| Internet-Draft | ARKG | October 2024 |
| Lundberg & Bradley | Expires 18 April 2025 | [Page] |
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.¶
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.¶
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/.¶
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This Internet-Draft will expire on 18 April 2025.¶
Copyright (c) 2024 IETF Trust and the persons identified as the document authors. All rights reserved.¶
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Asynchronous Remote Key Generation (ARKG) introduces a mechanism to generate public keys without access to the corresponding private keys. Such a mechanism is useful for many scenarios when a new public key is needed but the private key holder is not available to perform the key generation. This may occur when private keys are stored in a hardware security device, which may be unavailable or locked at the time a new public key is needed.¶
Some motivating use cases of ARKG include:¶
Single-use asymmetric keys: Envisioned for the European Union's digital identity framework, which is set to use single-use asymmetric keys to prevent colluding verifiers from using public keys as correlation handles. Each digital identity credential would thus be issued with a single-use proof-of-possession key, used only once to present the credential to a verifier. ARKG empowers both online and offline usage scenarios: for offline scenarios, ARKG enables pre-generation of public keys for single-use credentials without needing to access the hardware security device that holds the private keys. For online scenarios, ARKG gives the credential issuer assurance that all derived private keys are bound to the same secure hardware element. In both cases, application performance may be improved since public keys can be generated in a general-purpose execution environment instead of a secure enclave.¶
Enhanced forward secrecy: The use of ARKG can facilitate forward secrecy in certain contexts. For instance, section 8.5.4 of RFC 9052 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." As opposed to workarounds like exchanging a large number of keys in advance, ARKG enables the the sender to generate ephemeral recipient public keys on demand.¶
Backup key generation: For example, the W3C Web Authentication API [WebAuthn] (WebAuthn) generates a new key pair for each account on each web site. ARKG could allow for simultaneously generating a backup public key when registering a new public key. A primary authenticator could generate both a key pair for itself and a public key for a paired backup authenticator. The backup authenticator only needs to be paired with the primary authenticator once, and can then be safely stored until it is needed.¶
ARKG consists of three procedures:¶
Initialization: The delegating party generates a seed pair and discloses the public seed to a subordinate party, while securely retaining the private seed.¶
Public key generation: The subordinate party uses the public seed to autonomously generate a new public key along with a unique key handle for the public key. This can be repeated any number of times.¶
Private key derivation: The delegating party uses a key handle and the private seed to derive the private key corresponding to the public key generated along with the key handle. This can be repeated with any number of key handles.¶
Notably, ARKG can be built entirely using established cryptographic primitives. The required primitives are a public key blinding scheme and a key encapsulation mechanism (KEM), which may in turn use 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]¶
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.¶
The following notation is used throughout this document:¶
The symbol || represents octet string concatenation.¶
Literal text strings and octet strings are denoted using the CDDL syntax defined in Section 3.1 of [RFC8610].¶
Elliptic curve operations are written in additive notation:
+ denotes point addition, i.e., the curve group operation;
* denotes point multiplication, i.e., repeated point addition;
and + also denotes scalar addition modulo the curve order.
* has higher precedence than +, i.e., a + b * C is equivalent to a + (b * C).¶
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.¶
The following subsections define the abstract instance parameters used to construct the three ARKG functions, followed by the definitions of the three ARKG functions.¶
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 private key sk.¶
Function BL-Blind-Public-Key(pk, tau, info) -> pk_tau: Deterministically compute a blinded public key.¶
Input consists of a blinding public key pk,
a blinding factor tau
and a domain separation parameter info.¶
Output consists of the blinded public key pk_tau.¶
Function BL-Blind-Private-Key(sk, tau, info) -> sk_tau: Deterministically compute a blinded private key.¶
Input consists of a blinding private key sk,
a blinding factor tau
and a domain separation parameter info.¶
Output consists of the blinded private key sk_tau.¶
tau and info are an opaque octet strings of arbitrary length.
The representations of pk and pk_tau are defined by the protocol that invokes ARKG.
