Crypto Forum E. Lundberg, Ed. Internet-Draft J. Bradley Intended status: Informational Yubico Expires: 6 January 2027 5 July 2026 The Asynchronous Remote Key Generation (ARKG) algorithm draft-bradleylundberg-cfrg-arkg-11 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. 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/. Lundberg & Bradley Expires 6 January 2027 [Page 1] Internet-Draft ARKG July 2026 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 6 January 2027. Copyright Notice Copyright (c) 2026 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 Revised BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Revised BSD License. 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-Derive-Seed . . . . . . . . . . . . . . 8 2.2.1. Nondeterministic variants . . . . . . . . . . . . . . 9 2.3. The function ARKG-Derive-Public-Key . . . . . . . . . . . 9 2.3.1. Nondeterministic variants . . . . . . . . . . . . . . 10 2.4. The function ARKG-Derive-Private-Key . . . . . . . . . . 11 2.5. Using ctx values longer than 64 bytes . . . . . . . . . . 12 3. Generic ARKG instantiations . . . . . . . . . . . . . . . . . 12 3.1. Using elliptic curve addition for key blinding . . . . . 12 3.2. Using HMAC to adapt a KEM without ciphertext integrity . 14 3.3. Using ECDH as the KEM . . . . . . . . . . . . . . . . . . 16 3.4. Using X25519 or X448 as the KEM . . . . . . . . . . . . . 17 3.5. Using the same key for both key blinding and KEM . . . . 18 4. Concrete ARKG instantiations . . . . . . . . . . . . . . . . 19 4.1. ARKG-P256 . . . . . . . . . . . . . . . . . . . . . . . . 19 4.2. ARKG-P384 . . . . . . . . . . . . . . . . . . . . . . . . 19 4.3. ARKG-P521 . . . . . . . . . . . . . . . . . . . . . . . . 20 4.4. ARKG-P256k . . . . . . . . . . . . . . . . . . . . . . . 20 5. COSE bindings . . . . . . . . . . . . . . . . . . . . . . . . 21 5.1. COSE key type: ARKG public seed . . . . . . . . . . . . . 21 5.2. COSE algorithms . . . . . . . . . . . . . . . . . . . . . 23 Lundberg & Bradley Expires 6 January 2027 [Page 2] Internet-Draft ARKG July 2026 5.3. COSE signing arguments . . . . . . . . . . . . . . . . . 27 6. Security Considerations . . . . . . . . . . . . . . . . . . . 29 6.1. Security Properties . . . . . . . . . . . . . . . . . . . 29 6.2. Secret Values . . . . . . . . . . . . . . . . . . . . . . 29 6.3. KEM Ciphertext Integrity . . . . . . . . . . . . . . . . 31 7. Privacy Considerations . . . . . . . . . . . . . . . . . . . 31 7.1. Public Seed Secrecy . . . . . . . . . . . . . . . . . . . 32 8. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 32 8.1. COSE Key Types Registrations . . . . . . . . . . . . . . 32 8.2. COSE Key Type Parameters Registrations . . . . . . . . . 33 8.3. COSE Algorithms Registrations . . . . . . . . . . . . . . 33 8.4. COSE Signing Arguments Algorithm Parameters Registrations . . . . . . . . . . . . . . . . . . . . . . 36 9. Design rationale . . . . . . . . . . . . . . . . . . . . . . 37 9.1. Using a MAC . . . . . . . . . . . . . . . . . . . . . . . 37 10. Implementation Status . . . . . . . . . . . . . . . . . . . . 38 10.1. Related Internet-Drafts . . . . . . . . . . . . . . . . 39 10.2. Future Work . . . . . . . . . . . . . . . . . . . . . . 40 11. References . . . . . . . . . . . . . . . . . . . . . . . . . 40 11.1. Normative References . . . . . . . . . . . . . . . . . . 40 11.2. Informative References . . . . . . . . . . . . . . . . . 42 Appendix A. Test Vectors . . . . . . . . . . . . . . . . . . . . 44 A.1. ARKG-P256 . . . . . . . . . . . . . . . . . . . . . . . . 44 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . 47 Document History . . . . . . . . . . . . . . . . . . . . . . . . 48 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 52 1. Introduction 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- Lundberg & Bradley Expires 6 January 2027 [Page 3] Internet-Draft ARKG July 2026 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 (https://www.rfc-editor.org/rfc/rfc9052.html#name-direct-key- agreement) 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 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 Lundberg & Bradley Expires 6 January 2027 [Page 4] Internet-Draft ARKG July 2026 derivation function (KDF) and a message authentication code (MAC) scheme. Both conventional primitives and quantum-resistant alternatives exist that meet these requirements. [ASIACCS_SteWil24] 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. * 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). * LEN(x) is the length, in octets, of the octet string x. * The function I2OSP converts a nonnegative integer into an octet string as defined in Section 4.1 of [RFC8017]. 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. This construction of ARKG is fully deterministic, extracting input entropy as explicit parameters, as opposed to the internal random sampling typically used in the academic literature [CCS_FGKLMN20] [Wilson2023] [AC_BreCleFis24]. Implementations MAY choose to instead implement the ARKG-Derive-Seed and KEM-Encaps functions as Lundberg & Bradley Expires 6 January 2027 [Page 5] Internet-Draft ARKG July 2026 nondeterministic procedures omitting their respective ikm parameters and sampling random entropy internally; this choice does not affect interoperability between the functions ARKG-Derive-Seed, ARKG-Derive- Public-Key and ARKG-Derive-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. 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 [Wilson2023], consisting of: - Function BL-Generate-Keypair() -> (pk, sk): Generate a blinding key pair. Input consists of input keying material entropy ikm. Output consists of a blinding public key pk and a blinding private key sk. - Function BL-PRF(ikm_tau, ctx) -> tau: Derive a pseudorandom blinding factor. Input consists of input entropy ikm_tau and a domain separation parameter ctx. Output consists of the blinding factor tau. - 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-Private-Key(sk, tau) -> sk_tau: Deterministically compute a blinded private key. Input consists of a blinding private key sk, and the blinding factor tau. Output consists of the blinded private key sk_tau. Lundberg & Bradley Expires 6 January 2027 [Page 6] Internet-Draft ARKG July 2026 ikm is an opaque octet string of a suitable length as defined by the ARKG instance. ikm_tau is an opaque octet string generated as the k output of KEM-Encaps and KEM-Decaps. ctx is an opaque octet string of arbitrary length. The representations of pk and pk_tau are defined by the protocol that invokes ARKG. The representations of sk, tau and sk_tau are undefined implementation details. See [Wilson2023] for definitions of security properties required of the key blinding scheme BL. * KEM: A key encapsulation mechanism [Shoup], consisting of the functions: - KEM-Derive-Key-Pair(ikm) -> (pk, sk): Derive a key encapsulation key pair. Input consists of input keying material entropy ikm. Output consists of public key pk and private key sk. - KEM-Encaps(pk, ikm, ctx) -> (k, c): Derive a key encapsulation. Input consists of an encapsulation public key pk, input entropy ikm and a domain separation parameter ctx. Output consists of a shared secret k and an encapsulation ciphertext c. - KEM-Decaps(sk, c, ctx) -> k: Decapsulate a shared secret. Input consists of encapsulation private key sk, encapsulation ciphertext c and a domain separation parameter ctx. Output consists of the shared secret k on success, or an error otherwise. ikm is an opaque octet string of a suitable length as defined by the ARKG instance. k, c and ctx 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 ctx is required in order to create any ciphertext c that can be successfully decapsulated by the corresponding private key sk. Lundberg & Bradley Expires 6 January 2027 [Page 7] Internet-Draft ARKG July 2026 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 [ASIACCS_SteWil24] 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. 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-NAME, substituting for NAME some description of the chosen instantiation for 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. 2.2. The function ARKG-Derive-Seed This function is performed by the delegating party. The delegating party derives 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 derive public keys on behalf of the delegating party. Lundberg & Bradley Expires 6 January 2027 [Page 8] Internet-Draft ARKG July 2026 ARKG-Derive-Seed(ikm_bl, ikm_kem) -> (pk, sk) ARKG instance parameters: BL A key blinding scheme. KEM A key encapsulation mechanism. Inputs: ikm_bl Input keying material entropy for BL. ikm_kem Input keying material entropy for KEM. Output: (pk, sk) An ARKG seed pair with public seed pk and private seed sk. The output (pk, sk) is calculated as follows: (pk_bl, sk_bl) = BL-Derive-Key-Pair(ikm_bl) (pk_kem, sk_kem) = KEM-Derive-Key-Pair(ikm_kem) pk = (pk_bl, pk_kem) sk = (sk_bl, sk_kem) 2.2.1. Nondeterministic variants Applications that do not need a deterministic interface MAY choose to instead implement ARKG-Derive-Seed, KEM-Derive-Key-Pair and BL- Derive-Key-Pair as nondeterministic procedures omitting their respective ikm parameters and sampling random entropy internally; this choice does not affect interoperability with ARKG-Derive-Public- Key and ARKG-Derive-Private-Key. 2.3. The function ARKG-Derive-Public-Key This function is performed by the subordinate party, which holds the ARKG public seed pk = (pk_bl, pk_kem). 