as second argument
       and is incremented by 1 after each invocation.

   3.  The vector X_c is updated as follows.  Each element X_c[i] that
       refers to a non active timeslot, i.e. X_c[i] = N_C, is left as
       is.  Otherwise, X_c[i] takes as value Y[j], where j = X_c[i].

   As a result, the two permuted vectors X_s and X_c together provide a
   full communication pattern to use during the next slotframe.




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A.2.  Test Configuration

   N_S = 3 // Slotframe size, in timeslots

   N_C = 4 // Available channel offsets

   Channel hopping sequence = {0, 1, 2, 3}

   X_s = {1, 1, 2} // Original timeslot utilization pattern {Tx, Tx, Rx}

   X_c = {3, 1, 0} // Original channelOffset utilization pattern

   Starting ASN = 0

   Permutation cipher: AES-CCM-16-64-128

   K_s = { 0xce, 0xb0, 0x09, 0xae, 0xa4, 0x45, 0x44, 0x51,
           0xfe, 0xad, 0xf0, 0xe6, 0xb3, 0x6f, 0x45, 0x55 }

   K_c = { 0xce, 0xb0, 0x09, 0xae, 0xa4, 0x45, 0x44, 0x51,
           0xfe, 0xad, 0xf0, 0xe6, 0xb3, 0x6f, 0x45, 0x56 }

A.3.  Example Output

   ******************* ******************* *******************

   START ROUND 1 of 2

   The slotframe starts with: ASN = 0; z_s = 0; z_c = 0

   ******************* ******************* *******************

   -- Start shuffling the time offsets --

   ---------- ---------- ----------

   Counter (z_s): 0

   Plaintext: 0x0000000000 (5 bytes)

   Cipher nonce: 0x00000000000000000000000000 (13 bytes)

   Ciphertext: 0xbedca72db3 (5 bytes)

   Padded ciphertext: 0x000000bedca72db3 (8 bytes)

   Fisher-Yates swap index i: 2




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   Fisher-Yates swap-index j: 0

   ---------- ---------- ----------

   Counter (z_s): 1

   Plaintext: 0x0000000001 (5 bytes)

   Cipher nonce: 0x00000000000000000000000001 (13 bytes)

   Ciphertext: 0x23d36801f1 (5 bytes)

   Padded ciphertext: 0x00000023d36801f1 (8 bytes)

   Fisher-Yates swap index i: 1

   Fisher-Yates swap-index j: 1

   ---------- ---------- ----------

   -- Intermediate schedule --

   Timeslot utilization pattern X_s = {2, 1, 1}

   ChannelOffset utilization pattern X_c = {0, 1, 3}

   ---------- ---------- ----------

   -- Start shuffling the channel offset schedule --

   ---------- ---------- ----------

   Counter (z_c): 0

   Plaintext: 0x0000000000 (5 bytes)

   Cipher nonce: 0x00000000000000000000000000 (13 bytes)

   Ciphertext: 0x1e957fe44d (5 bytes)

   Padded ciphertext: 0x0000001e957fe44d (8 bytes)

   Fisher-Yates swap index i: 3

   Fisher-Yates swap-index j: 1

   ---------- ---------- ----------




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   Counter (z_c): 1

   Plaintext: 0x0000000001 (5 bytes)

   Cipher nonce: 0x00000000000000000000000001 (13 bytes)

   Ciphertext: 0x6e2b990263 (5 bytes)

   Padded ciphertext in bytes: 0x0000006e2b990263 (8 bytes)

   Fisher-Yates swap index i: 2

   Fisher-Yates swap-index j: 2

   ---------- ---------- ----------

   Counter (z_c): 2

   Plaintext: 0x0000000002 (5 bytes)

   Cipher nonce: 0x00000000000000000000000002 (13 bytes)

   Ciphertext: 0x4fae2cfe22 (5 bytes)

   Padded ciphertext: 0x0000004fae2cfe22 (8 bytes)

   Fisher-Yates swap index i: 1

   Fisher-Yates swap-index j: 0

   ---------- ---------- ----------

   Next slotframe starting with ASN = 3 will use:

   o  Shuffled timeslot schedule {2, 1, 1}, i.e. {Rx, Tx, Tx}.

   o  Shuffled channel offset schedule {3, 0, 1}.

   o  Shuffled frequencies schedule {2, 0, 2}.