The representations of sk and sk_tau are an undefined implementation detail.¶
See [Wilson] for definitions of security properties required of the key blinding scheme BL.¶
KEM: A key encapsulation mechanism [Shoup], consisting of the functions:¶
KEM-Generate-Keypair() -> (pk, sk): Generate a key encapsulation key pair.¶
No input.¶
Output consists of public key pk and private key sk.¶
KEM-Encaps(pk, info) -> (k, c): Generate a key encapsulation.¶
Input consists of an encapsulation public key pk
and a domain separation parameter info.¶
Output consists of a shared secret k and an encapsulation ciphertext c.¶
KEM-Decaps(sk, c, info) -> k: Decapsulate a shared secret.¶
Input consists of encapsulation private key sk, encapsulation ciphertext c
and a domain separation parameter info.¶
Output consists of the shared secret k on success, or an error otherwise.¶
k, c and info are opaque octet strings of arbitrary length.
The representation of pk is defined by the protocol that invokes ARKG.
The representation of sk is an undefined implementation detail.¶
The KEM MUST guarantee integrity of the ciphertext,
meaning that knowledge of the public key pk and the domain separation parameter info
is required in order to create any ciphertext c that can be successfully decapsulated by the corresponding private key sk.
Section 3.2 describes a general formula for how any KEM can be adapted to include this guarantee.
Section 9.1 discusses the reasons for this requirement.¶
See [Wilson] for definitions of additional security properties required of the key encapsulation mechanism KEM.¶
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-Private-Key output ECDSA keys,
then the ARKG instance will also output ECDSA keys.¶
We denote a concrete ARKG instance by the pattern ARKG-BL-KEM,
substituting the chosen instantiation for the BL and KEM.
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.¶
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)
ARKG instance parameters:
BL A key blinding scheme.
KEM A key encapsulation mechanism.
Inputs: None
Output:
(pk, sk) An ARKG seed pair with public seed pk
and private seed 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)
¶
Although the above definition expresses the key generation as opaque,
likely sampling uniformly random key distributions,
implementations MAY choose to implement the functions BL-Generate-Keypair(),
KEM-Generate-Keypair() and ARKG-Generate-Seed()
as deterministic functions of some out-of-band input.
This can be thought of as defining a single-use ARKG instance where these function outputs are static.
This use case is beyond the scope of this document
since the implementation of ARKG-Generate-Seed is internal to the delegating party,
even if applications choose to distribute the delegating party across multiple processing entities.¶
For example, one entity may randomly sample pk_bl, derive pk_kem deterministically from pk_bl
and submit only pk_bl to a separate service that uses the same procedure to also derive the same pk_kem.
This document considers both of these entities as parts of the same logical delegating party.¶
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.¶
ARKG-Derive-Public-Key((pk_kem, pk_bl), info) -> (pk', kh)
ARKG instance parameters:
BL A key blinding scheme.
KEM A key encapsulation mechanism.
Inputs:
pk_kem A key encapsulation public key.
pk_bl A key blinding public key.
info An octet string containing 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
private key sk' corresponding to pk'.
The output (pk', kh) is calculated as follows:
info_kem = 'ARKG-Derive-Key-KEM.' || info
info_bl = 'ARKG-Derive-Key-BL.' || info
(tau, c) = KEM-Encaps(pk_kem, info_kem)
pk' = BL-Blind-Public-Key(pk_bl, tau, info_bl)
kh = c
¶
If this procedure aborts due to an error, the procedure can safely be retried with the same arguments.¶
This function is performed by the delegating party, which holds the ARKG private seed (sk_kem, sk_bl).
The resulting private 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 private keys any number of times.¶
ARKG-Derive-Private-Key((sk_kem, sk_bl), kh, info) -> sk'
ARKG instance parameters:
BL A key blinding scheme.
KEM A key encapsulation mechanism.
Inputs:
sk_kem A key encapsulation private key.
sk_bl A key blinding private key.
kh A key handle output from ARKG-Derive-Public-Key.
info An octet string containing optional context
and application specific information
(can be a zero-length string).
Output:
sk' A blinded private key.
The output sk' is calculated as follows:
info_kem = 'ARKG-Derive-Key-KEM.' || info
info_bl = 'ARKG-Derive-Key-BL.' || info
tau = KEM-Decaps(sk_kem, kh, info_kem)
If decapsulation failed:
Abort with an error.
sk' = BL-Blind-Private-Key(sk_bl, tau, info_bl)
¶
Errors in this procedure are typically unrecoverable.
For example, KEM-Decaps may fail to decapsulate the KEM ciphertext kh if it fails an integrity check.
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-Private-Key.
