Address Protected Neighbor Discovery for Low-power and Lossy Networks
draft-ietf-6lo-ap-nd-15
The information below is for an old version of the document.
| Document | Type | Active Internet-Draft (6lo WG) | |
|---|---|---|---|
| Authors | Pascal Thubert , Behcet Sarikaya , Mohit Sethi , Rene Struik | ||
| Last updated | 2020-01-31 | ||
| Replaces | draft-sarikaya-6lo-ap-nd | ||
| Stream | Internet Engineering Task Force (IETF) | ||
| Formats | plain text html xml htmlized pdfized bibtex | ||
| Reviews |
OPSDIR Last Call review
(of
-12)
Has Nits
|
||
| Stream | WG state | Submitted to IESG for Publication | |
| Document shepherd | Shwetha Bhandari | ||
| Shepherd write-up | Show Last changed 2019-04-25 | ||
| IESG | IESG state | IESG Evaluation | |
| Consensus boilerplate | Yes | ||
| Telechat date |
(None)
Needs a YES. Needs 6 more YES or NO OBJECTION positions to pass. |
||
| Responsible AD | Suresh Krishnan | ||
| Send notices to | Shwetha Bhandari <shwethab@cisco.com> | ||
| IANA | IANA review state | Version Changed - Review Needed |
draft-ietf-6lo-ap-nd-15
6lo P. Thubert, Ed.
Internet-Draft Cisco
Updates: 8505 (if approved) B.S. Sarikaya
Intended status: Standards Track
Expires: 3 August 2020 M.S. Sethi
Ericsson
R.S. Struik
Struik Security Consultancy
31 January 2020
Address Protected Neighbor Discovery for Low-power and Lossy Networks
draft-ietf-6lo-ap-nd-15
Abstract
This document updates the 6LoWPAN Neighbor Discovery (ND) protocol
defined in RFC 6775 and RFC 8505. The new extension is called
Address Protected Neighbor Discovery (AP-ND) and it protects the
owner of an address against address theft and impersonation attacks
in a low-power and lossy network (LLN). Nodes supporting this
extension compute a cryptographic identifier (Crypto-ID) and use it
with one or more of their Registered Addresses. The Crypto-ID
identifies the owner of the Registered Address and can be used to
provide proof of ownership of the Registered Addresses. Once an
address is registered with the Crypto-ID and a proof-of-ownership is
provided, only the owner of that address can modify the registration
information, thereby enforcing Source Address Validation.
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 3 August 2020.
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Copyright Notice
Copyright (c) 2020 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 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 . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Terminology . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1. BCP 14 . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2. Abbreviations . . . . . . . . . . . . . . . . . . . . . . 4
2.3. Additional References . . . . . . . . . . . . . . . . . . 5
3. Updating RFC 8505 . . . . . . . . . . . . . . . . . . . . . . 5
4. New Fields and Options . . . . . . . . . . . . . . . . . . . 6
4.1. New Crypto-ID . . . . . . . . . . . . . . . . . . . . . . 6
4.2. Updated EARO . . . . . . . . . . . . . . . . . . . . . . 6
4.3. Crypto-ID Parameters Option . . . . . . . . . . . . . . . 7
4.4. NDP Signature Option . . . . . . . . . . . . . . . . . . 9
5. Protocol Scope . . . . . . . . . . . . . . . . . . . . . . . 11
6. Protocol Flows . . . . . . . . . . . . . . . . . . . . . . . 11
6.1. First Exchange with a 6LR . . . . . . . . . . . . . . . . 12
6.2. NDPSO generation and verification . . . . . . . . . . . . 14
6.3. Multihop Operation . . . . . . . . . . . . . . . . . . . 15
7. Security Considerations . . . . . . . . . . . . . . . . . . . 17
7.1. Inheriting from RFC 3971 . . . . . . . . . . . . . . . . 17
7.2. Related to 6LoWPAN ND . . . . . . . . . . . . . . . . . . 18
7.3. ROVR Collisions . . . . . . . . . . . . . . . . . . . . . 18
7.4. Implementation Attacks . . . . . . . . . . . . . . . . . 18
7.5. Cross-Protocol Attacks . . . . . . . . . . . . . . . . . 19
7.6. Compromised 6LR . . . . . . . . . . . . . . . . . . . . . 19
8. IANA considerations . . . . . . . . . . . . . . . . . . . . . 19
8.1. CGA Message Type . . . . . . . . . . . . . . . . . . . . 19
8.2. IPv6 ND option types . . . . . . . . . . . . . . . . . . 19
8.3. Crypto-Type Subregistry . . . . . . . . . . . . . . . . . 20
9. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 21
10. Normative References . . . . . . . . . . . . . . . . . . . . 21
11. Informative references . . . . . . . . . . . . . . . . . . . 22
Appendix A. Requirements Addressed in this Document . . . . . . 24
Appendix B. Representation Conventions . . . . . . . . . . . . . 24
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B.1. Signature Schemes . . . . . . . . . . . . . . . . . . . . 24
B.2. Integer Representation for ECDSA signatures . . . . . . . 25
B.3. Alternative Representations of Curve25519 . . . . . . . . 25
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 27
1. Introduction
Neighbor Discovery Optimizations for 6LoWPAN networks [RFC6775]
(6LoWPAN ND) adapts the original IPv6 Neighbor Discovery (IPv6 ND)
protocols defined in [RFC4861] and [RFC4862] for constrained low-
power and lossy network (LLN). In particular, 6LoWPAN ND introduces
a unicast host Address Registration mechanism that reduces the use of
multicast compared to the Duplicate Address Detection (DAD) mechanism
defined in IPv6 ND. 6LoWPAN ND defines a new Address Registration
Option (ARO) that is carried in the unicast Neighbor Solicitation
(NS) and Neighbor Advertisement (NA) messages exchanged between a
6LoWPAN Node (6LN) and a 6LoWPAN Router (6LR). It also defines the
Duplicate Address Request (DAR) and Duplicate Address Confirmation
(DAC) messages between the 6LR and the 6LoWPAN Border Router (6LBR).
In LLN networks, the 6LBR is the central repository of all the
registered addresses in its domain.
