CFRG E. Lundberg, Ed.
Internet-Draft J. Bradley
Intended status: Informational Yubico
Expires: 19 September 2024 18 March 2024
The Asynchronous Remote Key Generation (ARKG) algorithm
draft-bradleylundberg-cfrg-arkg-01
Abstract
Asynchronous Remote Key Generation (ARKG) is an abstract algorithm
that enables delegation of asymmetric public key generation without
giving access to the corresponding private keys. This capability
enables a variety of applications: a user agent can generate
pseudonymous public keys to prevent tracking; a message sender can
generate ephemeral recipient public keys to enhance forward secrecy;
two paired authentication devices can each have their own private
keys while each can register public keys on behalf of the other.
This document provides three main contributions: a specification of
the generic ARKG algorithm using abstract primitives; a set of
formulae for instantiating the abstract primitives using concrete
primitives; and an initial set of fully specified concrete ARKG
instances. We expect that additional instances will be defined in
the future.
About This Document
This note is to be removed before publishing as an RFC.
Status information for this document may be found at
https://datatracker.ietf.org/doc/draft-bradleylundberg-cfrg-arkg/.
Source for this draft and an issue tracker can be found at
https://github.com/Yubico/arkg-rfc.
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provisions of BCP 78 and BCP 79.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1. Requirements Language . . . . . . . . . . . . . . . . . . 5
1.2. Notation . . . . . . . . . . . . . . . . . . . . . . . . 5
2. The Asynchronous Remote Key Generation (ARKG) algorithm . . . 5
2.1. Instance parameters . . . . . . . . . . . . . . . . . . . 6
2.2. The function ARKG-Generate-Seed . . . . . . . . . . . . . 9
2.3. The function ARKG-Derive-Public-Key . . . . . . . . . . . 9
2.4. The function ARKG-Derive-Secret-Key . . . . . . . . . . . 10
3. Generic ARKG instantiations . . . . . . . . . . . . . . . . . 11
3.1. Using elliptic curve arithmetic for key blinding . . . . 12
3.2. Using ECDH as the KEM . . . . . . . . . . . . . . . . . . 13
3.3. Using both elliptic curve arithmetic for key blinding and
ECDH as the KEM . . . . . . . . . . . . . . . . . . . . . 14
3.4. Using HMAC as the MAC . . . . . . . . . . . . . . . . . . 15
3.5. Using HKDF as the KDF . . . . . . . . . . . . . . . . . . 15
4. Concrete ARKG instantiations . . . . . . . . . . . . . . . . 15
4.1. ARKG-P256-ECDH-P256-HMAC-SHA256-HKDF-SHA256 . . . . . . . 15
4.2. ARKG-P384-ECDH-P384-HMAC-SHA384-HKDF-SHA384 . . . . . . . 16
4.3. ARKG-P521-ECDH-P521-HMAC-SHA512-HKDF-SHA512 . . . . . . . 17
4.4. ARKG-P256k-ECDH-P256k-HMAC-SHA256-HKDF-SHA256 . . . . . . 17
4.5. ARKG-Ed25519-X25519-HMAC-SHA256-HKDF-SHA256 . . . . . . . 18
4.6. ARKG-X25519-X25519-HMAC-SHA256-HKDF-SHA256 . . . . . . . 18
5. COSE bindings . . . . . . . . . . . . . . . . . . . . . . . . 19
6. Security Considerations . . . . . . . . . . . . . . . . . . . 19
7. Privacy Considerations . . . . . . . . . . . . . . . . . . . 19
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8. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 19
9. Design rationale . . . . . . . . . . . . . . . . . . . . . . 19
9.1. Using a MAC . . . . . . . . . . . . . . . . . . . . . . . 19
9.2. Implementation Status . . . . . . . . . . . . . . . . . . 20
10. References . . . . . . . . . . . . . . . . . . . . . . . . . 20
11. References . . . . . . . . . . . . . . . . . . . . . . . . . 20
11.1. Normative References . . . . . . . . . . . . . . . . . . 20
11.2. Informative References . . . . . . . . . . . . . . . . . 21
Appendix A. Acknowledgements . . . . . . . . . . . . . . . . . . 22
Appendix B. Test Vectors . . . . . . . . . . . . . . . . . . . . 23
Appendix C. Document History . . . . . . . . . . . . . . . . . . 23
Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 23
1. Introduction
Asymmetric cryptography, also called public key cryptography, is a
fundamental component of much of modern information security.