See also Section 9.1.¶
This section defines generic formulae for instantiating the individual ARKG parameters, which can be used to define concrete ARKG instantiations.¶
Instantiations of ARKG whose output keys are elliptic curve keys
can use elliptic curve addition as the key blinding scheme BL [Frymann2020] [Wilson].
This section defines a general formula for such instantiations of BL.¶
This formula has the following parameters:¶
crv: An elliptic curve.¶
hash-to-crv-suite: A hash-to-curve suite [RFC9380]
suitable for hashing to the scalar field of crv.¶
DST_ext: A domain separation tag.¶
Then the BL parameter of ARKG may be instantiated as follows:¶
G is the generator of the prime order subgroup of crv.¶
N is the order of G.¶
The function hash_to_field is defined in Section 5 of [RFC9380].¶
BL-Generate-Keypair() -> (pk, sk)
Generate (pk, sk) using some procedure defined for the curve crv.
BL-Blind-Public-Key(pk, tau, info) -> pk_tau
tau' = hash_to_field(tau, 1) with the parameters:
DST: 'ARKG-BL-EC.' || DST_ext || info
F: GF(N), the scalar field
of the prime order subgroup of crv
p: N
m: 1
L: The L defined in hash-to-crv-suite
expand_message: The expand_message function
defined in hash-to-crv-suite
pk_tau = pk + tau' * G
BL-Blind-Private-Key(sk, tau, info) -> sk_tau
tau' = hash_to_field(tau, 1) with the parameters:
DST: 'ARKG-BL-EC.' || DST_ext || info
F: GF(N), the scalar field
of the prime order subgroup of crv.
p: N
m: 1
L: The L defined in hash-to-crv-suite
expand_message: The expand_message function
defined in hash-to-crv-suite
sk_tau_tmp = sk + tau'
If sk_tau_tmp = 0, abort with an error.
sk_tau = sk_tau_tmp
¶
Not all key encapsulation mechanisms guarantee ciphertext integrity, meaning that a valid KEM ciphertext can be created only with knowledge of the KEM public key. This section defines a general formula for adapting any KEM to guarantee ciphertext integrity by prepending a MAC to the KEM ciphertext.¶
For example, ECDH does not guarantee ciphertext integrity - any elliptic curve point is a valid ECDH ciphertext and can be successfully decapsulated using any elliptic curve private scalar.¶
This formula has the following parameters:¶
Hash: A cryptographic hash function.¶
DST_ext: A domain separation parameter.¶
Sub-Kem: A key encapsulation mechanism as described for the KEM parameter in Section 2.1,
except Sub-Kem MAY ignore the info parameter and MAY not guarantee ciphertext integrity.
Sub-Kem defines the functions Sub-Kem-Generate-Keypair, Sub-Kem-Encaps and Sub-Kem-Decaps.¶
The KEM parameter of ARKG may be instantiated using Sub-Kem,
HMAC [RFC2104] and HKDF [RFC5869] as follows:¶
L is the output length of Hash in octets.¶
LEFT(X, n) is the first n bytes of the byte array X.¶
DROP_LEFT(X, n) is the byte array X without the first n bytes.¶
We truncate the HMAC output to 128 bits (16 octets)
because as described in Section 9.1,
ARKG needs ciphertext integrity only to ensure correctness, not for security.
Extendable-output functions used as the Hash parameter SHOULD still be instantiated
with an output length appropriate for the desired security level,
in order to not leak information about the Sub-KEM shared secret key.¶
KEM-Generate-Keypair() -> (pk, sk)
(pk, sk) = Sub-Kem-Generate-Keypair()
KEM-Encaps(pk, info) -> (k, c)
info_sub = 'ARKG-KEM-HMAC.' || DST_ext || info
(k', c') = Sub-Kem-Encaps(pk, info_sub)
prk = HKDF-Extract with the arguments:
Hash: Hash
salt: not set
IKM: k'
mk = HKDF-Expand with the arguments:
Hash: Hash
PRK: prk
info: 'ARKG-KEM-HMAC-mac.' || DST_ext || info
L: L
t = HMAC-Hash-128(K=mk, text=c')
k = HKDF-Expand with the arguments:
Hash: Hash
PRK: prk
info: 'ARKG-KEM-HMAC-shared.' || DST_ext || info
L: The length of k' in octets.