The registration mechanism in "Neighbor Discovery Optimization for
Low-power and Lossy Networks" [RFC6775] (aka 6LoWPAN ND) prevents the
use of an address if that address is already registered in the subnet
(first come first serve). In order to validate address ownership,
the registration mechanism enables the 6LR and 6LBR to validate the
association between the registered address of a node, and its
Registration Ownership Verifier (ROVR). The ROVR is defined in
"Registration Extensions for 6LoWPAN Neighbor Discovery" [RFC8505]
and it can be derived from the MAC address of the device (using the
64-bit Extended Unique Identifier EUI-64 address format specified by
IEEE). However, the EUI-64 can be spoofed, and therefore, any node
connected to the subnet and aware of a registered-address-to-ROVR
mapping could effectively fake the ROVR. This would allow the an
attacker to steal the address and redirect traffic for that address.
[RFC8505] defines an Extended Address Registration Option (EARO)
option that allows to transport alternate forms of ROVRs, and is a
pre-requisite for this specification.
In this specification, a 6LN generates a cryptographic ID (Crypto-ID)
and places it in the ROVR field during the registration of one (or
more) of its addresses with the 6LR(s). Proof of ownership of the
Crypto-ID is passed with the first registration exchange to a new
6LR, and enforced at the 6LR. The 6LR validates ownership of the
cryptographic ID before it creates any new registration state, or
changes existing information.
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The protected address registration protocol proposed in this document
enables Source Address Validation (SAVI) [RFC7039]. This ensures
that only the actual owner uses a registered address in the IPv6
source address field. A 6LN can only use a 6LR for forwarding
packets only if it has previously registered the address used in the
source field of the IPv6 packet.
The 6lo adaptation layer in [RFC4944] and [RFC6282] requires a device
to form its IPv6 addresses based on its Layer-2 address to enable a
better compression. This is incompatible with Secure Neighbor
Discovery (SeND) [RFC3971] and Cryptographically Generated Addresses
(CGAs) [RFC3972], since they derive the Interface ID (IID) in IPv6
addresses with cryptographic keys.
2. Terminology
2.1. BCP 14
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.
2.2. Abbreviations
This document uses the following abbreviations:
6BBR: 6LoWPAN Backbone Router
6LBR: 6LoWPAN Border Router
6LN: 6LoWPAN Node
6LR: 6LoWPAN Router
ARO: Address Registration Option
EARO: Extended Address Registration Option
CIPO: Crypto-ID Parameters Option
LLN: Low-Power and Lossy Network
NA: Neighbor Advertisement
ND: Neighbor Discovery
NDP: Neighbor Discovery Protocol
NDPSO: NDP Signature Option
NS: Neighbor Solicitation
ROVR: Registration Ownership Verifier
RA: Router Advertisement
RS: Router Solicitation
RSAO: RSA Signature Option
TID: Transaction ID
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2.3. Additional References
The reader may get additional context for this specification from the
following references:
* "SEcure Neighbor Discovery (SEND)" [RFC3971],
* "Cryptographically Generated Addresses (CGA)" [RFC3972],
* "Neighbor Discovery for IP version 6" [RFC4861] ,
* "IPv6 Stateless Address Autoconfiguration" [RFC4862], and
* "IPv6 over Low-Power Wireless Personal Area Networks (6LoWPANs):
Overview, Assumptions, Problem Statement, and Goals " [RFC4919].
3. Updating RFC 8505
Section 5.3 of [RFC8505] introduces the ROVR as a generic object that
is designed for backward compatibility with the capability to
introduce new computation methods in the future. Section 7.3
discusses collisions when heterogeneous methods to compute the ROVR
field coexist inside a same network.
[RFC8505] was designed in preparation for this specification, which
is the RECOMMENDED method for building a ROVR field.
This specification introduces a new token called a cryptographic
identifier (Crypto-ID) that is transported in the ROVR field and used
to prove indirectly the ownership of an address that is being
registered by means of [RFC8505]. The Crypto-ID is derived from a
cryptographic public key and additional parameters.
The proof requires the support of Elliptic Curve Cryptography (ECC)
and that of a hash function as detailed in Section 6.2. To enable
the verification of the proof, the registering node needs to supply
certain parameters including a Nonce and a signature that will
demonstrate that the node has the private-key corresponding to the
public-key used to build the Crypto-ID.
The elliptic curves and the hash functions that can be used with this
specification are listed in Table 2 in Section 8.3. The signature
scheme that specifies which combination is used is signaled by a
Crypto-Type in a new IPv6 ND Crypto-ID Parameters Option (CIPO, see
Section 4.3) that contains the parameters that are necessary for the
proof, a Nonce option ([RFC3971]) and a NDP Signature option
(Section 4.4). The NA(EARO) is modified to enable a challenge and
transport a Nonce option as well.
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4. New Fields and Options
4.1. New Crypto-ID
The Crypto-ID is transported in the ROVR field of the EARO option and
the EDAR message, and is associated with the Registered Address at
the 6LR and the 6LBR. The ownership of a Crypto-ID can be
demonstrated by cryptographic mechanisms, and by association, the
ownership of the Registered Address can be acertained.
A node in possession of the necessary cryptographic primitives SHOULD
use Crypto-ID by default as ROVR in its registrations. Whether a
ROVR is a Crypto-ID is indicated by a new "C" flag in the NS(EARO)
message.
The Crypto-ID is derived from the public key and a modifier as
follows:
1. The hash function indicated by the Crypto-Type is applied to the
CIPO. Note that all the reserved and padding bits MUST be set to
zero.
2. The leftmost bits of the resulting hash, up to the size of the
ROVR field, are used as the Crypto-ID.
4.2. Updated EARO
This specification updates the EARO option to enable the use of the
ROVR field to transport the Crypto-ID.
The resulting format is as follows:
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Type | Length | Status | Opaque |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|Rsvd |C| I |R|T| TID | Registration Lifetime |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
... Registration Ownership Verifier (ROVR) ...
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 1: Enhanced Address Registration Option
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Type: 33
Length: 8-bit unsigned integer. The length of the option (including
the type and length fields) in units of 8 bytes.
Status: 8-bit unsigned integer. Indicates the status of a
registration in the NA response. In NS messages it MUST be set to
0 by the sender and ignored by the receiver.
Opaque: Defined in [RFC8505].
Rsvd (Reserved): 3-bit unsigned integer. It MUST be set to zero by
the sender and MUST be ignored by the receiver.