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, using different ikm or ctx arguments, in order to generate any number of public keys. Lundberg & Bradley Expires 6 January 2027 [Page 9] Internet-Draft ARKG July 2026 ARKG-Derive-Public-Key((pk_bl, pk_kem), ikm, ctx) -> (pk', kh) ARKG instance parameters: BL A key blinding scheme. KEM A key encapsulation mechanism. Inputs: pk_bl A key blinding public key. pk_kem A key encapsulation public key. ikm Input entropy for KEM encapsulation. ctx An octet string of length at most 64, 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: if LEN(ctx) > 64: Abort with an error. ctx' = I2OSP(LEN(ctx), 1) || ctx ctx_bl = 'ARKG-Derive-Key-BL.' || ctx' ctx_kem = 'ARKG-Derive-Key-KEM.' || ctx' (ikm_tau, c) = KEM-Encaps(pk_kem, ikm, ctx_kem) tau = BL-PRF(ikm_tau, ctx_bl) pk' = BL-Blind-Public-Key(pk_bl, tau) kh = c If this procedure aborts due to an error, the procedure can safely be retried with the same (pk_bl, pk_kem) and ctx arguments but a new ikm argument. See Section 2.5 for guidance on using ctx arguments longer than 64 bytes. 2.3.1. Nondeterministic variants Applications that do not need a deterministic interface MAY choose to instead implement ARKG-Derive-Public-Key and KEM-Encaps as nondeterministic procedures omitting their respective ikm parameter and sampling random entropy internally; this choice does not affect interoperability with ARKG-Derive-Private-Key. Lundberg & Bradley Expires 6 January 2027 [Page 10] Internet-Draft ARKG July 2026 BL-PRF and BL-Blind-Public-Key must always be deterministic for compatibility with ARKG-Derive-Private-Key. 2.4. The function ARKG-Derive-Private-Key This function is performed by the delegating party, which holds the ARKG private seed (sk_bl, sk_kem). 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_bl, sk_kem), kh, ctx) -> sk' ARKG instance parameters: BL A key blinding scheme. KEM A key encapsulation mechanism. Inputs: sk_bl A key blinding private key. sk_kem A key encapsulation private key. kh A key handle output from ARKG-Derive-Public-Key. ctx An octet string of length at most 64, 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: if LEN(ctx) > 64: Abort with an error. ctx' = I2OSP(LEN(ctx), 1) || ctx ctx_bl = 'ARKG-Derive-Key-BL.' || ctx' ctx_kem = 'ARKG-Derive-Key-KEM.' || ctx' ikm_tau = KEM-Decaps(sk_kem, kh, ctx_kem) If decapsulation failed: Abort with an error. tau = BL-PRF(ikm_tau, ctx_bl) sk' = BL-Blind-Private-Key(sk_bl, tau) Lundberg & Bradley Expires 6 January 2027 [Page 11] Internet-Draft ARKG July 2026 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 an honest and correct implementation of ARKG-Derive- Private-Key. See also Section 9.1. See Section 2.5 for guidance on using ctx arguments longer than 64 bytes. 2.5. Using ctx values longer than 64 bytes The ctx parameter of ARKG-Derive-Public-Key and ARKG-Derive-Private- Key is limited to a length of at most 64 bytes. This is because this value needs to be communicated from the _subordinate party_ to the _delegating party_ to use the same argument value in both functions, therefore it is necessary in some contexts to limit the size of this parameter in order to limit the size of overall protocol messages. If applications require ctx values longer than 64 bytes, implementors MAY use techniques such as that described in Section 5.3.3 of [RFC9380]. Precise procedure definitions are left as an application- specific implementation detail. 3. Generic ARKG instantiations This section defines generic formulae for instantiating the individual ARKG parameters, which can be used to define concrete ARKG instantiations. 3.1. Using elliptic curve addition for key blinding Instantiations of ARKG whose output keys are elliptic curve keys can use elliptic curve addition as the key blinding scheme BL [CCS_FGKLMN20] [Wilson2023]. 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. Lundberg & Bradley Expires 6 January 2027 [Page 12] Internet-Draft ARKG July 2026 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-Derive-Key-Pair(ikm) -> (pk, sk) DST_bl_sk = 'ARKG-BL-EC-KG.' || DST_ext sk = hash_to_field(ikm, 1) with the parameters: DST: DST_bl_sk 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 = sk * G BL-PRF(ikm_tau, ctx) -> tau DST_tau = 'ARKG-BL-EC.' || DST_ext || ctx tau = hash_to_field(ikm_tau, 1) with the parameters: DST: DST_tau 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 BL-Blind-Public-Key(pk, tau) -> pk_tau pk_tau = pk + tau * G BL-Blind-Private-Key(sk, tau) -> sk_tau sk_tau_tmp = sk + tau If sk_tau_tmp = 0, abort with an error. sk_tau = sk_tau_tmp Lundberg & Bradley Expires 6 January 2027 [Page 13] Internet-Draft ARKG July 2026 3.2. Using HMAC to adapt a KEM without ciphertext integrity 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 ctx parameter and MAY not guarantee ciphertext integrity. Sub-Kem defines the functions Sub-Kem-Derive-Key-Pair, 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-Derive-Key-Pair(ikm) -> (pk, sk) (pk, sk) = Sub-Kem-Derive-Key-Pair(ikm) KEM-Encaps(pk, ikm, ctx) -> (k, c) ctx_sub = 'ARKG-KEM-HMAC.' || DST_ext || ctx Lundberg & Bradley Expires 6 January 2027 [Page 14] Internet-Draft ARKG July 2026 (k', c') = Sub-Kem-Encaps(pk, ikm, ctx_sub) prk = HKDF-Extract with the arguments: Hash: Hash salt: not set IKM: k' info_mk = 'ARKG-KEM-HMAC-mac.' || DST_ext || ctx mk = HKDF-Expand with the arguments: Hash: Hash PRK: prk info: info_mk L: L t = HMAC-Hash-128(K=mk, text=c') info_k = 'ARKG-KEM-HMAC-shared.' || DST_ext || ctx k = HKDF-Expand with the arguments: Hash: Hash PRK: prk info: info_k L: The length of k' in octets. c = t || c' KEM-Decaps(sk, c, ctx) -> k t = LEFT(c, 16) c' = DROP_LEFT(c, 16) ctx_sub = 'ARKG-KEM-HMAC.' || DST_ext || ctx k' = Sub-Kem-Decaps(sk, c', ctx_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 || ctx 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 || ctx Lundberg & Bradley Expires 6 January 2027 [Page 15] Internet-Draft ARKG July 2026 L: The length of k' in octets. Else: Abort with an error. In concrete instances where Sub-Kem-Encaps and Sub-Kem-Decaps ignore the ctx parameter, implementations MAY eliminate the parameter and omit the computation of ctx_sub. 3.3. Using ECDH as the KEM Instantiations of ARKG can use ECDH [RFC6090] as the key encapsulation mechanism KEM [CCS_FGKLMN20] [ASIACCS_SteWil24]. This section defines a general formula for such instantiations of KEM. This formula has the following parameters: * crv: an elliptic curve valid for use with ECDH [RFC6090]. * Hash: A cryptographic hash function. * hash-to-crv-suite: A hash-to-curve suite [RFC9380] suitable for hashing to the scalar field of crv. * DST_ext: A domain separation parameter. The above parameters define the following intermediate value: * DST_aug: 'ARKG-ECDH.' || DST_ext. The KEM parameter of ARKG may be instantiated as described in section Section 3.2 with the parameters: * Hash: Hash. * DST_ext: DST_aug. * Sub-Kem: The functions Sub-Kem-Derive-Key-Pair, 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. Lundberg & Bradley Expires 6 January 2027 [Page 16] Internet-Draft ARKG July 2026 - N is the order of G. Sub-Kem-Derive-Key-Pair(ikm) -> (pk, sk) DST_kem_sk = 'ARKG-KEM-ECDH-KG.' || DST_aug sk = hash_to_field(ikm, 1) with the parameters: DST: DST_kem_sk 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 = sk * G Sub-Kem-Encaps(pk, ikm, ctx) -> (k, c) (pk', sk') = Sub-Kem-Derive-Key-Pair(ikm) k = ECDH(pk, sk') c = Elliptic-Curve-Point-to-Octet-String(pk') Sub-Kem-Decaps(sk, c, ctx) -> k pk' = Octet-String-to-Elliptic-Curve-Point(c) k = ECDH(pk', sk) Note: This instance intentionally ignores the ctx parameter of Sub- Kem-Encaps and Sub-Kem-Decaps. 3.4. Using X25519 or X448 as the KEM 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: Lundberg & Bradley Expires 6 January 2027 [Page 17] Internet-Draft ARKG July 2026 * Hash: SHA-512 [NIST.FIPS.180-4] if DH-Function is X25519, or SHAKE256 [NIST.FIPS.202] with output length 64 octets if DH- Function is X448. * DST_ext: 'ARKG-ECDHX.' || DST_ext. * Sub-Kem: The functions Sub-Kem-Derive-Key-Pair, Sub-Kem-Encaps and Sub-Kem-Decaps defined as follows: - 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-Derive-Key-Pair(ikm) -> (pk, sk) sk = ikm pk = DH-Function(sk, G) Sub-Kem-Encaps(pk, ikm, ctx) -> (k, c) (pk', sk') = Sub-Kem-Derive-Key-Pair(ikm) k = DH-Function(sk', pk) c = pk' Sub-Kem-Decaps(sk, c, ctx) -> k k = DH-Function(sk, c) Note: This instance intentionally ignores the ctx parameter of Sub- Kem-Encaps and Sub-Kem-Decaps. 