However, even the flexibility of asymmetric cryptosystems is not
always enough for all applications. For the sake of privacy and
forward secrecy it may be necessary to frequently generate new keys,
but it is not always feasible for the holder of the private keys to
be available whenever a new key pair is needed. For example, this is
often the case when using a hardware security device to hold private
keys, where the device may be detached or locked at the time a new
key pair is needed.
The Asynchronous Remote Key Generation (ARKG) algorithm enables the
holder of private keys to delegate generation of public keys without
giving access to the corresponding private keys. This enables a
public key consumer to autonomously generate public keys whenever one
is needed, while the private key holder can later derive the
corresponding private key using a "key handle" generated along with
the public key.
The algorithm consists of three procedures: (1) the _delegating
party_ generates a _seed pair_ and emits the _public seed_ to a
_subordinate party_, (2) the subordinate party uses the public seed
to generate a public key and a _key handle_ on behalf of the
delegating party, and (3) the delegating party uses the key handle
and the _private seed_ to derive the private key corresponding to the
public key generated by procedure (2). Procedure (1) is performed
once, and procedures (2) and (3) may be repeated any number of times
with the same seed pair. The required cryptographic primitives are a
public key blinding scheme, a key encapsulation mechanism (KEM), a
key derivation function (KDF) and a message authentication code (MAC)
scheme. Both conventional primitives and quantum-resistant
alternatives exist that meet these requirements. [Wilson]
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Some motivating use cases of ARKG include:
* Efficient single-use signing keys. The European Union has
proposed a digital identity system which, in order to protect
users' privacy, needs a unique key pair for each authentication
signature. In online usage the system could relatively easily
create a key on demand, submit it to a certification authority to
have a single-use certificate issued for that key, and then submit
that certificate with an authentication signature to a third party
to access a service.
However, the proposed system also includes offline use cases: A
user might for example need to use the system in a location with
poor or no internet connectivity to present a digital driver's
license or authorize a payment. For this, the system may need to
pre-emptively generate a large amount of single-use certificates
to be used offline.
One candidate implementation under evaluation to provide signing
and key management for this system is the W3C Web Authentication
API [WebAuthn] (WebAuthn), which requires a user gesture whenever
a WebAuthn operation is invoked. A WebAuthn-based implementation
of the proposed digital identity system could use ARKG to pre-
emptively generate key pairs for offline use without the need to
prompt for a user gesture for each key pair generated.
* Enhanced forward secrecy for encrypted messaging. For example,
section 8.5.4 of RFC 9052 (https://www.rfc-editor.org/rfc/
rfc9052.html#name-direct-key-agreement) defines COSE
representations for encrypted messages and notes that "Since COSE
is designed for a store-and-forward environment rather than an
online environment, [...] forward secrecy (see [RFC4949]) is not
achievable. A static key will always be used for the receiver of
the COSE object." Applications could work around this limitation
by exchanging a large number of keys in advance, but that number
limits how many messages can be sent before another such exchange
is needed. This also requires the sender to allocate storage
space for the keys, which may be challenging to support in
constrained hardware.
ARKG could enable the sender to generate ephemeral recipient
public keys on demand. This may enhance forward secrecy if the
sender keeps the ARKG public seed secret, since each recipient key
pair is used to encrypt only one message.
* Generating additional public keys as backup keys. For example,
the W3C Web Authentication API [WebAuthn] (WebAuthn) generates a
new key pair for each account on each web site. This makes it
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difficult for users to set up a backup authenticator, because each
time a key pair is created for the primary authenticator, another
key pair also needs to be created for the backup authenticator,
which may be stored in a safe but inconvenient location.
ARKG could enable the primary authenticator to also generate a
public key for a paired backup authenticator whenever it generates
a key pair for itself, allowing the user to set up the pairing
once and then leave the backup authenticator in safe storage until
the primary authenticator is lost.
1.1. Requirements Language
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.
1.2. Notation
The following notation is used throughout this document:
* The symbol || represents octet string concatenation.
* When literal text strings are to be interpreted as octet strings,
they are encoded using UTF-8.