C: This "C" flag is set to indicate that the ROVR field contains a
Crypto-ID and that the 6LN MAY be challenged for ownership as
specified in this document.
I, R, T, and TID: Defined in [RFC8505].
Registration Ownership Verifier (ROVR): When the "C" flag is set,
this field contains a Crypto-ID.
This specification uses Status values "Validation Requested" and
"Validation Failed", which are defined in [RFC8505]. No other new
Status values are defined.
4.3. Crypto-ID Parameters Option
This specification defines the Crypto-ID Parameters Option (CIPO).
The CIPO carries the parameters used to form a Crypto-ID.
In order to provide cryptographic agility [RFC7696], this
specification supports different elliptic curves, indicated by a
Crypto-Type field:
* NIST P-256 [FIPS186-4] MUST be supported by all implementations.
* The Edwards-Curve Digital Signature Algorithm (EdDSA) curve
Ed25519 (PureEdDSA) [RFC8032] MAY be supported as an alternate.
* the specification is open to future extensions for different
cryptographic algorithms and longer keys.
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0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Type | Length |Reserved1| Public Key Length |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Crypto-Type | Modifier | Reserved2 |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
| |
. .
. Public Key (variable length) .
. .
| |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
. .
. Padding .
. .
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 2: Crypto-ID Parameters Option
Type: 8-bit unsigned integer. to be assigned by IANA, see Table 1.
Length: 8-bit unsigned integer. The length of the option in units
of 8 octets.
Reserved1: 5-bit unsigned integer. It MUST be set to zero by the
sender and MUST be ignored by the receiver.
Public Key Length: 13-bit unsigned integer. The length of the
Public Key field in bytes.
Crypto-Type: 8-bit unsigned integer. The type of cryptographic
algorithm used in calculation Crypto-ID (see Table 2 in
Section 8.3). Although the different signature schemes target
similar cryptographic strength, they rely on different curves,
hash functions, signature algorithms, and/or representation
conventions.
Modifier: 8-bit unsigned integer. Set to an arbitrary value by the
creator of the Crypto-ID. The role of the modifier is to enable
the formation of multiple Crypto-IDs from a same key pair, which
reduces the traceability and thus improves the privacy of a
constrained node that could not maintain many key-pairs.
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Reserved2: 16-bit unsigned integer. It MUST be set to zero by the
sender and MUST be ignored by the receiver.
Public Key: A variable-length field, size indicated in the Public
Key Length field. JWK-Encoded Public Key [RFC7517].
Padding: A variable-length field completing the Public Key field to
align to the next 8-bytes boundary.
The implementation of multiple hash functions in a constrained
devices may consume excessive amounts of program memory.
[CURVE-REPRESENTATIONS] provides information on how to represent
Montgomery curves and (twisted) Edwards curves as curves in short-
Weierstrass form and illustrates how this can be used to implement
elliptic curve computations using existing implementations that
already provide, e.g., ECDSA and ECDH using NIST [FIPS186-4] prime
curves.
For more details on representation conventions, we refer to
Appendix B.
4.4. NDP Signature Option
The format of the NDP Signature Option (NDPSO) is illustrated in
Figure 3.
As opposed to the RSA Signature Option (RSAO) defined in section 5.2.
of SEND [RFC3971], the NDPSO does not have a key hash field. The
hash that can be used as index is the 128 leftmost bits of the ROVR
field in the EARO.
The CIPO may be present in the same message as the NDPSO. If not, it
can be found in an abstract table that was created by a previous
message and indexed by the hash.
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0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Type | Length | Pad Length | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +
| Reserved |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
| |
. .
. Digital Signature .
. .
| |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
. .
. Padding .
. .
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 3: NDP signature Option
Type: to be assigned by IANA, see Table 1.
Length: 8-bit unsigned integer. The length of the option in units
of 8 octets.
Pad Length: 8-bit unsigned integer. The length of the Padding
field.
Reserved: 40-bit unsigned integer. It MUST be set to zero by the
sender and MUST be ignored by the receiver.
Digital Signature: A variable-length field containing a digital
signature. The computation of the digital signature depends on
the Crypto-Type which is found in the associated CIPO. For the
values of the Crypto-Type that are defined in ths specification,
the signature is computed as detailed in Section 6.2.
Padding: A variable-length field making the option length a multiple
of 8, containing as many octets as specified in the Pad Length
field. Typically there is no need of a padding and the field is
NULL.
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5. Protocol Scope
The scope of the protocol specified here is a 6LoWPAN LLN, typically
a stub network connected to a larger IP network via a Border Router
called a 6LBR per [RFC6775]. A 6LBR has sufficient capability to
satisfy the needs of duplicate address detection.
The 6LBR maintains registration state for all devices in its attached
LLN. Together with the first-hop router (the 6LR), the 6LBR assures
uniqueness and grants ownership of an IPv6 address before it can be
used in the LLN. This is in contrast to a traditional network that
relies on IPv6 address auto-configuration [RFC4862], where there is
no guarantee of ownership from the network, and each IPv6 Neighbor
Discovery packet must be individually secured [RFC3971].
---+-------- ............
| External Network
|
+-----+
| | 6LBR
+-----+
o o o
o o o o
o o LLN o o o
o o o (6LR)
o (6LN)
Figure 4: Basic Configuration
In a mesh network, the 6LR is directly connected to the host device.
This specification mandates that the peer-wise layer-2 security is
deployed so that all the packets from a particular host are securely
identifiable by the 6LR. The 6LR may be multiple hops away from the
6LBR. Packets are routed between the 6LR and the 6LBR via other
6LRs. This specification mandates that a chain of trust is
established so that a packet that was validated by the first 6LR can
be safely routed by other on-path 6LRs to the 6LBR.
6. Protocol Flows
The 6LR/6LBR ensures first-come/first-serve by storing the EARO
information including the Crypto-ID associated to the node being
registered. The node can claim any address as long as it is the
first to make such a claim. After a successful registration, the
node becomes the owner of the registered address and the address is
bound to the Crypto-ID in the 6LR/6LBR registry.
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This specification enables the 6LR to verify the ownership of the
binding at any time assuming that the "C" flag is set. The
verification prevents other nodes from stealing the address and
trying to attract traffic for that address or use it as their source
address.