c = t || c'
KEM-Decaps(sk, c, info) -> k
t = LEFT(c, 16)
c' = DROP_LEFT(c, 16)
info_sub = 'ARKG-KEM-HMAC.' || DST_ext || info
k' = Sub-Kem-Decaps(sk, c', info_sub)
prk = HKDF-Extract with the arguments:
Hash: Hash
salt: not set
IKM: k'
mk = HKDF-Expand with the arguments:
Hash: Hash
PRK: prk
info: 'ARKG-KEM-HMAC-mac.' || DST_ext || info
L: L
t' = HMAC-Hash-128(K=mk, text=c')
If t = t':
k = HKDF-Expand with the arguments:
Hash: Hash
PRK: prk
info: 'ARKG-KEM-HMAC-shared.' || DST_ext || info
L: The length of k' in octets.
Else:
Abort with an error.
¶
Instantiations of ARKG can use ECDH [RFC6090] as the key encapsulation mechanism KEM [Frymann2020] [Wilson].
This section defines a general formula for such instantiations of KEM.¶
This formula has the following parameters:¶
The KEM parameter of ARKG may be instantiated as described in section Section 3.2 with the parameters:¶
Hash: Hash.¶
DST_ext: 'ARKG-ECDH.' || DST_ext.¶
Sub-Kem: The functions Sub-Kem-Generate-Keypair, Sub-Kem-Encaps and Sub-Kem-Decaps defined as follows:¶
Elliptic-Curve-Point-to-Octet-String and Octet-String-to-Elliptic-Curve-Point
are the conversion routines defined in sections 2.3.3 and 2.3.4 of [SEC1],
without point compression.¶
ECDH(pk, sk) represents the compact output of ECDH [RFC6090]
using public key (curve point) pk and private key (exponent) sk.¶
G is the generator of the prime order subgroup of crv.¶
N is the order of G.¶
Sub-Kem-Generate-Keypair() -> (pk, sk)
Generate (pk, sk) using some procedure defined for crv.
Sub-Kem-Encaps(pk, info) -> (k, c)
(pk', sk') = Sub-Kem-Generate-Keypair()
k = ECDH(pk, sk')
c = Elliptic-Curve-Point-to-Octet-String(pk')
Sub-Kem-Decaps(sk, c, info) -> k
pk' = Octet-String-to-Elliptic-Curve-Point(c)
k = ECDH(pk', sk)
¶
Instantiations of ARKG can use X25519 or X448 [RFC7748] as the key encapsulation mechanism KEM.
This section defines a general formula for such instantiations of KEM.¶
This formula has the following parameters:¶
DH-Function: the function X25519 or the function X448 [RFC7748].¶
DST_ext: A domain separation parameter.¶
The KEM parameter of ARKG may be instantiated as described in section Section 3.2 with the parameters:¶
Hash: SHA-512 [FIPS 180-4] if DH-Function is X25519,
or SHAKE256 [FIPS 202] with output length 64 octets if DH-Function is X448.¶
DST_ext: 'ARKG-ECDHX.' || DST_ext.¶
Sub-Kem: The functions Sub-Kem-Generate-Keypair, Sub-Kem-Encaps and Sub-Kem-Decaps defined as follows:¶
Random-Bytes(N) represents a cryptographically secure,
uniformly distributed random octet string of length N.¶
L is 32 if DH-Function is X25519, or 56 if DH-Function is X448.¶
G is the octet string h'0900000000000000 0000000000000000 0000000000000000 0000000000000000'
if DH-Function is X25519,
or the octet string h'0500000000000000 0000000000000000 0000000000000000 0000000000000000 0000000000000000 0000000000000000 0000000000000000'
if DH-Function is X448.¶
These are the little-endian encodings of the integers 9 and 5, which is the u-coordinate of the generator point of the respective curve group.¶
Sub-Kem-Generate-Keypair() -> (pk, sk)
sk = Random-Bytes(L)
pk = DH-Function(sk, G)
Sub-Kem-Encaps(pk, info) -> (k, c)
(pk', sk') = Sub-Kem-Generate-Keypair()
k = DH-Function(sk', pk)
c = pk'
Sub-Kem-Decaps(sk, c, info) -> k
k = DH-Function(sk, c)
¶
When an ARKG instance uses the same type of key for both the key blinding and the KEM - for example, if elliptic curve arithmetic is used for key blinding as described in Section 3.1 and ECDH is used as the KEM as described in Section 3.3 [Frymann2020] - then the two keys MAY be the same key. Representations of such an ARKG seed MAY allow for omitting the second copy of the constituent key, but such representations MUST clearly identify that the single constituent key is to be used both as the key blinding key and the KEM key.¶
This section defines an initial set of concrete ARKG instantiations.¶
TODO: IANA registry? COSE/JOSE?¶
The identifier ARKG-P256ADD-ECDH represents the following ARKG instance:¶