* Elliptic curve operations are written in multiplicative notation:
* denotes point multiplication, i.e., the curve group operation; ^
denotes point exponentiation, i.e., repeated point multiplication
of the base with itself; and + denotes scalar addition modulo the
curve order.
* Random(min_inc, max_exc) represents a cryptographically secure
random integer greater than or equal to min_inc and strictly less
than max_exc.
2. The Asynchronous Remote Key Generation (ARKG) algorithm
The ARKG algorithm consists of three functions, each performed by one
of two participants: the _delegating party_ or the _subordinate
party_. The delegating party generates an ARKG _seed pair_ and emits
the _public seed_ to the subordinate party while keeping the _private
seed_ secret. The subordinate party can then use the public seed to
generate derived public keys and _key handles_, and the delegating
party can use the private seed and a key handle to derive the
corresponding private key.
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The following subsections define the abstract instance parameters
used to construct the three ARKG functions, followed by the
definitions of the three ARKG functions.
2.1. Instance parameters
ARKG is composed of a suite of other algorithms. The parameters of
an ARKG instance are:
* BL: An asymmetric key blinding scheme [Wilson], consisting of:
- Function BL-Generate-Keypair() -> (pk, sk): Generate a blinding
key pair.
No input.
Output consists of a blinding public key pk and a blinding
secret key sk.
- Function BL-Blind-Public-Key(pk, tau) -> pk_tau:
Deterministically compute a blinded public key.
Input consists of a blinding public key pk and a blinding
factor tau.
Output consists of the blinded public key pk_tau.
- Function BL-Blind-Secret-Key(sk, tau) -> sk_tau:
Deterministically compute a blinded secret key.
Input consists of a blinding secret key sk and a blinding
factor tau.
Output consists of the blinded secret key sk_tau.
- Integer L_bl: The length of the blinding factor tau in octets.
pk and pk_tau are opaque octet strings of arbitrary length. tau is
an opaque octet string of length L_bl. The representations of sk,
sk_tau and L_bl are an undefined implementation detail.
See [Wilson] for definitions of security properties required of
the key blinding scheme BL.
* KEM: A key encapsulation mechanism, consisting of the functions:
- KEM-Generate-Keypair() -> (pk, sk): Generate a key
encapsulation key pair.
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No input.
Output consists of public key pk and secret key sk.
- KEM-Encaps(pk) -> (k, c): Generate a key encapsulation.
Input consists of an encapsulation public key pk.
Output consists of a shared secret k and an encapsulation
ciphertext c.
- KEM-Decaps(sk, c) -> k: Decapsulate a shared secret.
Input consists of encapsulation secret key sk and encapsulation
ciphertext c.
Output consists of the shared secret k on success, or an error
otherwise.
pk, k and c are opaque octet strings. The representation of sk is
an undefined implementation detail.
See [Wilson] for definitions of security properties required of
the key encapsulation mechanism KEM.
* MAC: A message authentication code (MAC) scheme, consisting of:
- Function MAC-Tag(k, m) -> t: Generate a message authentication
tag for a given message using a given key.
Input consists of the shared MAC key k and the message m.
Output consists of the MAC tag t.
- Function MAC-Verify(k, m, t) -> { 0, 1 }: Verify a message
authentication tag.
Input consists of the shared MAC key k, the message m and the
MAC tag t.
Output is 1 if and only if MAC-Tag(k, m) = t.
- Integer L_mac: The length of the MAC key k in octets.
k is an opaque octet string of length L_mac. m and t are opaque
octet strings of arbitrary length. The representation of L_mac is
an undefined implementation detail.
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See [Frymann2020] for definitions of security properties required
of the message authentication code scheme MAC.
* KDF: A variable-length key derivation function with the signature:
KDF(info, ikm, L) -> okm
Input consists of a domain separation parameter info, input key
material ikm and output length L.
Output consists of output key material okm of length L in octets.
info and ikm are opaque octet strings of arbitrary length. okm is
an opaque octet string of length L. L is an integer with
undefined representation.
See [Frymann2020] for definitions of security properties required
of the key derivation function KDF.
A concrete ARKG instantiation MUST specify the instantiation of each
of the above functions and values.
The output keys of the BL scheme are also the output keys of the ARKG
instance as a whole. For example, if BL-Blind-Public-Key and BL-
Blind-Secret-Key output ECDSA keys, then the ARKG instance will also
output ECDSA keys.