A node may use multiple IPv6 addresses at the same time. The node
MAY use the same Crypto-ID, to prove the ownership of multiple IPv6
addresses. The separation of the address and the cryptographic
material avoids the constrained device to compute multiple keys for
multiple addresses. The registration process allows the node to use
the same Crypto-ID for all of its addresses.
6.1. First Exchange with a 6LR
A 6LN registers to a 6LR that is one hop away from it with the "C"
flag set in the EARO, indicating that the ROVR field contains a
Crypto-ID. The Target Address in the NS message indicates the IPv6
address that the 6LN is trying to register. The on-link (local)
protocol interactions are shown in Figure 5. If the 6LR does not
have a state with the 6LN that is consistent with the NS(EARO), then
it replies with a challenge NA (EARO, status=Validation Requested)
that contains a Nonce Option (shown as NonceLR in Figure 5). The
Nonce option contains a Nonce value that, to the extent possible for
the implementation, was never employed in association with the key
pair used to generate the ROVR. This specification inherits from
[RFC3971] that simply indicates that the nonce is a random value.
Ideally, an implementation would use an unpredictable
cryptographically random value [RFC4086]. But that may be
impractical in some LLN scenarios where the devices do not have a
guaranteed sense of time and for which computing complex hashes is
detrimental to the battery lifetime. Alternatively, the device may
use an always-incrementing value saved in the same stable storage as
the key, so they are lost together, and starting at a best effort
random value, either as Nonce value or as a component to its
computation.
The 6LN replies to the challenge with an NS(EARO) that includes a new
Nonce option (shown as NonceLN in Figure 5), the CIPO (Section 4.3),
and the NDPSO containing the signature. The information associated
to a Crypto-ID stored by the 6LR on the first NS exchange where it
appears. The 6LR MUST store the CIPO parameters associated with the
Crypto-ID so it can be used for more than one address.
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6LN 6LR
| |
|<------------------------- RA -------------------------|
| | ^
|---------------- NS with EARO (Crypto-ID) ------------>| |
| | option
|<- NA with EARO (status=Validation Requested), NonceLR-| |
| | v
|------- NS with EARO, CIPO, NonceLN and NDPSO -------->|
| |
|<------------------- NA with EARO ---------------------|
| |
...
| |
|--------------- NS with EARO (Crypto-ID) ------------->|
| |
|<------------------- NA with EARO ---------------------|
| |
...
| |
|--------------- NS with EARO (Crypto-ID) ------------->|
| |
|<------------------- NA with EARO ---------------------|
| |
Figure 5: On-link Protocol Operation
The steps for the registration to the 6LR are as follows:
* Upon the first exchange with a 6LR, a 6LN will be challenged to
prove ownership of the Crypto-ID and the Target Address being
registered in the Neighbor Solicitation message. When a 6LR
receives a NS(EARO) registration with a new Crypto-ID as a ROVR,
and unless the registration is rejected for another reason, it
MUST challenge by responding with a NA(EARO) with a status of
"Validation Requested".
* The challenge is triggered when the registration for a Source
Link-Layer Address is not verifiable either at the 6LR or the
6LBR. In the latter case, the 6LBR returns a status of
"Validation Requested" in the DAR/DAC exchange, which is echoed by
the 6LR in the NA (EARO) back to the registering node. The
challenge MUST NOT alter a valid registration in the 6LR or the
6LBR.
* Upon receiving a first NA(EARO) with a status of "Validation
Requested" from a 6LR, the registering node SHOULD retry its
registration with a Crypto-ID Parameters Option (CIPO)
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(Section 4.3) that contains all the necessary material for
building the Crypto-ID, the NonceLN that it generated, and the NDP
signature (Section 4.4) option that proves its ownership of the
Crypto-ID and intent of registering the Target Address. In
subsequent revalidation with the same 6LR, the 6LN MAY try to omit
the CIPO to save bandwidth, with the expectation that the 6LR
saved it. If the validation fails and it gets challenged again,
then it SHOULD add the CIPO again.
* In order to validate the ownership, the 6LR performs the same
steps as the 6LN and rebuilds the Crypto-ID based on the
parameters in the CIPO. If the rebuilt Crypto-ID matches the
ROVR, the 6LN also verifies the signature contained in the NDPSO
option. If at that point the signature in the NDPSO option can be
verified, then the validation succeeds. Otherwise the validation
fails.
* If the 6LR fails to validate the signed NS(EARO), it responds with
a status of "Validation Failed". After receiving a NA(EARO) with
a status of "Validation Failed", the registering node SHOULD try
to register an alternate target address in the NS message.
6.2. NDPSO generation and verification
The signature generated by the 6LN to provide proof-of-ownership of
the private-key is carried in the NDP Signature Option (NDPSO). It
is generated by the 6LN in a fashion that depends on the Crypto-Type
(see Table 2 in Section 8.3) chosen by the 6LN as follows:
* Concatenate the following in the order listed:
1. The 128-bit Message Type tag [RFC3972] (in network byte order).
For this specification the tag is 0x8701 55c8 0cca dd32 6ab7 e415
f148 84d0. (The tag value has been generated by the editor of
this specification on random.org).
2. JWK-encoded public key
3. the 16-byte Target Address (in network byte order) sent in the
Neighbor Solicitation (NS) message. It is the address which the
6LN is registering with the 6LR and 6LBR.
4. NonceLR received from the 6LR (in network byte order) in the
Neighbor Advertisement (NA) message. The Nonce is at least 6
bytes long as defined in [RFC3971].
5. NonceLN sent from the 6LN (in network byte order). The Nonce is
at least 6 bytes long as defined in [RFC3971].
6. The length of the ROVR field in the NS message containing the
Crypto-ID that was sent.
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7. 1-byte (in network byte order) Crypto-Type value sent in the CIPO
option.
* Depending on the Crypto-Type, apply the hash function on this
concatenation.
* Depending on the Crypto-Type, sign the hash output with ECDSA (if
curve P-256 is used) or sign the hash with EdDSA (if curve Ed25519
(PureEdDSA)).
The 6LR on receiving the NDPSO and CIPO options first regenerates the
Crypto-ID based on the CIPO option to make sure that the leftmost
bits up to the size of the ROVR match. If and only if the check is
successful, it tries to verify the signature in the NDPSO option
using the following:
* Concatenate the following in the order listed:
1. 128-bit type tag (in network byte order)
2. JWK-encoded public key received in the CIPO option
3. the 16-byte Target Address (in network byte order) received in
the Neighbor Solicitation (NS) message. It is the address which
the 6LN is registering with the 6LR and 6LBR.