3.5. Using the same key for both key blinding and KEM 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 [CCS_FGKLMN20] - 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 Lundberg & Bradley Expires 6 January 2027 [Page 18] Internet-Draft ARKG July 2026 representations MUST clearly identify that the single constituent key is to be used both as the key blinding key and the KEM key. 4. Concrete ARKG instantiations This section defines an initial set of concrete ARKG instantiations. 4.1. ARKG-P256 The identifier ARKG-P256 represents the following ARKG instance: * BL: Elliptic curve addition as described in Section 3.1 with the parameters: - crv: The NIST curve secp256r1 [SEC2]. - hash-to-crv-suite: P256_XMD:SHA-256_SSWU_RO_ [RFC9380]. - DST_ext: 'ARKG-P256'. * KEM: ECDH as described in Section 3.3 with the parameters: - crv: The NIST curve secp256r1 [SEC2]. - Hash: SHA-256 [NIST.FIPS.180-4]. - hash-to-crv-suite: P256_XMD:SHA-256_SSWU_RO_ [RFC9380]. - DST_ext: 'ARKG-P256'. Each ikm_bl, ikm_kem and ikm input to the procedures in this ARKG instance SHOULD contain at least 256 bits of entropy. 4.2. ARKG-P384 The identifier ARKG-P384 represents the following ARKG instance: * BL: Elliptic curve addition as described in Section 3.1 with the parameters: - crv: The NIST curve secp384r1 [SEC2]. - hash-to-crv-suite: P384_XMD:SHA-384_SSWU_RO_ [RFC9380]. - DST_ext: 'ARKG-P384'. * KEM: ECDH as described in Section 3.3 with the parameters: Lundberg & Bradley Expires 6 January 2027 [Page 19] Internet-Draft ARKG July 2026 - crv: The NIST curve secp384r1 [SEC2]. - Hash: SHA-384 [NIST.FIPS.180-4]. - hash-to-crv-suite: P384_XMD:SHA-384_SSWU_RO_ [RFC9380]. - DST_ext: 'ARKG-P384'. Each ikm_bl, ikm_kem and ikm input to the procedures in this ARKG instance SHOULD contain at least 384 bits of entropy. 4.3. ARKG-P521 The identifier ARKG-P521 represents the following ARKG instance: * BL: Elliptic curve addition as described in Section 3.1 with the parameters: - crv: The NIST curve secp521r1 [SEC2]. - hash-to-crv-suite: P521_XMD:SHA-512_SSWU_RO_ [RFC9380]. - DST_ext: 'ARKG-P521'. * KEM: ECDH as described in Section 3.3 with the parameters: - crv: The NIST curve secp521r1 [SEC2]. - Hash: SHA-512 [NIST.FIPS.180-4]. - hash-to-crv-suite: P521_XMD:SHA-512_SSWU_RO_ [RFC9380]. - DST_ext: 'ARKG-P521'. Each ikm_bl, ikm_kem and ikm input to the procedures in this ARKG instance SHOULD contain at least 512 bits of entropy. 4.4. ARKG-P256k The identifier ARKG-P256k represents the following ARKG instance: * BL: Elliptic curve addition as described in Section 3.1 with the parameters: - crv: The SECG curve secp256k1 [SEC2]. - hash-to-crv-suite: secp256k1_XMD:SHA-256_SSWU_RO_ [RFC9380]. Lundberg & Bradley Expires 6 January 2027 [Page 20] Internet-Draft ARKG July 2026 - DST_ext: 'ARKG-P256k'. * KEM: ECDH as described in Section 3.3 with the parameters: - crv: The SECG curve secp256k1 [SEC2]. - Hash: SHA-256 [NIST.FIPS.180-4]. - hash-to-crv-suite: secp256k1_XMD:SHA-256_SSWU_RO_ [RFC9380]. - DST_ext: 'ARKG-P256k'. Each ikm_bl, ikm_kem and ikm input to the procedures in this ARKG instance SHOULD contain at least 256 bits of entropy. 5. COSE bindings This section proposes additions to COSE [RFC9052] to support ARKG use cases. These consist of a new key type to represent ARKG public seeds, algorithm identifiers for signing using an ARKG-derived private key, and new COSE_Sign_Args [I-D.cose-split-algs] algorithm parameters for ARKG. 5.1. COSE key type: ARKG public seed An ARKG public seed is represented as a COSE_Key structure [RFC9052] with kty value TBD (placeholder value -65537). Table 1 defines key type parameters pkbl (-1) and pkkem (-2) for the BL and KEM public key, respectively, as well as key type parameter dkalg (-3), representing the algorithm that derived public and private keys are to be used with. Lundberg & Bradley Expires 6 January 2027 [Page 21] Internet-Draft ARKG July 2026 +=======+=======+==========+===========+============================+ | Name | Label | Value | Required? | Description | | | | type | | | +=======+=======+==========+===========+============================+ | pkbl | -1 | COSE_Key | Required | BL key of ARKG public | | | | | | seed | +-------+-------+----------+-----------+----------------------------+ | pkkem | -2 | COSE_Key | Required | KEM key of ARKG | | | | | | public seed | +-------+-------+----------+-----------+----------------------------+ | dkalg | -3 | int / | Optional | alg parameter of | | | | tstr | | public and private | | | | | | keys derived from | | | | | | this ARKG public seed | +-------+-------+----------+-----------+----------------------------+ Table 1: COSE key type parameters for the ARKG-pub key type. When dkalg (-3) is present in an ARKG public seed, the alg (3) parameter of public keys derived using ARKG-Derive-Public-Key with that seed SHOULD be set to the dkalg (-3) value of the seed. The alg (3) parameter, when present, identifies the ARKG instance this public seed is to be used with. An initial set of COSE algorithm identifiers for this purpose is defined in Section 5.2. The following CDDL [RFC8610] example represents an ARKG-P256 public seed restricted to generating derived keys for use with the ESP256 [RFC9864] signature algorithm: Lundberg & Bradley Expires 6 January 2027 [Page 22] Internet-Draft ARKG July 2026 { 1: -65537, ; kty: ARKG-pub (placeholder value) ; kid: Opaque identifier 2: h'60b6dfddd31659598ae5de49acb220d8 704949e84d484b68344340e2565337d2', 3: -65700, ; alg: ARKG-P256 (placeholder value) -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', }, -3: -9 ; Derived key algorithm: ESP256 } The following is the same example encoded as CBOR: h'a6013a0001000002582060b6dfddd31659598ae5de49acb220d8704949e84d48 4b68344340e2565337d2033a000100a320a40102200121582069380fc1c3b096 52134feefba61776f97af875ce46ca20252c4165102966ebc52258208b515831 462ccb0bd55cba04bfd50da63faf18bd845433622daf97c06a10d0f121a40102 20012158205c099bec31faa581d14e208250d3ffda9ec7f543043008bc84967a 8d875b5d78225820539d57429fcb1c138da29010a155dca14566a8f55ac2f178 0810c49d4ed72d582228' 5.2. COSE algorithms This section defines COSE algorithm identifiers [RFC9052] for ARKG instances, and for signature algorithms combined with using a signing private key derived using ARKG. Table 2 defines algorithm identifiers to represent ARKG instances. Lundberg & Bradley Expires 6 January 2027 [Page 23] Internet-Draft ARKG July 2026 +============+==================+==============================+ | Name | Value | Description | +============+==================+==============================+ | ARKG-P256 | TBD (placeholder | The ARKG instance ARKG-P256 | | | -65700) | defined in Section 4.1. | +------------+------------------+------------------------------+ | ARKG-P384 | TBD (placeholder | The ARKG instance ARKG-P384 | | | -65701) | defined in Section 4.2. | +------------+------------------+------------------------------+ | ARKG-P521 | TBD (placeholder | The ARKG instance ARKG-P521 | | | -65702) | defined in Section 4.3. | +------------+------------------+------------------------------+ | ARKG-P256k | TBD (placeholder | The ARKG instance ARKG-P256k | | | -65703) | defined in Section 4.4. | +------------+------------------+------------------------------+ Table 2: COSE algorithm identifiers for ARKG instances. Table 3 defines algorithm identifiers to represent signing algorithms. These MAY be used to negotiate algorithm selection between a _digester_ and _signer_ as described in Section 2 of [I-D.cose-split-algs], and in key representations exchanged between such _digesters_ and _signers_, but SHOULD NOT appear in COSE structures consumed by signature verifiers. COSE structures consumed by signature verifiers SHOULD instead use the corresponding algorithm identifier listed in the "verification algorithm" column. All algorithm identifiers in Table 3 denote signature algorithm suites where: * Key generation consists of executing ARKG-Derive-Seed to derive or generate an ARKG seed pair, and disclosing the public seed. * Signing consists of first executing ARKG-Derive-Public-Key to derive a verification public key and key handle, then executing ARKG-Derive-Private-Key with that key handle to derive the private signing key, and finally using the derived private signing key to generate a signature valid under the derived verification public key. Multiple signings can also be done with the same verification public key and key handle. * Verification consists of executing the verification algorithm indicated in the table, using the derived verification public key. Lundberg & Bradley Expires 6 January 2027 [Page 24] Internet-Draft ARKG July 2026 +=================+============+============+=====================+ |Name |Value |Verification|Description | | | |algorithm | | +=================+============+============+=====================+ |ESP256-ARKG |TBD |-9 (ESP256) |ESP256 [RFC9864] | | | | |using private key | | | | |derived