Instantiations MUST satisfy the following compatibility criteria:
* The output shared secret k of KEM-Encaps and KEM-Decaps is a valid
input key material ikm of KDF.
* Output key material okm of length L_bl of KDF is a valid input
blinding factor tau of BL-Blind-Public-Key and BL-Blind-Secret-
Key.
It is permissible for some KDF outputs to not be valid blinding
factors, as long as this happens with negligible probability - see
Section 9.1.
* Output key material okm of length L_mac of KDF is a valid input
MAC key k of MAC-Tag(k, m) and MAC-Verify(k, m, t).
It is permissible for some KDF outputs to not be valid MAC keys,
as long as this happens with negligible probability - see
Section 9.1.
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We denote a concrete ARKG instance by the pattern ARKG-BL-KEM-MAC-
KDF, substituting the chosen instantiation for the BL, KEM, MAC and
KDF parts. Note that this pattern cannot in general be unambiguously
parsed; implementations MUST NOT attempt to construct an ARKG
instance by parsing such a pattern string. Concrete ARKG instances
MUST always be identified by lookup in a registry of fully specified
ARKG instances. This is to prevent usage of algorithm combinations
that may be incompatible or insecure.
2.2. The function ARKG-Generate-Seed
This function is performed by the delegating party. The delegating
party generates the ARKG seed pair (pk, sk) and keeps the private
seed sk secret, while the public seed pk is provided to the
subordinate party. The subordinate party will then be able to
generate public keys on behalf of the delegating party.
ARKG-Generate-Seed() -> (pk, sk)
Options:
BL A key blinding scheme.
KEM A key encapsulation mechanism.
Inputs: None
Output:
(pk, sk) An ARKG seed key pair with public key pk
and private key sk.
The output (pk, sk) is calculated as follows:
(pk_kem, sk_kem) = KEM-Generate-Keypair()
(pk_bl, sk_bl) = BL-Generate-Keypair()
pk = (pk_kem, pk_bl)
sk = (sk_kem, sk_bl)
2.3. The function ARKG-Derive-Public-Key
This function is performed by the subordinate party, which holds the
ARKG public seed pk = (pk_kem, pk_bl). The resulting public key pk'
can be provided to external parties to use in asymmetric cryptography
protocols, and the resulting key handle kh can be used by the
delegating party to derive the private key corresponding to pk'.
This function may be invoked any number of times with the same public
seed, in order to generate any number of public keys.
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ARKG-Derive-Public-Key((pk_kem, pk_bl), info) -> (pk', kh)
Options:
BL A key blinding scheme.
KEM A key encapsulation mechanism.
MAC A MAC scheme.
KDF A key derivation function.
L_bl The length in octets of the blinding factor tau
of the key blinding scheme BL.
L_mac The length in octets of the MAC key
of the MAC scheme MAC.
Inputs:
pk_kem A key encapsulation public key.
pk_bl A key blinding public key.
info Optional context and application specific
information (can be a zero-length string).
Output:
pk' A blinded public key.
kh A key handle for deriving the blinded
secret key sk' corresponding to pk'.
The output (pk, sk) is calculated as follows:
(k, c) = KEM-Encaps(pk_kem)
tau = KDF("arkg-blind" || 0x00 || info, k, L_bl)
mk = KDF("arkg-mac" || 0x00 || info, k, L_mac)
tag = MAC-Tag(mk, c || info)
pk' = BL-Blind-Public-Key(pk_bl, tau)
kh = (c, tag)
If this procedure aborts due to an error, for example because KDF
returns an invalid tau or mk, the procedure can safely be retried
with the same arguments.
2.4. The function ARKG-Derive-Secret-Key
This function is performed by the delegating party, which holds the
ARKG private seed (sk_kem, sk_bl). The resulting secret key sk' can
be used in asymmetric cryptography protocols to prove possession of
sk' to an external party that has the corresponding public key.
This function may be invoked any number of times with the same
private seed, in order to derive the same or different secret keys
any number of times.
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ARKG-Derive-Secret-Key((sk_kem, sk_bl), kh, info) -> sk'
Options:
BL A key blinding scheme.
KEM A key encapsulation mechanism.
MAC A MAC scheme.
KDF A key derivation function.
L_bl The length in octets of the blinding factor tau
of the key blinding scheme BL.