4. NonceLR sent in the Neighbor Advertisement (NA) message. The
Nonce is at least 6 bytes long as defined in [RFC3971].
5. NonceLN received from the 6LN (in network byte order) in the NS
message. The Nonce is at least 6 bytes long as defined in
[RFC3971].
6. The length of the ROVR field in the NS message containing the
Crypto-ID that was received.
7. 1-byte (in network byte order) Crypto-Type value received in the
CIPO option.
* Depending on the Crypto-Type indicated by the (6LN) in the CIPO,
apply the hash function on this concatenation.
* Verify the signature with the public-key received and the locally
computed values. If the verification succeeds, the 6LR and 6LBR
add the state information about the Crypto-ID, public-key and
Target Address being registered to their database.
6.3. Multihop Operation
In a multihop 6LoWPAN, the registration with Crypto-ID is propagated
to 6LBR as described in this section. If the 6LR and the 6LBR
maintain a security association, then there is no need to propagate
the proof of ownership to the 6LBR.
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A new device that joins the network auto-configures an address and
performs an initial registration to a neighboring 6LR with an NS
message that carries an Address Registration Option (EARO) [RFC8505].
The 6LR validates the address with an 6LBR using a DAR/DAC exchange,
and the 6LR confirms (or denies) the address ownership with an NA
message that also carries an Address Registration Option.
Figure 6 illustrates a registration flow all the way to a 6LowPAN
Backbone Router (6BBR) [BACKBONE-ROUTER].
6LN 6LR 6LBR 6BBR
| | | |
| NS(EARO) | | |
|--------------->| | |
| | Extended DAR | |
| |-------------->| |
| | | |
| | | proxy NS(EARO) |
| | |--------------->|
| | | | NS(DAD)
| | | | ------>
| | | |
| | | | <wait>
| | | |
| | | proxy NA(EARO) |
| | |<---------------|
| | Extended DAC | |
| |<--------------| |
| NA(EARO) | | |
|<---------------| | |
| | | |
Figure 6: (Re-)Registration Flow
In a multihop 6LoWPAN, a 6LBR sends RAs with prefixes downstream and
the 6LR receives and relays them to the nodes. 6LR and 6LBR
communicate using ICMPv6 Duplicate Address Request (DAR) and
Duplicate Address Confirmation (DAC) messages. The DAR and DAC use
the same message format as NS and NA, but have different ICMPv6 type
values.
In AP-ND we extend DAR/DAC messages to carry cryptographically
generated ROVR. In a multihop 6LoWPAN, the node exchanges the
messages shown in Figure 6. The 6LBR must identify who owns an
address (EUI-64) to defend it, if there is an attacker on another
6LR.
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7. Security Considerations
7.1. Inheriting from RFC 3971
Observations regarding the following threats to the local network in
[RFC3971] also apply to this specification.
Neighbor Solicitation/Advertisement Spoofing: Threats in section
9.2.1 of RFC3971 apply. AP-ND counters the threats on NS(EARO)
messages by requiring that the NDP Signature and CIPO options be
present in these solicitations.
Duplicate Address Detection DoS Attack: Inside the LLN, Duplicate
Addresses are sorted out using the ROVR, which differentiates it
from a movement. DAD coming from the backbone are not forwarded
over the LLN, which provides some protection against DoS attacks
inside the resource-constrained part of the network. Over the
backbone, the EARO option is present in NS/NA messages. This
protects against misinterpreting a movement for a duplication, and
enables the backbone routers to determine which one has the
freshest registration and is thus the best candidate to validate
the registration for the device attached to it. But this
specification does not guarantee that the backbone router claiming
an address over the backbone is not an attacker.
Router Solicitation and Advertisement Attacks: This specification
does not change the protection of RS and RA which can still be
protected by SEND.
Replay Attacks Using Nonces (NonceLR and NonceLN) generated by both
the 6LR and 6LN provides an efficient protection against replay
attacks of challenge response flow. The quality of the protection
still depends on the quality of the Nonce, in particular of a
random generator if they are computed that way.
Neighbor Discovery DoS Attack: A rogue node that managed to access
the L2 network may form many addresses and register them using AP-
ND. The perimeter of the attack is all the 6LRs in range of the
attacker. The 6LR MUST protect itself against overflows and
reject excessive registration with a status 2 "Neighbor Cache
Full". This effectively blocks another (honest) 6LN from
registering to the same 6LR, but the 6LN may register to other
6LRs that are in its range but not in that of the rogue.
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7.2. Related to 6LoWPAN ND
The threats discussed in 6LoWPAN ND [RFC6775][RFC8505] also apply
here. Compared with SeND, this specification saves about 1Kbyte in
every NS/NA message. Also, this specification separates the
cryptographic identifier from the registered IPv6 address so that a
node can have more than one IPv6 address protected by the same
cryptographic identifier. SeND forces the IPv6 address to be
cryptographic since it integrates the CGA as the IID in the IPv6
address. This specification frees the device to form its addresses
in any fashion, thereby enabling not only 6LoWPAN compression which
derives IPv6 addresses from Layer-2 addresses but also privacy
addresses.
7.3. ROVR Collisions
A collision of Registration Ownership Verifiers (ROVR) (i.e., the
Crypto-ID in this specification) is possible, but it is a rare event.
The formula for calculating the probability of a collision is 1 -
e^{-k^2/(2n)} where n is the maximum population size (2^64 here,
1.84E19) and K is the actual population (number of nodes). If the
Crypto-ID is 64-bits (the least possible size allowed), the chance of
a collision is 0.01% when the network contains 66 million nodes.
Moreover, the collision is only relevant when this happens within one
stub network (6LBR). In the case of such a collision, an attacker
may be able to claim the registered address of an another legitimate
node. However for this to happen, the attacker would also need to
know the address which was registered by the legitimate node. This
registered address is never broadcasted on the network and therefore
providing an additional 64-bits that an attacker must correctly
guess. To prevent address disclosure, it is RECOMMENDED that nodes
derive the address being registered independently of the ROVR.