by ARKG-P256 | | | | |(Section 4.1). | +-----------------+------------+------------+---------------------+ |ESP256-split-ARKG|TBD |-9 (ESP256) |ESP256-split | | |(placeholder| |[I-D.cose-split-algs]| | |-65539) | |using private key | | | | |derived by ARKG-P256 | | | | |(Section 4.1). | +-----------------+------------+------------+---------------------+ |ESP384-ARKG |TBD |-51 (ESP384)|ESP384 [RFC9864] | | | | |using private key | | | | |derived by ARKG-P384 | | | | |(Section 4.2). | +-----------------+------------+------------+---------------------+ |ESP384-split-ARKG|TBD |-51 (ESP384)|ESP384-split | | | | |[I-D.cose-split-algs]| | | | |using private key | | | | |derived by ARKG-P384 | | | | |(Section 4.2). | +-----------------+------------+------------+---------------------+ |ESP512-ARKG |TBD |-52 (ESP512)|ESP512 [RFC9864] | | | | |using private key | | | | |derived by ARKG-P521 | | | | |(Section 4.3). | +-----------------+------------+------------+---------------------+ |ESP512-split-ARKG|TBD |-52 (ESP512)|ESP512-split | | | | |[I-D.cose-split-algs]| | | | |using private key | | | | |derived by ARKG-P521 | | | | |(Section 4.3). | +-----------------+------------+------------+---------------------+ |ES256K-ARKG |TBD |-47 (ES256K)|ES256K [RFC8812] | | | | |using private key | | | | |derived by ARKG-P256k| | | | |(Section 4.4). | +-----------------+------------+------------+---------------------+ Table 3: COSE algorithms for signing with an ARKG-derived key. As an example of the intended uses of these algorithm identifiers, consider a split signing [I-D.cose-split-algs] use case with signing keys derived using ARKG-P256: Lundberg & Bradley Expires 6 January 2027 [Page 25] Internet-Draft ARKG July 2026 * First, a _digester_ and _signer_ use the algorithm identifier -65539 (ESP256-split-ARKG, placeholder value) to negotiate a signing protocol and their respective roles in it. This identifier expresses that the _signer_ will generate ARKG seed pairs, the _digester_ will use ARKG-Derive-Public-Key with those public seeds to derive public keys, and the _signer_ will use ARKG-Derive-Private-Key and ESP256-split [I-D.cose-split-algs] to sign data with private keys corresponding to those derived public keys. * The _signer_, acting as the ARKG _delegating party_, then generates an ARKG-P256 seed pair and discloses the public seed to the _digester_. The public seed is encoded as a COSE_Key, with 1 (kty): -65537 (ARKG-pub, placeholder value) to indicate it is an ARKG public seed, 3 (alg): -67000 (ARKG-P256, placeholder value) to indicate which instance of ARKG-Derive-Public-Key to use it with, and -3 (dkalg): -9 (ESP256) to indicate which verification algorithm third-party verifiers may use to verify signatures made by keys derived from this public seed. * The _digester_ uses the ARKG public seed in ARKG-Derive-Public- Key. The resulting public key is encoded as a COSE_Key with 1 (kty): 2 (EC2) to indicate it is an elliptic curve key and 3 (alg): -9 (ESP256) to indicate its verification algorithm. The _digester_ then provides this derived public key to some third party. * That third party later requests a signature by the derived public key. The _digester_ relays this request to the _signer_, along with some identifier for the ARKG seed pair if necessary, and uses a COSE_Sign_Args structure to convey ARKG-Derive-Private-Key inputs to the _signer_. The COSE_Sign_Args structure has 3 (alg): -65539 (ESP256-split-ARKG, placeholder value) to indicate the _digester_'s intent as initially negotiated, and includes the kh and ctx arguments for the _signer_ to use in ARKG-Derive-Private- Key. Since the negotiated algorithm is ESP256-split-ARKG, the _digester_ performs the hash step of the ECDSA signing procedure as defined in Section 2.1 of [I-D.cose-split-algs], and provides the digest as the "data to be signed" input to the _signer_. The _signer_ uses the indicated ARKG private seed in ARKG-Derive- Private-Key and uses the resulting derived private key to generate the requested signature. Lundberg & Bradley Expires 6 January 2027 [Page 26] Internet-Draft ARKG July 2026 * The third party receives the signature, uses the 3 (alg): -9 (ESP256) attribute of the public key to identify the verification algorithm to run, and uses that algorithm to verify the signature. Note how in this example, the identifier -65539 (ESP256-split-ARKG, placeholder value) is not exposed to the third-party verifier; it is used only between _digester_ and _signer_ to negotiate and execute a signing protocol. The verifier does not need to know the internal details of the signing protocol, only what algorithm to use to verify the signature. Consider also an example using ESP256-ARKG instead: * A _digester_ and _signer_ use the algorithm identifier TBD (ESP256-ARKG) to negotiate a signing protocol. This identifier expresses that the _signer_ will generate ARKG seed pairs, the _digester_ will use ARKG-Derive-Public-Key with those public seeds to derive public keys, and the _signer_ will use ARKG-Derive- Private-Key and ESP256 [RFC9864] to sign data with private keys corresponding to those derived public keys. * The example proceeds just like the the ESP256-split-ARKG example above, except the _signer_ uses the derived private key with ESP256 instead of ESP256-split. Therefore, the _digester_ relays the "data to be signed" unaltered from the third party to the _signer_ in this case. 5.3. COSE signing arguments This section defines ARKG-specific parameters for the COSE_Sign_Args structure [I-D.cose-split-algs]. These consist of the parameters -1 and -2 respectively for the kh and ctx parameters of ARKG-Derive- Private-Key. Table 4 defines these algorithm parameters for COSE_Sign_args. kh and ctx are both REQUIRED for all the relevant alg values. Lundberg & Bradley Expires 6 January 2027 [Page 27] Internet-Draft ARKG July 2026 +======+=======+======+===========+===================+=============+ | Name | Label | Type | Required? | Algorithm | Description | +======+=======+======+===========+===================+=============+ | kh | -1 | bstr | Required | ESP256-ARKG, | kh argument | | | | | | ESP256- | to ARKG- | | | | | | split-ARKG, | Derive- | | | | | | ESP384-ARKG, | Private- | | | | | | ESP384- | Key. | | | | | | split-ARKG, | | | | | | | ESP512-ARKG, | | | | | | | ESP512- | | | | | | | split-ARKG, | | | | | | | ES256K-ARKG | | +------+-------+------+-----------+-------------------+-------------+ | ctx | -2 | bstr | Required | ESP256-ARKG, | ctx | | | | | | ESP256- | argument to | | | | | | split-ARKG, | ARKG- | | | | | | ESP384-ARKG, | Derive- | | | | | | ESP384- | Private- | | | | | | split-ARKG, | Key. | | | | | | ESP512-ARKG, | | | | | | | ESP512- | | | | | | | split-ARKG, | | | | | | | ES256K-ARKG | | +------+-------+------+-----------+-------------------+-------------+ Table 4: Algorithm parameters for COSE_Sign_Args. The following CDDL example conveys the kh and ctx arguments for signing data using the ESP256-split algorithm [I-D.cose-split-algs] and a key derived using ARKG-P256: { 3: -65539, ; alg: ESP256-split with ARKG-P256 (placeholder value) ; ARKG-P256 key handle ; (HMAC-SHA-256-128 followed by SEC1 uncompressed ECDH public key) -1: h'27987995f184a44cfa548d104b0a461d 0487fc739dbcdabc293ac5469221da91b220e04c681074ec4692a76ffacb9043de c2847ea9060fd42da267f66852e63589f0c00dc88f290d660c65a65a50c86361', ; info argument to ARKG-Derive-Private-Key -2: 'ARKG-P256.test vectors', } The following is the same example encoded as CBOR: Lundberg & Bradley Expires 6 January 2027 [Page 28] Internet-Draft ARKG July 2026 h'a3033a0001000220585127987995f184a44cfa548d104b0a461d0487fc739dbc dabc293ac5469221da91b220e04c681074ec4692a76ffacb9043dec2847ea906 0fd42da267f66852e63589f0c00dc88f290d660c65a65a50c86361215641524b 472d503235362e7465737420766563746f7273' 6. Security Considerations 6.1. Security Properties ARKG satisfies two security properties, defined in [CCS_FGKLMN20]. Informally, they are: * *Public key unlinkability*: Derived public keys are indistinguishable from randomly sampled public keys, even with knowledge of the ARKG public seed. Consequently, it is also not distinguishable whether two derived public keys were derived from the same ARKG public seed or from different public seeds. This property holds under the assumption that the adversary does not know the tau or ikm_tau value that was computed in ARKG- Derive-Public-Key when deriving the public key. Indeed, knowledge of tau along with a public seed pk and derived public key pk' is sufficient to determine with certainty whether pk' is derived from pk. This also means that is is possible to _prove_, by revealing tau, that pk' is derived from pk, and therefore that knowledge of the corresponding derived private key sk' implies knowledge of the private seed sk. This property is called _PK-unlinkability_ in [CCS_FGKLMN20]. * *Private key security*: Derived private keys cannot be recovered without knowledge of the ARKG private seed, even with knowledge of other public and private keys derived from the same seed. Consequently, signatures by derived private keys enjoy the same unforgeability properties as signatures made by equivalent keys generated without ARKG. This property is called _SK-security_ in [CCS_FGKLMN20], specifically the _msKS_ variant ("malicious-strong SK-security") which is the strongest of the four variants defined. 