L_mac The length in octets of the MAC key
of the MAC scheme MAC.
Inputs:
sk_kem A key encapsulation secret key.
sk_bl A key blinding secret key.
kh A key handle output from ARKG-Derive-Public-Key.
info Optional context and application specific
information (can be a zero-length string).
Output:
sk' A blinded secret key.
The output sk' is calculated as follows:
(c, tag) = kh
k = KEM-Decaps(sk_kem, c)
mk = KDF("arkg-mac" || 0x00 || info, k, L_mac)
If MAC-Verify(mk, c || info, tag) = 0:
Abort with an error.
tau = KDF("arkg-blind" || 0x00 || info, k, L_bl)
sk' = BL-Blind-Secret-Key(sk_bl, tau)
Errors in this procedure are typically unrecoverable. For example,
KDF might return an invalid tau or mk, or the tag may be invalid.
ARKG instantiations SHOULD be chosen in a way that such errors are
impossible if kh was generated by an honest and correct
implementation of ARKG-Derive-Public-Key. Incorrect or malicious
implementations of ARKG-Derive-Public-Key do not degrade the security
of a correct and honest implementation of ARKG-Derive-Secret-Key. See
also Section 9.1.
3. Generic ARKG instantiations
This section defines generic formulae for instantiating the
individual ARKG parameters, which can be used to define concrete ARKG
instantiations.
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3.1. Using elliptic curve arithmetic for key blinding
Instantiations of ARKG whose output keys are elliptic curve keys can
use elliptic curve arithmetic as the key blinding scheme BL.
Frymann2020 [Wilson] This section defines a general formula for such
instantiations of BL.
Let crv be an elliptic curve. Then the BL parameter of ARKG may be
instantiated as follows:
* Elliptic curve points are encoded to and from octet strings using
the procedures defined in sections 2.3.3 and 2.3.4 of SEC 1
[SEC1].
* Elliptic curve scalar values are encoded to and from octet strings
using the procedures defined in sections 2.3.7 and 2.3.8 of SEC 1
[SEC1].
* N is the order of crv.
* G is the generator of crv.
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BL-Generate-Keypair() -> (pk, sk)
sk = Random(1, N)
pk_tmp = G^sk
If pk_tmp equals the point at infinity, abort with an error.
pk = pk_tmp
TODO: Also reject G?
BL-Blind-Public-Key(pk, tau) -> pk_tau
If tau = 0 or tau >= N, abort with an error.
pk_tau_tmp = pk * (G^tau)
If pk_tau_tmp equals the point at infinity, abort with an error.
pk_tau = pk_tau_tmp
TODO: Also reject G?
BL-Blind-Secret-Key(sk, tau) -> sk_tau
If tau = 0 or tau >= N, abort with an error.
sk_tau_tmp = sk + tau
If sk_tau_tmp = 0, abort with an error.
sk_tau = sk_tau_tmp
TODO: Also reject 1?
3.2. Using ECDH as the KEM
Instantiations of ARKG can use ECDH [RFC6090] as the key
encapsulation mechanism. This section defines a general formula for
such instantiations of KEM.
Let crv be an elliptic curve used for ECDH. Then the KEM parameter
of ARKG may be instantiated as follows:
* Elliptic curve points are encoded to and from octet strings using
the procedures defined in sections 2.3.3 and 2.3.4 of SEC 1
[SEC1].
* Elliptic curve coordinate field elements are encoded to and from
octet strings using the procedures defined in sections 2.3.5 and
2.3.6 of SEC 1 [SEC1].
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* Elliptic curve scalar values are encoded to and from octet strings
using the procedures defined in sections 2.3.7 and 2.3.8 of SEC 1
[SEC1].
* ECDH(pk, sk) represents the compact output of ECDH [RFC6090] using
public key (curve point) pk and secret key (exponent) sk.
* N is the order of crv.
* G is the generator of crv.
KEM-Generate-Keypair() -> (pk, sk)
sk = Random(1, N)
pk_tmp = G^sk
If pk_tmp equals the point at infinity, abort with an error.
pk = pk_tmp
TODO: Also reject G?