BL: Elliptic curve addition as described in Section 3.1 with the parameters:¶
KEM: ECDH as described in Section 3.3 with the parameters:¶
The identifier ARKG-P384ADD-ECDH represents the following ARKG instance:¶
BL: Elliptic curve addition as described in Section 3.1 with the parameters:¶
KEM: ECDH as described in Section 3.3 with the parameters:¶
The identifier ARKG-P521ADD-ECDH represents the following ARKG instance:¶
BL: Elliptic curve addition as described in Section 3.1 with the parameters:¶
KEM: ECDH as described in Section 3.3 with the parameters:¶
The identifier ARKG-P256kADD-ECDH represents the following ARKG instance:¶
BL: Elliptic curve addition as described in Section 3.1 with the parameters:¶
KEM: ECDH as described in Section 3.3 with the parameters:¶
The identifier ARKG-curve25519ADD-X25519 represents the following ARKG instance:¶
BL: Elliptic curve addition as described in Section 3.1 with the parameters:¶
hash-to-crv-suite: curve25519_XMD:SHA-512_ELL2_RO_ [RFC9380].¶
DST_ext: 'ARKG-curve25519ADD-X25519'.¶
WARNING: Some algorithms on curve25519, including X25519 [RFC7748],
construct private key scalars within a particular range
to enable optimizations and constant-time guarantees.
This BL scheme does not guarantee that blinded private scalars remain in that range,
so implementations using this ARKG instance MUST NOT rely on such a guarantee.¶
Note: Input and output keys of this BL scheme are curve scalars and curve points.
Some algorithms on curve25519, including X25519 [RFC7748],
define the private key input as a random octet string and applies some preprocessing to it
before interpreting the result as a private key scalar,
and define public keys as a particular octet string encoding of a curve point.
This BL scheme is not compatible with such preprocessing
since it breaks the relationship between the blinded private key and the blinded public key.
Implementations using this ARKG instance MUST apply BL-Blind-Private-Key
to the interpreted private key scalar, not the random private key octet string,
and implementations of BL-Blind-Public-Key MUST interpret the public key input as a curve point,
not an opaque octet string.¶
KEM: X25519 as described in Section 3.4 with the parameters:¶
The identifier ARKG-curve448ADD-X448 represents the following ARKG instance:¶
BL: Elliptic curve addition as described in Section 3.1 with the parameters:¶
WARNING: Some algorithms on curve25519, including X448 [RFC7748],
construct private key scalars within a particular range
to enable optimizations and constant-time guarantees.
This BL scheme does not guarantee that blinded private scalars remain in that range,
so implementations using this ARKG instance MUST NOT rely on such a guarantee.¶
Note: Input and output keys of this BL scheme are curve scalars and curve points.
Some algorithms on curve25519, including X448 [RFC7748],
define the private key input as a random octet string and applies some preprocessing to it
before interpreting the result as a private key scalar,
and define public keys as a particular octet string encoding of a curve point.
This BL scheme is not compatible with such preprocessing
since it breaks the relationship between the blinded private key and the blinded public key.
Implementations using this ARKG instance MUST apply BL-Blind-Private-Key
to the interpreted private key scalar, not the random private key octet string,
and implementations of BL-Blind-Public-Key MUST interpret the public key input as a curve point,
not an opaque octet string.¶
KEM: X448 as described in Section 3.4 with the parameters:¶
The identifier ARKG-edwards25519ADD-X25519 represents the following ARKG instance:¶
BL: Elliptic curve addition as described in Section 3.1 with the parameters:¶
hash-to-crv-suite: edwards25519_XMD:SHA-512_ELL2_RO_ [RFC9380].¶
DST_ext: 'ARKG-edwards25519ADD-X25519'.¶
WARNING: Some algorithms on edwards25519, including EdDSA [RFC8032],
construct private key scalars within a particular range
to enable optimizations and constant-time guarantees.