6.2. Secret Values Both security properties discussed in Section 6.1 rely on the secrecy of the ARKG private seed. This is the primary secret which must be kept confidential in all circumstances. Lundberg & Bradley Expires 6 January 2027 [Page 29] Internet-Draft ARKG July 2026 The ARKG functions also use other values of varying levels of sensitivity: * The ikm_bl and ikm_kem arguments to ARKG-Derive-Seed: These uniquely determine the ARKG private seed, and so must be at least equally well protected as the private seed itself. Note that implementations can choose to not store ikm_bl or ikm_kem if the resulting pk and sk are instead stored directly. See also Section 2.2.1 for discussion of nondeterministic variants that eliminate the ikm_bl and ikm_kem parameters; note however that the same considerations apply to any and all random entropy used to replace them. * The arguments to ARKG-Derive-Public-Key, and all intermediate variables used during its execution, do not need to be kept confidential for private key security to hold. No special protection of them is needed during execution of ARKG-Derive- Public-Key, they do not need to be securely erased, and no additional protection is needed for outputs in transit between subordinate party and delegating party. The private key derived by ARKG-Derive-Public-Key remains secure even if ARKG-Derive- Public-Key is executed entirely in public. However, some of these values enable varying levels of attack on privacy or public key unlinkability if known. Some of them ultimately become private key material, so they should not be revealed unnecessarily. The subsequent list items expand on these considerations. * The ikm argument to ARKG-Derive-Public-Key determines ikm_tau and therefore tau. ikm must therefore be confidential for public key unlinkability to hold; the considerations in Section 7.1 also apply to ikm. Since ikm is used to derive private key material, it should not be revealed unnecessarily. See also Section 2.3.1 for discussion of nondeterministic variants that eliminate the ikm parameters; note however that the same considerations apply to any and all random entropy used to replace it. Lundberg & Bradley Expires 6 January 2027 [Page 30] Internet-Draft ARKG July 2026 * The ctx argument to ARKG-Derive-Public-Key and ARKG-Derive- Private-Key is fuctionally similar to ikm, but intended for domain separation rather than a primary entropy source. It is not intended to be kept confidential and can safely be a public constant, or an application constant appended with a key index, or similar. * The pk' output from ARKG-Derive-Public-Key may safely be made public, but may become a correlation handle if the same pk' is shared with multiple recipients. Privacy considerations for public keys in general apply. * The kh output from ARKG-Derive-Public-Key does not need to be kept confidential, but - unlike the pk' output - also does not need to be revealed to third parties. It should not be revealed unnecessarily since it encodes private key material. * The kh argument to ARKG-Derive-Private-Key is equivalent to the kh output from ARKG-Derive-Public-Key; the same considerations apply. * The values prk, mk and k in the procedures of Section 3.2 do not need to be kept confidential for private key security to hold, but knowledge of at least one of them enables distinguishing the kh output produced by that execution of ARKG-Derive-Public-Key. This could enable a limited de-anonymization attack against that particular kh value. k should not be revealed unnecessarily since it encodes private key material. 6.3. KEM Ciphertext Integrity Section 2.1 requires that the KEM scheme guarantees ciphertext integrity, meaning that a valid KEM ciphertext can be created only with knowledge of the KEM public key. This is not a security requirement; failure to satisfy this property does not weaken either of the security properties discussed in Section 6.1. It may however degrade the correctness of the ARKG instance, as explained in Section 9.1, potentially causing protocol failures that may be difficult to troubleshoot or for end-users to understand. 7. Privacy Considerations Lundberg & Bradley Expires 6 January 2027 [Page 31] Internet-Draft ARKG July 2026 7.1. Public Seed Secrecy The security properties described in Section 6.1 hold even if the ARKG public seed is publicly known, as the name suggests, but there are situations when it may nevertheless be desirable to keep an ARKG public seed confidential. * If ARKG is used to derive multiple "pseudonym" public keys, then the public seed is a correlation handle that may reveal that some pseudonyms are related, even without conclusive proof that they were derived from that seed. The public seed should therefore not be revealed along with such pseudonyms. * Knowledge of an ARKG public seed is sufficient to derive public keys from it, and prove that they were derived from that seed by revealing tau (see Section 6.1). A malicious actor could use this to, for example: - make purchases at the seed owner's expense, if the seller does not require proof of private key possession at the time of the purchase. - accuse the seed owner of wrongdoing by planting incriminating keys in their name. To prevent such and other abuse, it is prudent to keep the public seed confidential. * Knowledge of the KEM component of an ARKG public seed is sufficient to generate ARKG key handles valid for that ARKG private seed. If this is undesirable - for example if it could lead to the delegating party being overloaded - then the KEM component of the public seed should be kept confidential. 8. IANA Considerations 8.1. COSE Key Types Registrations 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] Lundberg & Bradley Expires 6 January 2027 [Page 32] Internet-Draft ARKG July 2026 - Reference: Section 5.1 of this document 8.2. COSE Key Type Parameters Registrations This section registers the following values in the IANA "COSE Key Type Parameters" registry [IANA.cose]. * Key Type: TBD (ARKG-pub, placeholder -65537) - Name: pk_bl - Label: -1 - CBOR Type: COSE_Key - Description: ARKG key blinding public key - Reference: Section 5.1 of this document * Key Type: TBD (ARKG-pub, placeholder -65537) - Name: pk_kem - Label: -2 - CBOR Type: COSE_Key - Description: ARKG key encapsulation public key - Reference: Section 5.1 of this document 8.3. COSE Algorithms Registrations This section registers the following values in the IANA "COSE Algorithms" registry [IANA.cose]. * Name: ARKG-P256 - Value: TBD (placeholder -65700) - Description: ARKG using ECDH and additive blinding on secp256r1 - Reference: Section 5.2 of this document - Recommended: TBD * Name: ARKG-P384 Lundberg & Bradley Expires 6 January 2027 [Page 33] Internet-Draft ARKG July 2026 - Value: TBD (placeholder -65701) - Description: ARKG using ECDH and additive blinding on secp384r1 - Reference: Section 5.2 of this document - Recommended: TBD * Name: ARKG-P521 - Value: TBD (placeholder -65702) - Description: ARKG using ECDH and additive blinding on secp521r1 - Reference: Section 5.2 of this document - Recommended: TBD * Name: ARKG-P256k - Value: TBD (placeholder -65703) - Description: ARKG using ECDH and additive blinding on secp256k1 - Reference: Section 5.2 of this document - Recommended: TBD * Name: ESP256-ARKG - Value: TBD - Description: ESP256 using private key derived by ARKG-P256 - Reference: [RFC9864], Section 5.2 of this document - Recommended: TBD * Name: ESP256-split-ARKG - Value: TBD (placeholder -65539) - Description: ESP256-split using private key derived by ARKG-P256 - Reference: [I-D.cose-split-algs], Section 5.2 of this document - Recommended: TBD Lundberg & Bradley Expires 6 January 2027 [Page 34] Internet-Draft ARKG July 2026 * Name: ESP384-ARKG - Value: TBD - Description: ESP384 using private key derived by ARKG-P384 - Reference: [RFC9864], Section 5.2 of this document - Recommended: TBD * Name: ESP384-split-ARKG - Value: TBD - Description: ESP384-split using private key derived by ARKG-P384 - Reference: [I-D.cose-split-algs], Section 5.2 of this document - Recommended: TBD * Name: ESP512-ARKG - Value: TBD - Description: ESP512 using private key derived by ARKG-P521 - Reference: [RFC9864], Section 5.2 of this document - Recommended: TBD * Name: ESP512-split-ARKG - Value: TBD - Description: ESP512-split using private key derived by ARKG-P521 - Reference: [I-D.cose-split-algs], Section 5.2 of this document - Recommended: TBD * Name: ESP256K-ARKG - Value: TBD - Description: ESP256K using private key derived by ARKG-P256k Lundberg & Bradley Expires 6 January 2027 [Page 