KEM-Encaps(pk) -> (k, c)
(pk', sk') = KEM-Generate-Keypair()
k = ECDH(pk, sk')
c = pk'
KEM-Decaps(sk, c) -> k
pk' = c
k = ECDH(pk', sk)
3.3. Using both elliptic curve arithmetic for key blinding and ECDH as
the KEM
If elliptic curve arithmetic is used for key blinding and ECDH is
used as the KEM, as described in the previous sections, then both of
them MAY use the same curve or MAY use different curves. If both use
the same curve, then it is also possible to use the same public key
as both the key blinding public key and the KEM public key.
[Frymann2020]
TODO: Caveats? I think I read in some paper or thesis about specific
drawbacks of using the same key for both.
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3.4. Using HMAC as the MAC
Let Hash be a cryptographic hash function. Then the MAC parameter of
ARKG may be instantiated using HMAC [RFC2104] as follows:
MAC-Tag(k, m) -> t
t = HMAC-Hash(K=k, text=m)
MAC-Verify(k, m, t) -> { 0, 1 }
t' = HMAC-Hash(K=k, text=m)
If t = t':
return 1
Else:
return 0
3.5. Using HKDF as the KDF
Let Hash be a cryptographic hash function. Then the KDF parameter of
ARKG may be instantiated using HKDF [RFC5869] as follows:
KDF(info, ikm, L) -> okm
PRK = HKDF-Extract with the arguments:
Hash: Hash
salt: not set
IKM: ikm
okm = HKDF-Expand with the arguments:
Hash: Hash
PRK: PRK
info: info
L: L
4. Concrete ARKG instantiations
This section defines an initial set of concrete ARKG instantiations.
TODO: IANA registry? COSE/JOSE?
4.1. ARKG-P256-ECDH-P256-HMAC-SHA256-HKDF-SHA256
The identifier ARKG-P256-ECDH-P256-HMAC-SHA256-HKDF-SHA256 represents
the following ARKG instance:
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* BL: Elliptic curve arithmetic as described in Section 3.1 with the
parameter:
- crv: The NIST curve secp256r1 [SEC2].
* KEM: ECDH as described in Section 3.2 with the parameter:
- crv: The NIST curve secp256r1 [SEC2].
* MAC: HMAC as described in Section 3.4 with the parameter:
- Hash: SHA-256 [FIPS 180-4].
* KDF: HKDF as described in Section 3.5 with the parameter:
- Hash: SHA-256 [FIPS 180-4].
* L_bl: 32
* L_mac: 32
4.2. ARKG-P384-ECDH-P384-HMAC-SHA384-HKDF-SHA384
The identifier ARKG-P384-ECDH-P384-HMAC-SHA384-HKDF-SHA384 represents
the following ARKG instance:
* BL: Elliptic curve arithmetic as described in Section 3.1 with the
parameter:
- crv: The NIST curve secp384r1 [SEC2].
* KEM: ECDH as described in Section 3.2 with the parameter:
- crv: The NIST curve secp384r1 [SEC2].
* MAC: HMAC as described in Section 3.4 with the parameter:
- Hash: SHA-384 [FIPS 180-4].
* KDF: HKDF as described in Section 3.5 with the parameter:
- Hash: SHA-384 [FIPS 180-4].
* L_bl: 48
* L_mac: 48
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4.3. ARKG-P521-ECDH-P521-HMAC-SHA512-HKDF-SHA512
The identifier ARKG-P521-ECDH-P521-HMAC-SHA512-HKDF-SHA512 represents
the following ARKG instance:
* BL: Elliptic curve arithmetic as described in Section 3.1 with the
parameter:
- crv: The NIST curve secp521r1 [SEC2].
* KEM: ECDH as described in Section 3.2 with the parameter:
- crv: The NIST curve secp521r1 [SEC2].
* MAC: HMAC as described in Section 3.4 with the parameter:
- Hash: SHA-512 [FIPS 180-4].
* KDF: HKDF as described in Section 3.5 with the parameter:
- Hash: SHA-512 [FIPS 180-4].
* L_bl: 64
* L_mac: 64
4.4. ARKG-P256k-ECDH-P256k-HMAC-SHA256-HKDF-SHA256
The identifier ARKG-P256k-ECDH-P256k-HMAC-SHA256-HKDF-SHA256
represents the following ARKG instance:
* BL: Elliptic curve arithmetic as described in Section 3.1 with the
parameter:
- crv: The SECG curve secp256k1 [SEC2].