This BL scheme does not guarantee that blinded private scalars remain in that range,
so implementations using this ARKG instance MUST NOT rely on such a guarantee.¶
Note: Input and output keys of this BL scheme are curve scalars and curve points.
Some algorithms on edwards25519, including EdDSA [RFC8032],
define the private key input as a random octet string and applies some preprocessing to it
before interpreting the result as a private key scalar,
and define public keys as a particular octet string encoding of a curve point.
This BL scheme is not compatible with such preprocessing
since it breaks the relationship between the blinded private key and the blinded public key.
Implementations using this ARKG instance MUST apply BL-Blind-Private-Key
to the interpreted private key scalar, not the random private key octet string,
and implementations of BL-Blind-Public-Key MUST interpret the public key input as a curve point,
not an opaque octet string.¶
KEM: X25519 as described in Section 3.4 with the parameters:¶
The identifier ARKG-edwards448ADD-X448 represents the following ARKG instance:¶
BL: Elliptic curve addition as described in Section 3.1 with the parameters:¶
hash-to-crv-suite: edwards448_XOF:SHAKE256_ELL2_RO_ [RFC9380].¶
DST_ext: 'ARKG-edwards448ADD-X448'.¶
WARNING: Some algorithms on edwards25519, including EdDSA [RFC8032],
construct private key scalars within a particular range
to enable optimizations and constant-time guarantees.
This BL scheme does not guarantee that blinded private scalars remain in that range,
so implementations using this ARKG instance MUST NOT rely on such a guarantee.¶
Note: Input and output keys of this BL scheme are curve scalars and curve points.
Some algorithms on edwards25519, including EdDSA [RFC8032],
define the private key input as a random octet string and applies some preprocessing to it
before interpreting the result as a private key scalar,
and define public keys as a particular octet string encoding of a curve point.
This BL scheme is not compatible with such preprocessing
since it breaks the relationship between the blinded private key and the blinded public key.
Implementations using this ARKG instance MUST apply BL-Blind-Private-Key
to the interpreted private key scalar, not the random private key octet string,
and implementations of BL-Blind-Public-Key MUST interpret the public key input as a curve point,
not an opaque octet string.¶
KEM: X448 as described in Section 3.4 with the parameters:¶
This section proposes additions to COSE [RFC9052] to support ARKG use cases. The novelty lies primarily in a new key type definition to represent ARKG public seeds and new key type definitions to represent references to private keys rather than the keys themselves.¶
An ARKG public seed is represented as a COSE_Key structure [RFC9052]
with kty value TBD (placeholder value -65537).
This key type defines key type parameters -1 and -2 for the BL and KEM public key, respectively.¶
The alg parameter, when present,
defines the alg parameter of ARKG derived public keys derived from this ARKG public seed.¶
The following CDDL [RFC8610] example represents an ARKG-P256ADD-ECDH public seed
restricted to generating derived public keys for use with the ESP256 [fully-spec-algs] signature algorithm:¶
{
1: -65537, ; kty: ARKG-pub
; kid: Opaque identifier
2: h'60b6dfddd31659598ae5de49acb220d8
704949e84d484b68344340e2565337d2',
3: -9, ; alg: ESP256
-1: { ; BL public key
1: 2, ; kty: EC2
-1: 1, ; crv: P256
-2: h'69380FC1C3B09652134FEEFBA61776F9
7AF875CE46CA20252C4165102966EBC5',
-3: h'8B515831462CCB0BD55CBA04BFD50DA6
3FAF18BD845433622DAF97C06A10D0F1',
},
-2: { ; KEM public key
1: 2, ; kty: EC2
-1: 1, ; crv: P256
-2: h'5C099BEC31FAA581D14E208250D3FFDA
9EC7F543043008BC84967A8D875B5D78',
-3: h'539D57429FCB1C138DA29010A155DCA1
4566A8F55AC2F1780810C49D4ED72D58',
}
}
¶
The following is the same example encoded as CBOR:¶
h'a5013a0001000002582060b6dfddd31659598ae5de49acb220d8704949e84d48 4b68344340e2565337d2032820a40102200121582069380fc1c3b09652134fee fba61776f97af875ce46ca20252c4165102966ebc52258208b515831462ccb0b d55cba04bfd50da63faf18bd845433622daf97c06a10d0f121a4010220012158 205c099bec31faa581d14e208250d3ffda9ec7f543043008bc84967a8d875b5d 78225820539d57429fcb1c138da29010a155dca14566a8f55ac2f1780810c49d 4ed72d588'¶
TODO: This should eventually move to a separate "algoritm IDs for two-party signing" spec, see: https://mailarchive.ietf.org/arch/msg/cose/BjIO9qDNbuVinxAph7F-Z88GpFY/¶
While keys used by many other algorithms can usually be referenced by a single atomic identifier,
such as that used in the kid parameter in a COSE_Key object or in the unprotected header of a COSE_Recipient,
users of the function ARKG-Derive-Secret-Key need to represent
a reference to an ARKG private seed along with a key handle for a derived private key.¶
A COSE key reference is a COSE_Key object whose kty value is defined to represent a reference to a key.