35] Internet-Draft ARKG July 2026 - Reference: [RFC8812], Section 5.2 of this document - Recommended: TBD 8.4. COSE Signing Arguments Algorithm Parameters Registrations This section registers the following values in the IANA "COSE Signing Arguments Algorithm Parameters" registry [I-D.cose-split-algs]: * Name: kh - Label: -1 - Type: bstr - Required: yes - Algorithm: ESP256-ARKG, ESP256-split-ARKG, ESP384-ARKG, ESP384- split-ARKG, ESP512-ARKG, ESP512-split-ARKG, ES256K-ARKG - Description: kh argument to ARKG-Derive-Private-Key. - Capabilities: [alg(-65539, TBD)] - Change Controller: IETF - Reference: Section 5.3 of this document * Name: ctx - Label: -2 - Type: bstr - Required: yes - Algorithm: ESP256-ARKG, ESP256-split-ARKG, ESP384-ARKG, ESP384- split-ARKG, ESP512-ARKG, ESP512-split-ARKG, ES256K-ARKG - Description: ctx argument to ARKG-Derive-Private-Key. - Capabilities: [alg(-65539, TBD)] - Change Controller: IETF - Reference: Section 5.3 of this document Lundberg & Bradley Expires 6 January 2027 [Page 36] Internet-Draft ARKG July 2026 9. Design rationale 9.1. Using a MAC The ARKG construction by Stebila et al. [ASIACCS_SteWil24] 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. [CCS_FGKLMN20], 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. [CCS_FGKLMN20]: 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 KDF_1 parameter in [CCS_FGKLMN20], and the use of HMAC and HKDF in Section 3.2 corresponds to the MAC and KDF_2 parameters in [CCS_FGKLMN20]. 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. Lundberg & Bradley Expires 6 January 2027 [Page 37] Internet-Draft ARKG July 2026 10. Implementation Status This section is to be removed from the specification by the RFC Editor before publication as an RFC. There are currently two known implementations using features defined by this specification: * wwWallet (https://github.com/wwWallet), an EU Digital Identity pilot project. wwWallet was entered into the "EUDI Wallet Prototypes" competition held by SprinD GmbH (https://www.sprind.org/en/actions/challenges/eudi-wallet- prototypes), and a branch of the wallet was submitted in the competition. The competition entry implements ARKG for efficiently generating single-use hardware-bound holder binding keys. The implementation (https://github.com/gunet/funke-s3a-wallet- frontend/blob/stage-3/src/services/keystore.ts) uses the COSE_Key_Ref data structure defined in an earlier version of [I-D.cose-split-algs] (version -01 of the Individual-Draft I- D.draft-lundberg-cose-two-party-signing-algs-01) in order to send ARKG inputs to a WebAuthn authenticator, and uses the placeholder value for ESP256-split-ARKG defined in Section 5.2 to negotiate creation and usage of ARKG-derived keys for signing operations. Work to update the implementation to instead use COSE_Sign_Args as defined in [I-D.cose-split-algs] is ongoing. * Yubico (https://www.yubico.com/), a hardware security key vendor, has produced limited-availability prototypes of their YubiKey product with an ARKG implementation interoperable with wwWallet. The YubiKey implementation uses the COSE_Sign_Args data structure defined in [I-D.cose-split-algs] to receive ARKG inputs from a WebAuthn Relying Party, and uses the placeholder value for ESP256- split-ARKG defined in Section 5.2 to negotiate creation and usage of ARKG-derived keys for signing operations. Table 5 summarizes implementation status for individual features. Lundberg & Bradley Expires 6 January 2027 [Page 38] Internet-Draft ARKG July 2026 +===================+==================+ | Feature | Implementations | +===================+==================+ | ARKG-P256 | wwWallet, Yubico | +-------------------+------------------+ | ARKG-P384 | - | +-------------------+------------------+ | ARKG-P521 | - | +-------------------+------------------+ | ARKG-P256k | - | +-------------------+------------------+ | ESP256-ARKG | - | +-------------------+------------------+ | ESP256-split-ARKG | wwWallet, Yubico | +-------------------+------------------+ | ESP384-ARKG | - | +-------------------+------------------+ | ESP384-split-ARKG | - | +-------------------+------------------+ | ESP512-ARKG | - | +-------------------+------------------+ | ESP512-split-ARKG | - | +-------------------+------------------+ | ES256K-ARKG | - | +-------------------+------------------+ | COSE_Sign_Args | wwWallet, Yubico | +-------------------+------------------+ Table 5: Implementation status of individual features. 10.1. Related Internet-Drafts Parts of this specification depend upon definitions from [I-D.cose-split-algs]: * The algorithm identifiers ESP256-split-ARKG, ESP384-split-ARKG and ESP512-split-ARKG defined in Section 5.2 depend respectively on the algorithm identifiers ESP256-split, ESP384-split and ESP512-split defined in [I-D.cose-split-algs]. * The ARKG-specific COSE_Sign_Args parameter definitions in Section 5.3 depend on [I-D.cose-split-algs] for the definition of the COSE_Sign_Args structure. Lundberg & Bradley Expires 6 January 2027 [Page 39] Internet-Draft ARKG July 2026 10.2. Future Work Hierarchical Deterministic Keys (HDK) [I-D.dijkhuis-cfrg-hdkeys] is a possible application of ARKG which has identified a limitation in the present construction, as discussed in HDK GitHub issue #94 (https://github.com/sander/hierarchical-deterministic-keys/ issues/94). ARKG can be used recursively - for example, ARKG-P256 can be used to derive P-256 keys that are themselves used as ARKG seeds - but then requires one invocation of ARKG-Derive-Private-Key per layer of recursion in order to derive higher-layer private keys. This can be an issue if the base ARKG private seed is hardware-bound, since it would require multiple calls to the secure hardware device, especially if each of those calls requires a user gesture for authorization. Therefore a modified ARKG construction has been proposed, along with a draft for a potential security proof (https://github.com/Yubico/arkg-rfc/blob/pqarkg-h/pqarkg-h-security/ pqarkg-h.pdf), which enables multiple layers of recursive ARKG to be condensed into a single invocation of ARKG-Derive-Private-Key. We would have liked to use this modified construction in this specification, but have not been able to get the potential proof appropriately peer reviewed in a timely manner, so prototypes have moved forward with the present construction. The modified construction may be revisited in the future if there is demand for applications, in which case new algorithm identifiers and such can be defined for the modified construction. 11. References 11.1. Normative References [I-D.cose-split-algs] Lundberg, E. and M. B. Jones, "Split Signing Algorithms for COSE", Work in Progress, Internet-Draft, draft-ietf- cose-split-signing-algs-00, 24 April 2026, . [IANA.cose] IANA, "CBOR Object Signing and Encryption (COSE)", . [NIST.FIPS.180-4] Dang, Q. H. and NIST, "Secure Hash Standard", NIST Federal Information Processing Standards Publications 180-4, DOI 10.6028/NIST.FIPS.180-4, July 2015, . Lundberg & Bradley Expires 6 January 2027 [Page 40] Internet-Draft ARKG July 2026 [NIST.FIPS.202] Dworkin, M., Dworkin, M. J., and NIST, "SHA-3 Standard: Permutation-Based Hash and Extendable-Output Functions", FIPS PUB 202, NIST Federal Information Processing Standards Publications 202, DOI 10.6028/nist.fips.202, DOI 10.6028/NIST.FIPS.202, August 2015, . [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, . [RFC7748] Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves for Security", RFC 7748, DOI 10.17487/RFC7748, January 2016, . [RFC8017] Moriarty, K., Ed., Kaliski, B., Jonsson, J., and A. Rusch, "PKCS #1: RSA Cryptography Specifications Version 2.2", RFC 8017, DOI 10.17487/RFC8017, November 2016, . [RFC8032] Josefsson, S. and I. Liusvaara, "Edwards-Curve Digital Signature Algorithm (EdDSA)", RFC 8032, DOI 10.17487/RFC8032, January 2017, . Lundberg & Bradley Expires 6 January 2027 [Page 41] Internet-Draft ARKG July 2026 [RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174, May 2017, . [RFC8610] Birkholz, H., Vigano, C., and C. Bormann, "Concise Data Definition Language (CDDL): A Notational Convention to Express Concise Binary Object Representation (CBOR) and JSON Data Structures", RFC 8610, DOI 10.17487/RFC8610, June 2019, . [RFC8812] Jones, M., "CBOR Object Signing and Encryption (COSE) and JSON Object Signing and Encryption (JOSE) Registrations for Web Authentication (WebAuthn) Algorithms", RFC 8812, DOI 10.17487/RFC8812, August 2020, . [RFC9052] Schaad, J., "CBOR Object Signing and Encryption (COSE): Structures and Process", STD 96, RFC 9052, DOI 10.17487/RFC9052, August 2022, . [RFC9380] Faz-Hernandez, A., Scott, S., Sullivan, N., Wahby, R. S., and C. A. Wood, "Hashing to Elliptic Curves", RFC 9380, DOI 10.17487/RFC9380, August 2023, . [RFC9864] Jones, M.B. and O. Steele, "Fully-Specified Algorithms for JSON Object Signing and Encryption (JOSE) and CBOR Object Signing and Encryption (COSE)", RFC 9864, DOI 10.17487/RFC9864, October 2025, . [SEC1] Certicom Research, "SEC 1: Elliptic Curve Cryptography", 2009, . [SEC2] Certicom Research, "SEC 2: Recommended Elliptic Curve Domain Parameters", 2010, . 