7.4. Implementation Attacks
The signature schemes referenced in this specification comply with
NIST [FIPS186-4] or Crypto Forum Research Group (CFRG) standards
[RFC8032] and offer strong algorithmic security at roughly 128-bit
security level. These signature schemes use elliptic curves that
were either specifically designed with exception-free and constant-
time arithmetic in mind [RFC7748] or where one has extensive
implementation experience of resistance to timing attacks
[FIPS186-4]. However, careless implementations of the signing
operations could nevertheless leak information on private keys. For
example, there are micro-architectural side channel attacks that
implementors should be aware of [breaking-ed25519]. Implementors
should be particularly aware that a secure implementation of Ed25519
requires a protected implementation of the hash function SHA-512,
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whereas this is not required with implementations of SHA-256 used
with ECDSA.
7.5. Cross-Protocol Attacks
The same private key MUST NOT be reused with more than one signature
scheme in this specification.
7.6. Compromised 6LR
This specification distributes the challenge and its validation at
the edge of the network, between the 6LN and its 6LR. The central
6LBR is offloaded, which avoids DOS attacks targeted at that central
entity. This also saves back and forth exchanges across a
potentially large and constrained network.
The downside is that the 6LBR needs to trust the 6LR for performing
the checking adequately, and the communication between the 6LR and
the 6LBR must be protected to avoid tempering with the result of the
test.
If a 6LR is compromised, it may pretend that it owns any address and
defeat the protection. It may also admit any rogue and let it take
ownership of any address in the network, provided that the 6LR knows
the ROVR field used by the real owner of the address.
8. IANA considerations
8.1. CGA Message Type
This document defines a new 128-bit value under the CGA Message Type
[RFC3972] name space: 0x8701 55c8 0cca dd32 6ab7 e415 f148 84d0.
8.2. IPv6 ND option types
This document registers two new ND option types under the subregistry
"IPv6 Neighbor Discovery Option Formats":
+------------------------------+-----------------+---------------+
| Option Name | Suggested Value | Reference |
+==============================+=================+===============+
| NDP Signature Option (NDPSO) | 38 | This document |
+------------------------------+-----------------+---------------+
| Crypto-ID Parameters Option | 39 | This document |
| (CIPO) | | |
+------------------------------+-----------------+---------------+
Table 1: New ND options
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8.3. Crypto-Type Subregistry
IANA is requested to create a new subregistry "Crypto-Type
Subregistry" in the "Internet Control Message Protocol version 6
(ICMPv6) Parameters". The registry is indexed by an integer in the
interval 0..255 and contains an Elliptic Curve, a Hash Function, a
Signature Algorithm, and Representation Conventions, as shown in
Table 2, which together specify a signature scheme. The following
Crypto-Type values are defined in this document:
+----------------+-----------------+-------------+-----------------+
| Crypto-Type | 0 (ECDSA256) | 1 (Ed25519) | 2 (ECDSA25519) |
| value | | | |
+================+=================+=============+=================+
| Elliptic curve | NIST P-256 | Curve25519 | Curve25519 |
| | [FIPS186-4] | [RFC7748] | [RFC7748] |
+----------------+-----------------+-------------+-----------------+
| Hash function | SHA-256 | SHA-512 | SHA-256 |
| | [RFC6234] | [RFC6234] | [RFC6234] |
+----------------+-----------------+-------------+-----------------+
| Signature | ECDSA | Ed25519 | ECDSA |
| algorithm | [FIPS186-4] | [RFC8032] | [FIPS186-4] |
+----------------+-----------------+-------------+-----------------+
| Representation | Weierstrass, | Edwards, | Weierstrass, |
| conventions | (un)compressed, | compressed, | (un)compressed, |
| | MSB/msb first | LSB/lsb | MSB/msb first |
| | | first | |
+----------------+-----------------+-------------+-----------------+
| Defining | This document | This | This document |
| specification | | document | |
+----------------+-----------------+-------------+-----------------+
Table 2: Crypto-Types
New Crypto-Type values providing similar or better security (with
less code) may be defined in the future.
Assignment of new values for new Crypto-Type MUST be done through
IANA with either "Specification Required" or "IESG Approval" as
defined in [RFC8126].
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9. Acknowledgments
Many thanks to Charlie Perkins for his in-depth review and
constructive suggestions. The authors are also especially grateful
to Robert Moskowitz for his comments that led to many improvements.
The authors wish to thank Mirja Kuhlewind, Eric Vyncke, Vijay
Gurbani, Al Morton and Adam Montville for their constructive reviews
during the IESG process.
10. Normative References
[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>.
[RFC6775] Shelby, Z., Ed., Chakrabarti, S., Nordmark, E., and C.
Bormann, "Neighbor Discovery Optimization for IPv6 over
Low-Power Wireless Personal Area Networks (6LoWPANs)",
RFC 6775, DOI 10.17487/RFC6775, November 2012,
<https://www.rfc-editor.org/info/rfc6775>.
[RFC7517] Jones, M., "JSON Web Key (JWK)", RFC 7517,
DOI 10.17487/RFC7517, May 2015,
<https://www.rfc-editor.org/info/rfc7517>.
[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>.
[RFC3971] Arkko, J., Ed., Kempf, J., Zill, B., and P. Nikander,
"SEcure Neighbor Discovery (SEND)", RFC 3971,
DOI 10.17487/RFC3971, March 2005,
<https://www.rfc-editor.org/info/rfc3971>.
[RFC8505] Thubert, P., Ed., Nordmark, E., Chakrabarti, S., and C.
Perkins, "Registration Extensions for IPv6 over Low-Power
Wireless Personal Area Network (6LoWPAN) Neighbor
Discovery", RFC 8505, DOI 10.17487/RFC8505, November 2018,
<https://www.rfc-editor.org/info/rfc8505>.
[FIPS186-4]
FIPS 186-4, "Digital Signature Standard (DSS), Federal
Information Processing Standards Publication 186-4", US
Department of Commerce/National Institute of Standards and
Technology , July 2013.
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[SEC1] SEC1, "SEC 1: Elliptic Curve Cryptography, Version 2.0",
Standards for Efficient Cryptography , June 2009.
11. Informative references
[RFC3972] Aura, T., "Cryptographically Generated Addresses (CGA)",
RFC 3972, DOI 10.17487/RFC3972, March 2005,
<https://www.rfc-editor.org/info/rfc3972>.