The kid parameter MUST be present when kty is a key reference type.
These requirements are encoded in the CDDL [RFC8610] type COSE_Key_Ref:¶
COSE_Key_Ref = COSE_Key .within {
1 ^ => $COSE_kty_ref ; kty: Any reference type
2 ^ => any, ; kid is required
any => any, ; Any other entries allowed by COSE_Key
}
¶
The following CDDL example represents a reference to a key derived by ARKG-P256ADD-ECDH
and restricted for use with the ESP256 [fully-spec-algs] signature algorithm:¶
{
1: -65538, ; kty: Ref-ARKG-derived
; kid: Opaque identifier of ARKG-pub
2: h'60b6dfddd31659598ae5de49acb220d8
704949e84d484b68344340e2565337d2',
3: -65539, ; alg: ESP256-ARKG
; ARKG-P256ADD-ECDH key handle
; (HMAC-SHA-256-128 followed by
SEC1 uncompressed ECDH public key)
-1: h'ae079e9c52212860678a7cee25b6a6d4
048219d973768f8e1adb8eb84b220b0ee3
a2532828b9aa65254fe3717a29499e9b
aee70cea75b5c8a2ec2eb737834f7467
e37b3254776f65f4cfc81e2bc4747a84',
; info argument to ARKG-Derive-Private-Key
-2: 'Example application info',
}
¶
The following is the same example encoded as CBOR:¶
h'a5013a0001000102582060b6dfddd31659598ae5de49acb220d8704949e84d48 4b68344340e2565337d2033a00010002205851ae079e9c52212860678a7cee25 b6a6d4048219d973768f8e1adb8eb84b220b0ee3a2532828b9aa65254fe3717a 29499e9baee70cea75b5c8a2ec2eb737834f7467e37b3254776f65f4cfc81e2b c4747a842158184578616d706c65206170706c69636174696f6e20696e666f'¶
This section registers the following values in the IANA "COSE Key Types" registry [IANA.cose].¶
Name: ARKG-pub¶
Value: TBD (Placeholder -65537)¶
Description: ARKG public seed¶
Capabilities: [kty(-65537), pk_bl, pk_kem]¶
Reference: Section 5.1 of this document¶
Name: Ref-ARKG-derived¶
Value: TBD (Placeholder -65538)¶
Description: Reference to private key derived by ARKG¶
Capabilities: [kty(-65538), kh]¶
Reference: Section 5.2 of this document¶
Name: Ref-OKP¶
Value: TBD (Requested assignment -1)¶
Description: Reference to a key pair of key type "OKP"¶
Capabilities: [kty(-1), crv]¶
Reference: Section 5.2 of this document¶
Name: Ref-EC2¶
Value: TBD (Requested assignment -2)¶
Description: Reference to a key pair of key type "EC2"¶
Capabilities: [kty(-1), crv]¶
Reference: Section 5.2 of this document¶
These registrations add the following choices to the CDDL [RFC8610] type socket $COSE_kty_ref:¶
$COSE_kty_ref /= -65538 ; Placeholder value $COSE_kty_ref /= -1 ; Value TBD $COSE_kty_ref /= -2 ; Value TBD¶
TODO: These should eventually move to a separate "algoritm IDs for two-party signing" spec, see: https://mailarchive.ietf.org/arch/msg/cose/BjIO9qDNbuVinxAph7F-Z88GpFY/¶
This section registers the following values in the IANA "COSE Key Type Parameters" registry [IANA.cose].¶
TODO: These should eventually move to a separate "algoritm IDs for two-party signing" spec, see: https://mailarchive.ietf.org/arch/msg/cose/BjIO9qDNbuVinxAph7F-Z88GpFY/¶
This section registers the following values in the IANA "COSE Algorithms" registry [IANA.cose].¶
Name: ESP256-ARKG¶
Value: TBD (Placeholder -65539)¶
Description: ESP256 with key derived by ARKG-P256ADD-ECDH¶
Capabilities: [kty]¶
Change Controller: TBD¶
Reference: [fully-spec-algs], Section 4.1 of this document¶
Recommended: Yes¶
Name: ESP384-ARKG¶
Value: TBD (Placeholder -65540)¶
Description: ESP384 with key derived by ARKG-P384ADD-ECDH¶
Capabilities: [kty]¶
Change Controller: TBD¶
Reference: [fully-spec-algs], Section 4.2 of this document¶
Recommended: Yes¶
Name: ESP512-ARKG¶
Value: TBD (Placeholder -65541)¶
Description: ESP512 with key derived by ARKG-P521ADD-ECDH¶
Capabilities: [kty]¶