* KEM: ECDH as described in Section 3.2 with the parameter:
- crv: The SECG curve secp256k1 [SEC2].
* MAC: HMAC as described in Section 3.4 with the parameter:
- Hash: SHA-256 [FIPS 180-4].
* KDF: HKDF as described in Section 3.5 with the parameter:
- Hash: SHA-256 [FIPS 180-4].
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* L_bl: 32
* L_mac: 32
4.5. ARKG-Ed25519-X25519-HMAC-SHA256-HKDF-SHA256
The identifier ARKG-Ed25519-X25519-HMAC-SHA256-HKDF-SHA256 represents
the following ARKG instance:
* BL: Elliptic curve arithmetic as described in Section 3.1 with the
parameter:
- crv: The curve Ed25519 [REF?].
* KEM: ECDH as described in Section 3.2 with the parameter:
- crv: The curve X25519 [REF?].
* MAC: HMAC as described in Section 3.4 with the parameter:
- Hash: SHA-256 [FIPS 180-4].
* KDF: HKDF as described in Section 3.5 with the parameter:
- Hash: SHA-256 [FIPS 180-4].
* L_bl: 32
* L_mac: 32
4.6. ARKG-X25519-X25519-HMAC-SHA256-HKDF-SHA256
The identifier ARKG-X25519-X25519-HMAC-SHA256-HKDF-SHA256 represents
the following ARKG instance:
* BL: Elliptic curve arithmetic as described in Section 3.1 with the
parameter:
- crv: The curve X25519 [REF?].
* KEM: ECDH [RFC6090] as described in Section 3.2 with the
parameter:
- crv: The curve X25519 [REF?].
* MAC: HMAC as described in Section 3.4 with the parameter:
- Hash: SHA-256 [FIPS 180-4].
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* KDF: HKDF as described in Section 3.5 with the parameter:
- Hash: SHA-256 [FIPS 180-4].
* L_bl: 32
* L_mac: 32
5. COSE bindings
TODO?: Define COSE representations for interoperability: - ARKG
public seed (for interoperability between different implementers of
ARKG-Generate-Seed and ARKG-Derive-Public-Key) - ARKG key handle (for
interoperability between different implementers of ARKG-Derive-
Public-Key and ARKG-Derive-Secret-Key)
6. Security Considerations
TODO
7. Privacy Considerations
TODO
8. IANA Considerations
TODO
9. Design rationale
9.1. Using a MAC
The ARKG construction by Wilson [Wilson] omits the MAC and instead
encodes application context in the PRF labels, arguing this leads to
invalid keys/signatures in cases that would have a bad MAC. We
choose to keep the MAC from the construction by Frymann et al.
[Frymann2020] for two purposes.
The first is so that the delegating party can distinguish between key
handles addressed to it and those addressed to other delegating
parties. We anticipate use cases where a private key usage request
may contain key handles for several delegating parties eligible to
fulfill the request, and the delegate party to be used can be chosen
opportunistically depending on which are available at the time.
Without the MAC, choosing the wrong key handle would cause the ARKG-
Derive-Secret-Key procedure to silently derive the wrong key instead
of returning an explicit error, which would in turn lead to an
invalid signature or similar final output. This would make it
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difficult or impossible to diagnose the root cause of the issue and
present actionable user feedback. The MAC also allows ARKG key
handles to be transmitted via heterogeneous data channels, possibly
including a mix of ARKG key handles and similar values used for other
algorithms.
The second purpose is so that the delegating party can be assured
that no errors should happen during the execution of ARKG-Derive-
Secret-Key, such as out-of-range or invalid key values. For example,
key generation in ARKG-Derive-Public-Key might be done by randomly
testing candidates [NIST.SP.800-56Ar3] and retrying ARKG-Derive-
Public-Key until a valid candidate is found. A MAC enables ARKG-
Derive-Secret-Key to assume that the first candidate from a given
pseudo-random seed will be successful, and otherwise return an
explicit error rejecting the key handle as invalid. ARKG-Derive-
Public-Key is likely to run on powerful general-purpose hardware,
such as a laptop, smartphone or server, while ARKG-Derive-Secret-Key
might run on more constrained hardware such as a cryptographic smart
card, which benefits greatly from such optimizations.