[RFC4861] Narten, T., Nordmark, E., Simpson, W., and H. Soliman,
"Neighbor Discovery for IP version 6 (IPv6)", RFC 4861,
DOI 10.17487/RFC4861, September 2007,
<https://www.rfc-editor.org/info/rfc4861>.
[RFC4862] Thomson, S., Narten, T., and T. Jinmei, "IPv6 Stateless
Address Autoconfiguration", RFC 4862,
DOI 10.17487/RFC4862, September 2007,
<https://www.rfc-editor.org/info/rfc4862>.
[RFC7748] Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves
for Security", RFC 7748, DOI 10.17487/RFC7748, January
2016, <https://www.rfc-editor.org/info/rfc7748>.
[RFC8032] Josefsson, S. and I. Liusvaara, "Edwards-Curve Digital
Signature Algorithm (EdDSA)", RFC 8032,
DOI 10.17487/RFC8032, January 2017,
<https://www.rfc-editor.org/info/rfc8032>.
[RFC4944] Montenegro, G., Kushalnagar, N., Hui, J., and D. Culler,
"Transmission of IPv6 Packets over IEEE 802.15.4
Networks", RFC 4944, DOI 10.17487/RFC4944, September 2007,
<https://www.rfc-editor.org/info/rfc4944>.
[RFC6282] Hui, J., Ed. and P. Thubert, "Compression Format for IPv6
Datagrams over IEEE 802.15.4-Based Networks", RFC 6282,
DOI 10.17487/RFC6282, September 2011,
<https://www.rfc-editor.org/info/rfc6282>.
[RFC4919] Kushalnagar, N., Montenegro, G., and C. Schumacher, "IPv6
over Low-Power Wireless Personal Area Networks (6LoWPANs):
Overview, Assumptions, Problem Statement, and Goals",
RFC 4919, DOI 10.17487/RFC4919, August 2007,
<https://www.rfc-editor.org/info/rfc4919>.
[RFC4086] Eastlake 3rd, D., Schiller, J., and S. Crocker,
"Randomness Requirements for Security", BCP 106, RFC 4086,
DOI 10.17487/RFC4086, June 2005,
<https://www.rfc-editor.org/info/rfc4086>.
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[RFC8126] Cotton, M., Leiba, B., and T. Narten, "Guidelines for
Writing an IANA Considerations Section in RFCs", BCP 26,
RFC 8126, DOI 10.17487/RFC8126, June 2017,
<https://www.rfc-editor.org/info/rfc8126>.
[RFC6234] Eastlake 3rd, D. and T. Hansen, "US Secure Hash Algorithms
(SHA and SHA-based HMAC and HKDF)", RFC 6234,
DOI 10.17487/RFC6234, May 2011,
<https://www.rfc-editor.org/info/rfc6234>.
[RFC7039] Wu, J., Bi, J., Bagnulo, M., Baker, F., and C. Vogt, Ed.,
"Source Address Validation Improvement (SAVI) Framework",
RFC 7039, DOI 10.17487/RFC7039, October 2013,
<https://www.rfc-editor.org/info/rfc7039>.
[RFC7217] Gont, F., "A Method for Generating Semantically Opaque
Interface Identifiers with IPv6 Stateless Address
Autoconfiguration (SLAAC)", RFC 7217,
DOI 10.17487/RFC7217, April 2014,
<https://www.rfc-editor.org/info/rfc7217>.
[RFC7696] Housley, R., "Guidelines for Cryptographic Algorithm
Agility and Selecting Mandatory-to-Implement Algorithms",
BCP 201, RFC 7696, DOI 10.17487/RFC7696, November 2015,
<https://www.rfc-editor.org/info/rfc7696>.
[BACKBONE-ROUTER]
Thubert, P., Perkins, C., and E. Levy-Abegnoli, "IPv6
Backbone Router", Work in Progress, Internet-Draft, draft-
ietf-6lo-backbone-router-13, 26 September 2019,
<https://tools.ietf.org/html/draft-ietf-6lo-backbone-
router-13>.
[CURVE-REPRESENTATIONS]
Struik, R., "Alternative Elliptic Curve Representations",
Work in Progress, Internet-Draft, draft-ietf-lwig-curve-
representations-08, 24 July 2019,
<https://tools.ietf.org/html/draft-ietf-lwig-curve-
representations-08>.
[breaking-ed25519]
Samwel, N., Batina, L., Bertoni, G., Daemen, J., and R.
Susella, "Breaking Ed25519 in WolfSSL", Cryptographers'
Track at the RSA Conference , 2018,
<https://link.springer.com/
chapter/10.1007/978-3-319-76953-0_1>.
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Appendix A. Requirements Addressed in this Document
In this section we state requirements of a secure neighbor discovery
protocol for low-power and lossy networks.
* The protocol MUST be based on the Neighbor Discovery Optimization
for Low-power and Lossy Networks protocol defined in [RFC6775].
RFC6775 utilizes optimizations such as host-initiated interactions
for sleeping resource-constrained hosts and elimination of
multicast address resolution.
* New options to be added to Neighbor Solicitation messages MUST
lead to small packet sizes, especially compared with existing
protocols such as SEcure Neighbor Discovery (SEND). Smaller
packet sizes facilitate low-power transmission by resource-
constrained nodes on lossy links.
* The support for this registration mechanism SHOULD be extensible
to more LLN links than IEEE 802.15.4 only. Support for at least
the LLN links for which a 6lo "IPv6 over foo" specification
exists, as well as Low-Power Wi-Fi SHOULD be possible.
* As part of this extension, a mechanism to compute a unique
Identifier should be provided with the capability to form a Link
Local Address that SHOULD be unique at least within the LLN
connected to a 6LBR.
* The Address Registration Option used in the ND registration SHOULD
be extended to carry the relevant forms of Unique Interface
Identifier.
* The Neighbor Discovery should specify the formation of a site-
local address that follows the security recommendations from
[RFC7217].