Change Controller: TBD¶
Reference: [fully-spec-algs], Section 4.3 of this document¶
Recommended: Yes¶
Name: ES256K-ARKG¶
Name: Ed25519-ARKG¶
Value: TBD (Placeholder -65543)¶
Description: Ed25519 with key derived by ARKG-edwards25519ADD-X25519¶
Capabilities: [kty]¶
Change Controller: TBD¶
Reference: [fully-spec-algs], Section 4.7 of this document¶
Recommended: Yes¶
Name: Ed448-ARKG¶
Value: TBD (Placeholder -65544)¶
Description: Ed448 with key derived by ARKG-edwards448ADD-X448¶
Capabilities: [kty]¶
Change Controller: TBD¶
Reference: [fully-spec-algs], Section 4.8 of this document¶
Recommended: Yes¶
The ARKG construction by Wilson [Wilson] omits the MAC and instead encodes application context in the PRF labels, arguing that 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], but allow it to be omitted in case the chosen KEM already guarantees ciphertext integrity.¶
The reason for this is to ensure that the delegating party can distinguish key handles that belong to its ARKG seed.
For example, this is important for applications using the W3C Web Authentication API [WebAuthn],
which do not know beforehand which authenticators are connected and available.
Instead, authentication requests may include references to several eligible authenticators,
and the one to use is chosen opportunistically by the WebAuthn client depending on which are available at the time.
Consider using ARKG in such a scenario to sign some data with a derived private key:
a user may have several authenticators and thus several ARKG seeds,
so the signing request might include several well-formed ARKG key handles,
but only one of them belongs to the ARKG seed of the authenticator that is currently connected.
Without an integrity check,
choosing the wrong key handle might cause the ARKG-Derive-Private-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 difficult or impossible to diagnose the root cause of the issue and present actionable user feedback.
For this reason, we require the KEM to guarantee ciphertext integrity
so that ARKG-Derive-Private-Key can fail early if the key handle belongs to a different ARKG seed.¶
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 BL as described in Section 3.1
and KEM as described in Section 3.3.
The use of hash_to_field in Section 3.1 corresponds to the KDF1 parameter in [Frymann2020],
and the use of HMAC and HKDF in Section 3.2 corresponds to the MAC and KDF2 parameters in [Frymann2020].
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.¶
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.¶
TODO¶
00 Initial Version¶
01 Editorial Fixes to formatting and references.¶
02¶
Rewritten introduction.¶
Renamed ARKG-Derive-Secret-Key to ARKG-Derive-Private-Key.¶
Overhauled EC instantiations to use hash_to_field and account for non-prime order curve key generation.¶
Eliminated top-level MAC and KDF instance parameters.¶
Added info parameter to instance parameter functions.¶
Added requirement of KEM ciphertext integrity and generic formula for augmenting any KEM using HMAC.¶
Added curve/edwards25519/448 instances.¶
Added proposal for COSE bindings and key reference types.¶
03¶
Renamed section "Using HMAC to adapt a KEM without {integrity protection => ciphertext integrity}".¶
Fixed info argument to HMAC in section "Using HMAC to adapt a KEM without ciphertext integrity".¶
Added reference to Shoup for definition of key encapsulation mechanism.¶
Added CDDL definition of COSE_Key_Ref¶
Editorial fixes to references.¶
Renamed proposed COSE Key Types.¶