11.2. Informative References [AC_BreCleFis24] Brendel, J., Clermont, S., and M. Fischlin, "Post-Quantum Asynchronous Remote Key Generation for FIDO2 Account Recovery. ASIACRYPT '24", 2023, . Lundberg & Bradley Expires 6 January 2027 [Page 42] Internet-Draft ARKG July 2026 [ASIACCS_SteWil24] Stebila, D. and S. M. Wilson, "Quantum-Safe Account Recovery for WebAuthn. ASIACCS '24", 2023, . [BIP32] Wuille, P., "BIP 32 Hierarchical Deterministic Wallets", 2012, . [CCS_FGKLMN20] 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, . [EUROSP_FryGarMan23] 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, . [I-D.dijkhuis-cfrg-hdkeys] Dijkhuis, S., "Hierarchical Deterministic Keys", Work in Progress, Internet-Draft, draft-dijkhuis-cfrg-hdkeys-06, 19 January 2025, . [Shoup] Shoup, V., "A Proposal for an ISO Standard for Public Key Encryption (version 2.0)", 2001, . [WebAuthn] "Web Authentication: An API for accessing Public Key Credentials - Level 3", W3C WD webauthn-3, W3C webauthn-3, . [WebAuthn-Recovery] Lundberg, E. and D. Nilsson, "WebAuthn recovery extension: Asynchronous delegated key generation without shared secrets. GitHub", 2019, . [Wilson2023] Wilson, S. M., "Post-Quantum Account Recovery for Passwordless Authentication. Master's thesis", 2023, . Lundberg & Bradley Expires 6 January 2027 [Page 43] Internet-Draft ARKG July 2026 Appendix A. Test Vectors This section lists test vectors for validating implementations. Test vectors are listed in CDDL [RFC8610] syntax using variable names defined in Section 2 and Section 3. Elliptic curve points are encoded using the Elliptic-Curve-Point-to-Octet-String procedure defined in section 2.3.3 of [SEC1], without point compression. A.1. ARKG-P256 Lundberg & Bradley Expires 6 January 2027 [Page 44] Internet-Draft ARKG July 2026 ; Inputs: ctx = 'ARKG-P256.test vectors' ikm_bl = h'000102030405060708090a0b0c0d0e0f101112131415161718191a1b1c1d1e1f' ikm_kem = h'202122232425262728292a2b2c2d2e2f303132333435363738393a3b3c3d3e3f' ikm = h'404142434445464748494a4b4c4d4e4f505152535455565758595a5b5c5d5e5f' ; Derive-Seed: DST_bl_sk = h'41524b472d424c2d45432d4b472e41524b472d50323536' DST_kem_sk = h'41524b472d4b454d2d454344482d4b472e41524b472d454344482e41524b472d50323536' pk_bl = h'046d3bdf31d0db48988f16d47048fdd24123cd286e42d0512daa9f726b4ecf18df 65ed42169c69675f936ff7de5f9bd93adbc8ea73036b16e8d90adbfabdaddba7' pk_kem = h'04c38bbdd7286196733fa177e43b73cfd3d6d72cd11cc0bb2c9236cf85a42dcff5 dfa339c1e07dfcdfda8d7be2a5a3c7382991f387dfe332b1dd8da6e0622cfb35' sk_bl = 0xd959500a78ccf850ce46c80a8c5043c9a2e33844232b3829df37d05b3069f455 sk_kem = 0x74e0a4cd81ca2d24246ff75bfd6d4fb7f9dfc938372627feb2c2348f8b1493b5 ; Derive-Public-Key: ctx_bl = h'41524b472d4465726976652d4b65792d424c2e1641524b472d503235362e7465737420766563746f7273' ctx_kem = h'41524b472d4465726976652d4b65792d4b454d2e1641524b472d503235362e7465737420766563746f7273' ctx_sub = h'41524b472d4b454d2d484d41432e41524b472d454344482e41524b472d5032353641524b472d4465726976652d4b65792d4b454d2e1641524b472d503235362e7465737420766563746f7273' DST_kem_sk = h'41524b472d4b454d2d454344482d4b472e41524b472d454344482e41524b472d50323536' k_prime = h'fa027ebc49603a2a41052479f6e9f6d046175df2f00cecb403f53ffcd1cc698f' c_prime = h'0487fc739dbcdabc293ac5469221da91b220e04c681074ec4692a76ffacb9043dec2847ea9060fd42da267f66852e63589f0c00dc88f290d660c65a65a50c86361' info_mk = h'41524b472d4b454d2d484d41432d6d61632e41524b472d454344482e41524b472d5032353641524b472d4465726976652d4b65792d4b454d2e1641524b472d503235362e7465737420766563746f7273' mk = h'796c615d19ca0044df0a22d64ba8d5367dca18da32b871a3e255db0af7eb53c9' t = h'27987995f184a44cfa548d104b0a461d' info_k = h'41524b472d4b454d2d484d41432d7368617265642e41524b472d454344482e41524b472d5032353641524b472d4465726976652d4b65792d4b454d2e1641524b472d503235362e7465737420766563746f7273' k = h'cf5e8ddbb8078a6a0144d4412f22f89407ecee30ec128ce07836af9fc51c05d0' c = h'27987995f184a44cfa548d104b0a461d0487fc739dbcdabc293ac5469221da91b220e04c681074ec4692a76ffacb9043dec2847ea9060fd42da267f66852e63589f0c00dc88f290d660c65a65a50c86361' ikm_tau = h'cf5e8ddbb8078a6a0144d4412f22f89407ecee30ec128ce07836af9fc51c05d0' DST_tau = h'41524b472d424c2d45432e41524b472d5032353641524b472d4465726976652d4b65792d424c2e1641524b472d503235362e7465737420766563746f7273' tau = 0x9e042fde2e12c1f4002054a8feac60088cc893b4838423c26a20af686c8c16e3 pk_prime = h'04572a111ce5cfd2a67d56a0f7c684184b16ccd212490dc9c5b579df749647d107 dac2a1b197cc10d2376559ad6df6bc107318d5cfb90def9f4a1f5347e086c2cd' kh = h'27987995f184a44cfa548d104b0a461d0487fc739dbcdabc293ac5469221da91b220e04c681074ec4692a76ffacb9043dec2847ea9060fd42da267f66852e63589f0c00dc88f290d660c65a65a50c86361' ; Derive-Private-Key: sk_prime = 0x775d7fe9a6dfba43ce671cb38afca3d272c4d14aff97bd67559eb500a092e5e7 Lundberg & Bradley Expires 6 January 2027 [Page 45] Internet-Draft ARKG July 2026 ; Inputs: ctx = 'ARKG-P256.test vectors' ikm_bl = h'000102030405060708090a0b0c0d0e0f101112131415161718191a1b1c1d1e1f' ikm_kem = h'202122232425262728292a2b2c2d2e2f303132333435363738393a3b3c3d3e3f' ikm = h'a0a1a2a3a4a5a6a7a8a9aaabacadaeafb0b1b2b3b4b5b6b7b8b9babbbcbdbebf' ; Derive-Seed: DST_bl_sk = h'41524b472d424c2d45432d4b472e41524b472d50323536' DST_kem_sk = h'41524b472d4b454d2d454344482d4b472e41524b472d454344482e41524b472d50323536' pk_bl = h'046d3bdf31d0db48988f16d47048fdd24123cd286e42d0512daa9f726b4ecf18df 65ed42169c69675f936ff7de5f9bd93adbc8ea73036b16e8d90adbfabdaddba7' pk_kem = h'04c38bbdd7286196733fa177e43b73cfd3d6d72cd11cc0bb2c9236cf85a42dcff5 dfa339c1e07dfcdfda8d7be2a5a3c7382991f387dfe332b1dd8da6e0622cfb35' sk_bl = 0xd959500a78ccf850ce46c80a8c5043c9a2e33844232b3829df37d05b3069f455 sk_kem = 0x74e0a4cd81ca2d24246ff75bfd6d4fb7f9dfc938372627feb2c2348f8b1493b5 ; Derive-Public-Key: ctx_bl = h'41524b472d4465726976652d4b65792d424c2e1641524b472d503235362e7465737420766563746f7273' ctx_kem = h'41524b472d4465726976652d4b65792d4b454d2e1641524b472d503235362e7465737420766563746f7273' ctx_sub = h'41524b472d4b454d2d484d41432e41524b472d454344482e41524b472d5032353641524b472d4465726976652d4b65792d4b454d2e1641524b472d503235362e7465737420766563746f7273' DST_kem_sk = h'41524b472d4b454d2d454344482d4b472e41524b472d454344482e41524b472d50323536' k_prime = h'38c79546fc4a144ae2068ff0b515fc9af032b8255a78a829e71be47676a63117' c_prime = h'0457fd1e438280c127dd55a6138d1baf0a35e3e9671f7e42d8345f47374afa83247a078fa2196cd69497aed59ef92c05cb6b03d306ec24f2f4ff2db09cd95d1b11' info_mk = h'41524b472d4b454d2d484d41432d6d61632e41524b472d454344482e41524b472d5032353641524b472d4465726976652d4b65792d4b454d2e1641524b472d503235362e7465737420766563746f7273' mk = h'0806abac4c1d205c3a8826cd178fbf7f91741268e3ca73634035efd76085d2a9' t = h'b7507a82771776fbac41a18d94e19a7e' info_k = h'41524b472d4b454d2d484d41432d7368617265642e41524b472d454344482e41524b472d5032353641524b472d4465726976652d4b65792d4b454d2e1641524b472d503235362e7465737420766563746f7273' k = h'dcdd95c742ddf25b8a95f3d76326cb3593b7860bb3e04c5e5b25cc15ce1e5c84' c = h'b7507a82771776fbac41a18d94e19a7e0457fd1e438280c127dd55a6138d1baf0a35e3e9671f7e42d8345f47374afa83247a078fa2196cd69497aed59ef92c05cb6b03d306ec24f2f4ff2db09cd95d1b11' ikm_tau = h'dcdd95c742ddf25b8a95f3d76326cb3593b7860bb3e04c5e5b25cc15ce1e5c84' DST_tau = h'41524b472d424c2d45432e41524b472d5032353641524b472d4465726976652d4b65792d424c2e1641524b472d503235362e7465737420766563746f7273' tau = 0x88cf9464b041a52cf2b837281afc67302ec9cb32da1fe515381b79c0d0c92322 pk_prime = h'04ea7d962c9f44ffe8b18f1058a471f394ef81b674948eefc1865b5c021cf858f5 77f9632b84220e4a1444a20b9430b86731c37e4dcb285eda38d76bf758918d86' kh = h'b7507a82771776fbac41a18d94e19a7e0457fd1e438280c127dd55a6138d1baf0a35e3e9671f7e42d8345f47374afa83247a078fa2196cd69497aed59ef92c05cb6b03d306ec24f2f4ff2db09cd95d1b11' ; Derive-Private-Key: sk_prime = 0x6228e470290e9d7cc0feff32a74caafa14c608c956337eba23997f5904cff226 Lundberg & Bradley Expires 6 January 2027 [Page 46] Internet-Draft ARKG July 2026 ; Inputs: ctx = 'ARKG-P256.test vectors.0' ikm_bl = h'000102030405060708090a0b0c0d0e0f101112131415161718191a1b1c1d1e1f' ikm_kem = h'202122232425262728292a2b2c2d2e2f303132333435363738393a3b3c3d3e3f' ikm = h'404142434445464748494a4b4c4d4e4f505152535455565758595a5b5c5d5e5f' ; Derive-Seed: DST_bl_sk = h'41524b472d424c2d45432d4b472e41524b472d50323536' DST_kem_sk = h'41524b472d4b454d2d454344482d4b472e41524b472d454344482e41524b472d50323536' pk_bl = h'046d3bdf31d0db48988f16d47048fdd24123cd286e42d0512daa9f726b4ecf18df 65ed42169c69675f936ff7de5f9bd93adbc8ea73036b16e8d90adbfabdaddba7' pk_kem = h'04c38bbdd7286196733fa177e43b73cfd3d6d72cd11cc0bb2c9236cf85a42dcff5 dfa339c1e07dfcdfda8d7be2a5a3c7382991f387dfe332b1dd8da6e0622cfb35' sk_bl = 0xd959500a78ccf850ce46c80a8c5043c9a2e33844232b3829df37d05b3069f455 sk_kem = 0x74e0a4cd81ca2d24246ff75bfd6d4fb7f9dfc938372627feb2c2348f8b1493b5 ; Derive-Public-Key: ctx_bl = h'41524b472d4465726976652d4b65792d424c2e1841524b472d503235362e7465737420766563746f72732e30' ctx_kem = h'41524b472d4465726976652d4b65792d4b454d2e1841524b472d503235362e7465737420766563746f72732e30' ctx_sub = h'41524b472d4b454d2d484d41432e41524b472d454344482e41524b472d5032353641524b472d4465726976652d4b65792d4b454d2e1841524b472d503235362e7465737420766563746f72732e30' DST_kem_sk = h'41524b472d4b454d2d454344482d4b472e41524b472d454344482e41524b472d50323536' k_prime = h'fa027ebc49603a2a41052479f6e9f6d046175df2f00cecb403f53ffcd1cc698f' c_prime = h'0487fc739dbcdabc293ac5469221da91b220e04c681074ec4692a76ffacb9043dec2847ea9060fd42da267f66852e63589f0c00dc88f290d660c65a65a50c86361' info_mk = h'41524b472d4b454d2d484d41432d6d61632e41524b472d454344482e41524b472d5032353641524b472d4465726976652d4b65792d4b454d2e1841524b472d503235362e7465737420766563746f72732e30' mk = h'd342e45f224a7278f11cf1468922c8879f4529125181d4159e4bf9ee69842f04' t = h'81c4e65b552e52350b49864b98b87d51' info_k = h'41524b472d4b454d2d484d41432d7368617265642e41524b472d454344482e41524b472d5032353641524b472d4465726976652d4b65792d4b454d2e1841524b472d503235362e7465737420766563746f72732e30' k = h'cde7e271f8da72e5fd2557de362420ddb170dce520362131670eb1080823a113' c = h'81c4e65b552e52350b49864b98b87d510487fc739dbcdabc293ac5469221da91b220e04c681074ec4692a76ffacb9043dec2847ea9060fd42da267f66852e63589f0c00dc88f290d660c65a65a50c86361' ikm_tau = h'cde7e271f8da72e5fd2557de362420ddb170dce520362131670eb1080823a113' DST_tau = h'41524b472d424c2d45432e41524b472d5032353641524b472d4465726976652d4b65792d424c2e1841524b472d503235362e7465737420766563746f72732e30' tau = 0x513ea417b6cdc3536178fa81da36b4e5ecdc142c2d46a52e05257f21794e3789 pk_prime = h'04b79b65d6bbb419ff97006a1bd52e3f4ad53042173992423e06e52987a037cb61 dd82b126b162e4e7e8dc5c9fd86e82769d402a1968c7c547ef53ae4f96e10b0e' kh = h'81c4e65b552e52350b49864b98b87d510487fc739dbcdabc293ac5469221da91b220e04c681074ec4692a76ffacb9043dec2847ea9060fd42da267f66852e63589f0c00dc88f290d660c65a65a50c86361' ; Derive-Private-Key: sk_prime = 0x2a97f4232f9abba32fbfc28c6686f8afd2d851c2a95a3ed2f0a384b9ad55068d Acknowledgements ARKG was first proposed under this name by Frymann et al. [CCS_FGKLMN20], 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. [CCS_FGKLMN20] generalized the constructions by Lundberg, Nilsson and Wuille from elliptic curves to any discrete logarithm (DL) problem, Lundberg & Bradley Expires 6 January 2027 [Page 47] Internet-Draft ARKG July 2026 and also proved the security of arbitrary asymmetric protocols composed with ARKG. Further generalizations to include quantum- resistant instantiations were developed independently by Brendel et al. [AC_BreCleFis24], Frymann et al. [EUROSP_FryGarMan23] and Wilson [Wilson2023]. This document adopts the construction proposed by Wilson [Wilson2023], modified by the inclusion of a MAC in the key handles as done in the original construction by Frymann et al. [CCS_FGKLMN20]. The construction by Wilson [Wilson2023] was later refined by Stebila et al. [ASIACCS_SteWil24], but this revision replaced the "key blinding scheme" component with a "key-blinding signature scheme" component which is not one-for-one compatible with the construction in the present revision of this specification. The authors would like to thank all of these authors for their research and development work that led to the creation of this document. Document History -11 * Editorial fixes. * Clarified meaning of COSE algorithm identifiers for signing algorithms, and added "walk-through" examples of usage. * Added subsection "Security Properties" to Security Considerations. * Added subsection "Secret Values" to Security Considerations. * Added subsection "KEM Ciphertext Integrity" to Security Considerations. * Added subsection "Public Seed Secrecy" to Privacy Considerations. * Updated "Split Signing Algorithms for COSE" reference from individual-draft to WG draft. * Fixed undefined references WebAuthn, FIPS 180-4 and FIPS 202. -10 * Fixed tau misspelled as tau' in body of BL-Blind-Private-Key in section "Using elliptic curve addition for key blinding". * Fixed definitions and references misspelling ESP512 as ESP521. * Minor editorial clarifications. * Updated informative references to research papers and changed citation style for the same. * Made "Acknowledgements" and "Document History" sections un- numbered. * Added Implementation Status section. Lundberg & Bradley Expires 6 January 2027 [Page 48] Internet-Draft ARKG July 2026 -09 * Fixed hash_to_field argument ikm_tau misnamed as tau in section "Using elliptic curve addition for key blinding". * Updated to match draft -02 of I-D.draft-lundberg-cose-two-party- signing-algs-02. - COSE algorithm identifier definitions for ARKG instances moved from section "COSE key type: ARKG public seed" to new section "COSE algorithms". - Added COSE algorithm identifier definitions for signature algorithms with key derived using ARKG. - COSE key type Ref-ARKG-Derived deleted in favour of new COSE_Sign_Args algorithm parameters. - Section "COSE key reference type: ARKG derived private key" replaced with "COSE signing arguments". - Added section "COSE Signing Arguments Algorithm Parameters Registrations". -08 * Fixed incorrectly swapped ikm_bl and ikm_kem arguments in ARKG- Derive-Seed definition. * Extracted parameter function BL-PRF and modified signatures of BL- Blind-Public-Key and BL-Blind-Private-Key accordingly. This is an editorial refactorization; overall operation of concrete ARKG instances is unchanged. * Removed three redundant sets of ARKG-P256 test vectors. * Added intermediate values to ARKG-P256 test vectors. * Changed second set of ARKG-P256 test vectors to use a 32-byte ikm instead of h'00'. * Clarified in sections "Using HMAC to adapt a KEM without ciphertext integrity", "Using ECDH as the KEM" and "Using X25519 or X448 as the KEM" that ctx_sub is intentionally ignored in those instances. -07 Lundberg & Bradley Expires 6 January 2027 [Page 49] Internet-Draft ARKG July 2026 * Fixed hash_to_field DST in Sub-Kem-Derive-Key-Pair in section "Using ECDH as the KEM" to agree with test vectors. -06 * Changed DST construction in section "Using ECDH as the KEM" to include the "ARKG-ECDH." prefix everywhere in the formula. Previously the prefix was added in the argument to the "Using HMAC to adapt a KEM without ciphertext integrity" formula but not in the Sub-Kem functions defined in "Using ECDH as the KEM". -05 * Deleted concrete instances ARKG-curve25519ADD-X25519, ARKG- curve448ADD-X448, ARKG-edwards25519ADD-X25519 and ARKG- edwards448ADD-X448 since implementations with a non-prime order generator, including EdDSA, are incompatible with the additive blinding scheme defined in section "Using elliptic curve addition for key blinding". * Remodeled procedures to be fully deterministic: - BL-Generate-Keypair() replaced with BL-Derive-Key-Pair(ikm). - KEM-Generate-Keypair() replaced with KEM-Derive-Key-Pair(ikm). - ARKG-Generate-Seed() replaced with ARKG-Derive-Seed(ikm_bl, ikm_kem). - Parameter ikm added to ARKG-Derive-Public-Key. - Instance parameter hash-to-crv-suite added to generic formula "Using ECDH as the KEM", affecting concrete instances ARKG- P256ADD-ECDH, ARKG-P384ADD-ECDH, ARKG-P521ADD-ECDH and ARKG- P256kADD-ECDH. - Section "Deterministic key generation" deleted. * Flipped order of (pk_bl, pk_kem) and (sk_bl, sk_kem) parameter and return value tuples for consistent ordering between BL and KEM throughout document. * info parameter renamed to ctx. * ctx length limited to at most 64 bytes. * Encoding of ctx in ARKG-Derive-Public-Key and ARKG-Derive-Private- Key now embeds the length of ctx. Lundberg & Bradley Expires 6 January 2027 [Page 50] Internet-Draft ARKG July 2026 * Renamed concrete instances and corresponding DST_ext values: - ARKG-P256ADD-ECDH to ARKG-P256 - ARKG-P384ADD-ECDH to ARKG-P384 - ARKG-P521ADD-ECDH to ARKG-P521 - ARKG-P256kADD-ECDH to ARKG-P256k * Added ARKG-P256 test vectors. -04 * Extracted COSE_Key_Ref definition and COSE algorithm registrations to draft-lundberg-cose-two-party-signing-algs. * Redefined alg (3) parameter and added dkalg (-3) in ARKG-pub COSE_Key. * Defined alg (3) and inst (-3) parameters of Ref-ARKG-derived COSE key type. -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. -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. Lundberg & Bradley Expires 6 January 2027 [Page 51] Internet-Draft ARKG July 2026 * 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. -01 * Editorial fixes to formatting and references -00 * Initial Version Contributors Dain Nilsson Yubico Peter Altmann Agency for Digital Government Sweden Michael B. Jones Self-Issued Consulting United States URI: https://self-issued.info/ Sander Dijkhuis Cleverbase Netherlands Authors' Addresses Emil Lundberg (editor) Yubico Gävlegatan 22 Stockholm Sweden Lundberg & Bradley Expires 6 January 2027 [Page 52] Internet-Draft ARKG July 2026 Email: emil@emlun.se John Bradley Yubico Email: ve7jtb@ve7jtb.com Lundberg & Bradley Expires 6 January 2027 [Page 53]