Appendix B. Representation Conventions
B.1. Signature Schemes
The signature scheme ECDSA256 corresponding to Crypto-Type 0 is
ECDSA, as specified in [FIPS186-4], instantiated with the NIST prime
curve P-256, as specified in Appendix B of [FIPS186-4], and the hash
function SHA-256, as specified in [RFC6234], where points of this
NIST curve are represented as points of a short-Weierstrass curve
(see [FIPS186-4]) and are encoded as octet strings in most-
significant-bit first (msb) and most-significant-byte first (MSB)
order. The signature itself consists of two integers (r and s),
which are each encoded as fixed-size octet strings in most-
significant-bit first and most-significant-byte first order. For
details on ECDSA, see [FIPS186-4]; for details on the integer
encoding, see Appendix B.2.
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The signature scheme Ed25519 corresponding to Crypto-Type 1 is EdDSA,
as specified in [RFC8032], instantiated with the Montgomery curve
Curve25519, as specified in [RFC7748], and the hash function SHA-512,
as specified in [RFC6234], where points of this Montgomery curve are
represented as points of the corresponding twisted Edwards curve (see
Appendix B.3) and are encoded as octet strings in least-significant-
bit first (lsb) and least-significant-byte first (LSB) order. The
signature itself consists of a bit string that encodes a point of
this twisted Edwards curve, in compressed format, and an integer
encoded in least-significant-bit first and least-significant-byte
first order. For details on EdDSA and on the encoding conversions,
see the specification of pure Ed25519 in . [RFC8032]
The signature scheme ECDSA25519 corresponding to Crypto-Type 2 is
ECDSA, as specified in [FIPS186-4], instantiated with the Montgomery
curve Curve25519, as specified in [RFC7748], and the hash function
SHA-256, as specified in [RFC6234], where points of this Montgomery
curve are represented as points of a corresponding curve in short-
Weierstrass form (see Appendix B.3) and are encoded as octet strings
in most-significant-bit first and most-significant-byte first order.
The signature itself consists of a bit string that encodes two
integers, each encoded as fixed-size octet strings in most-
significant-bit first and most-significant-byte first order. For
details on ECDSA, see [FIPS186-4]; for details on the integer
encoding, see Appendix B.2
B.2. Integer Representation for ECDSA signatures
With ECDSA, each signature is a pair (r, s) of integers [FIPS186-4].
Each integer is encoded as a fixed-size 256-bit bit string, where
each integer is represented according to the Field Element to Octet
String and Octet String to Bit String conversion rules in [SEC1] and
where the ordered pair of integers is represented as the
rightconcatenation of the resulting representation values. The
inverse operation follows the corresponding Bit String to Octet
String and Octet String to Field Element conversion rules of [SEC1].
B.3. Alternative Representations of Curve25519
The elliptic curve Curve25519, as specified in [RFC7748], is a so-
called Montgomery curve. Each point of this curve can also be
represented as a point of a twisted Edwards curve or as a point of an
elliptic curve in short-Weierstrass form, via a coordinate
transformation (a so-called isomorphic mapping). The parameters of
the Montgomery curve and the corresponding isomorphic curves in
twisted Edwards curve and short-Weierstrass form are as indicated
below. Here, the domain parameters of the Montgomery curve
Curve25519 and of the twisted Edwards curve Edwards25519 are as
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specified in [RFC7748]; the domain parameters of the elliptic curve
Wei25519 in short-Weierstrass curve comply with Section 6.1.1 of
[FIPS186-4]. For details of the coordinate transformation referenced
above, see [RFC7748] and [CURVE-REPRESENTATIONS].
General parameters (for all curve models):
p 2^{255}-19
(=0x7fffffff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff
ffffffed)
h 8
n
723700557733226221397318656304299424085711635937990760600195093828
5454250989
(=2^{252} + 0x14def9de a2f79cd6 5812631a 5cf5d3ed)
Montgomery curve-specific parameters (for Curve25519):
A 486662
B 1
Gu 9 (=0x9)
Gv
147816194475895447910205935684099868872646061346164752889648818377
55586237401
(=0x20ae19a1 b8a086b4 e01edd2c 7748d14c 923d4d7e 6d7c61b2 29e9c5a2
7eced3d9)
Twisted Edwards curve-specific parameters (for Edwards25519):
a -1 (-0x01)
d -121665/121666
(=3709570593466943934313808350875456518954211387984321901638878553
3085940283555)
(=0x52036cee 2b6ffe73 8cc74079 7779e898 00700a4d 4141d8ab 75eb4dca
135978a3)
Gx
151122213495354007725011514095885315114540126930418572060461132839
49847762202
(=0x216936d3 cd6e53fe c0a4e231 fdd6dc5c 692cc760 9525a7b2 c9562d60
8f25d51a)
Gy 4/5
(=4631683569492647816942839400347516314130799386625622561578303360
3165251855960)
(=0x66666666 66666666 66666666 66666666 66666666 66666666 66666666
66666658)
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Weierstrass curve-specific parameters (for Wei25519):
a
192986815395526992372618308347813179755449974442734273399095973345
73241639236
(=0x2aaaaaaa aaaaaaaa aaaaaaaa aaaaaaaa aaaaaaaa aaaaaaaa aaaaaa98
4914a144)
b
557517466698189089076452890782571408182411037279010123152944008379
56729358436
(=0x7b425ed0 97b425ed 097b425e d097b425 ed097b42 5ed097b4 260b5e9c
7710c864)
GX
192986815395526992372618308347813179755449974442734273399095973346
52188435546
(=0x2aaaaaaa aaaaaaaa aaaaaaaa aaaaaaaa aaaaaaaa aaaaaaaa aaaaaaaa
aaad245a)
GY
147816194475895447910205935684099868872646061346164752889648818377
55586237401
(=0x20ae19a1 b8a086b4 e01edd2c 7748d14c 923d4d7e 6d7c61b2 29e9c5a2
7eced3d9)
Authors' Addresses
Pascal Thubert (editor)
Cisco Systems, Inc
Building D
45 Allee des Ormes - BP1200
06254 MOUGINS - Sophia Antipolis
France
Phone: +33 497 23 26 34
Email: pthubert@cisco.com
Behcet Sarikaya
Email: sarikaya@ieee.org
Mohit Sethi
Ericsson
FI-02420 Jorvas
Finland
Email: mohit@piuha.net
Thubert, et al. Expires 3 August 2020 [Page 27]
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Rene Struik
Struik Security Consultancy
Email: rstruik.ext@gmail.com
Thubert, et al. Expires 3 August 2020 [Page 28]