It is straightforward to see that adding the MAC to the construction
by Wilson does not weaken the security properties defined by Frymann
et al. [Frymann2020]: the construction by Frymann et al. can be
reduced to the ARKG construction in this document by instantiating
KEM as group exponentiation and instantiating BL as group
multiplication to blind public keys and modular integer addition to
blind secret keys. The MAC and KDF parameters correspond trivially
to the MAC and KDF parameters in [Frymann2020], where KDF_1(_k_) =
KDF(_k_, _l__1) and KDF_2(_k_) = KDF(_k_, _l__2) with fixed labels
_l__1 and _l__2. Hence if one can break PK-unlinkability or SK-
security of the ARKG construction in this document, one can also
break the same property of the construction by Frymann et al.
9.2. Implementation Status
TODO
10. References
TODO
TODO: Ask authors for canonical reference addresses
11. References
11.1. Normative References
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[BIP32] Wuille, P., "BIP 32 Hierarchical Deterministic Wallets",
2012, .
[RFC2104] Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-
Hashing for Message Authentication", RFC 2104,
DOI 10.17487/RFC2104, February 1997,
.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
.
[RFC4949] Shirey, R., "Internet Security Glossary, Version 2",
FYI 36, RFC 4949, DOI 10.17487/RFC4949, August 2007,
.
[RFC5869] Krawczyk, H. and P. Eronen, "HMAC-based Extract-and-Expand
Key Derivation Function (HKDF)", RFC 5869,
DOI 10.17487/RFC5869, May 2010,
.
[RFC6090] McGrew, D., Igoe, K., and M. Salter, "Fundamental Elliptic
Curve Cryptography Algorithms", RFC 6090,
DOI 10.17487/RFC6090, February 2011,
.
[RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
May 2017, .
[SEC1] Certicom Research, "SEC 1 Elliptic Curve Cryptography",
2020, .
11.2. Informative References
[Clermont] Clermont, S. A. and Technische Universität Darmstadt,
"Post Quantum Asynchronous Remote Key Generation. Master's
thesis", 2022, .
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[Frymann2020]
Frymann, N., Gardham, D., Kiefer, F., Lundberg, E.,
Manulis, M., and D. Nilsson, "Asynchronous Remote Key
Generation: An Analysis of Yubico's Proposal for W3C
WebAuthn. CCS '20: Proceedings of the 2020 ACM SIGSAC
Conference on Computer and Communications Security", 2020,
.
[Frymann2023]
Frymann, N., Gardham, D., and M. Manulis, "Asynchronous
Remote Key Generation for Post-Quantum Cryptosystems from
Lattices. 2023 IEEE 8th European Symposium on Security and
Privacy", 2023, .
[WebAuthn-Recovery]
Lundberg, E. and D. Nilsson, "WebAuthn recovery extension:
Asynchronous delegated key generation without shared
secrets. GitHub", 2019,
.
[Wilson] Wilson, S. M. and University of Waterloo,, "Post-Quantum
Account Recovery for Passwordless Authentication. Master's
thesis", 2023, .
Appendix A. Acknowledgements
ARKG was first proposed under this name by Frymann et al.
[Frymann2020], who analyzed a proposed extension to W3C Web
Authentication by Lundberg and Nilsson [WebAuthn-Recovery], which was
in turn inspired by a similar construction by Wuille [BIP32] used to
create privacy-preserving Bitcoin addresses. Frymann et al.
[Frymann2020] generalized the constructions by Lundberg, Nilsson and
Wuille from elliptic curves to any discrete logarithm (DL) problem,
and also proved the security of arbitrary asymmetric protocols
composed with ARKG. Further generalizations to include quantum-
resistant instantiations were developed independently by Clermont
[Clermont], Frymann et al. [Frymann2023] and Wilson [Wilson].
This document adopts the construction proposed by Wilson [Wilson],
modified by the inclusion of a MAC in the key handles as done in the
original construction by Frymann et al. [Frymann2020].
The authors would like to thank all of these authors for their
research and development work that led to the creation of this
document.
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Appendix B. Test Vectors
TODO
Appendix C. Document History
-00 Initial Version
Contributors
Dain Nilsson
Yubico
Authors' Addresses
Emil Lundberg (editor)
Yubico
Kungsgatan 44
Stockholm
Sweden
Email: emil@emlun.se
John Bradley
Yubico
Email: ve7jtb@ve7jtb.com
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