   ******************* ******************* *******************

   START ROUND 2 OF 2

   The slotframe starts with: ASN = 3; z_s = 2; z_c = 3

   ******************* ******************* *******************




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   -- Start shuffling the time offsets --

   ---------- ---------- ----------

   Counter (z_s): 2

   Plaintext: 0x0000000002 (5 bytes)

   Cipher nonce: 0x00000000000000000000000002 (13 bytes)

   Ciphertext: 0xd9a0c0f8eb (5 bytes)

   Padded ciphertext: 0x000000d9a0c0f8eb (8 bytes)

   Fisher-Yates swap index i: 2

   Fisher-Yates swap-index j: 2

   ---------- ---------- ----------

   Counter (z_s): 3

   Plaintext: 0x0000000003 (5 bytes)

   Cipher nonce: 0x00000000000000000000000003 (13 bytes)

   Ciphertext: 0x7aabd818ac (5 bytes)

   Padded ciphertext: 0x0000007aabd818ac (8 bytes)

   Fisher-Yates swap index i: 1

   Fisher-Yates swap-index j: 0

   ---------- ---------- ----------

   -- Intermediate schedules --

   Timeslot utilization pattern X_s = {1, 1, 2}

   ChannelOffset utilization pattern X_c = {1, 3, 0}

   ---------- ---------- ----------

   -- Start shuffling the channel offset schedule --

   ---------- ---------- ----------




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   Counter (z_c): 3

   Plaintext: 0x0000000003 (5 bytes)

   Cipher nonce: 0x00000000000000000000000003 (13 bytes)

   Ciphertext: 0x947cf7c1d4 (5 bytes)

   Padded ciphertext: 0x000000947cf7c1d4 (8 bytes)

   Fisher-Yates swap index i: 3

   Fisher-Yates swap-index j: 0

   ---------- ---------- ----------

   Counter (z_c): 4

   Plaintext: 0x0000000004 (5 bytes)

   Cipher nonce: 0x00000000000000000000000004 (13 bytes)

   Ciphertext: 0xa9255744e7 (5 bytes)

   Padded ciphertext: 0x000000a9255744e7 (8 bytes)

   Fisher-Yates swap index i: 2

   Fisher-Yates swap-index j: 1

   ---------- ---------- ----------

   Counter (z_c): 5

   Plaintext: 0x0000000005 (5 bytes)

   Cipher nonce: 0x00000000000000000000000005 (13 bytes)

   Ciphertext: 0xa70a456e9e (5 bytes)

   Padded ciphertext: 0x000000a70a456e9e (8 bytes)

   Fisher-Yates swap index i: 1

   Fisher-Yates swap-index j: 0

   ---------- ---------- ----------




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   Next slotframe starting with ASN = 6 will use:

   o  Shuffled timeslot schedule {1, 1, 2}, i.e. {Tx, Tx, Rx}.

   o  Shuffled channel offset schedule {3, 0, 2}.

   o  Shuffled frequencies schedule {1, 3, 2}.

Acknowledgments

   The authors sincerely thank Tengfei Chang, Michael Richardson,
   Yasuyuki Tanaka, Pascal Thubert and Malisa Vucinic for their comments
   and feedback.

   The work on this document has been partly supported by the EIT-
   Digital High Impact Initiative ACTIVE, and by the VINNOVA and Celtic-
   Next project CRITISEC.

Authors' Addresses

   Marco Tiloca
   RISE AB
   Isafjordsgatan 22
   Kista  SE-16440 Stockholm
   Sweden

   Email: marco.tiloca@ri.se


   Simon Duquennoy
   Yanzi Networks AB
   Isafjordsgatan 32C
   Kista  SE-16440 Stockholm
   Sweden

   Email: simon.duquennoy@yanzinetworks.com


   Gianluca Dini
   University of Pisa
   Largo L. Lazzarino 2
   Pisa  56122
   Italy

   Email: gianluca.dini@unipi.it






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