Crypto Forum E. Lundberg, Ed. Internet-Draft J. Bradley Intended status: Informational Yubico Expires: 29 November 2024 28 May 2024 The Asynchronous Remote Key Generation (ARKG) algorithm draft-bradleylundberg-cfrg-arkg-02 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 29 November 2024 [Page 1] Internet-Draft ARKG May 2024 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 29 November 2024. Copyright Notice Copyright (c) 2024 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 . . . . . . . . . . . . . . . . . . . 5 2.2. The function ARKG-Generate-Seed . . . . . . . . . . . . . 7 2.2.1. Deterministic key generation . . . . . . . . . . . . 8 2.3. The function ARKG-Derive-Public-Key . . . . . . . . . . . 8 2.4. The function ARKG-Derive-Private-Key . . . . . . . . . . 9 3. Generic ARKG instantiations . . . . . . . . . . . . . . . . . 10 3.1. Using elliptic curve addition for key blinding . . . . . 10 3.2. Using HMAC to adapt a KEM without integrity protection . 12 3.3. Using ECDH as the KEM . . . . . . . . . . . . . . . . . . 14 3.4. Using X25519 or X448 as the KEM . . . . . . . . . . . . . 16 3.5. Using the same key for both key blinding and KEM . . . . 17 4. Concrete ARKG instantiations . . . . . . . . . . . . . . . . 17 4.1. ARKG-P256ADD-ECDH . . . . . . . . . . . . . . . . . . . . 17 4.2. ARKG-P384ADD-ECDH . . . . . . . . . . . . . . . . . . . . 18 4.3. ARKG-P521ADD-ECDH . . . . . . . . . . . . . . . . . . . . 18 4.4. ARKG-P256kADD-ECDH . . . . . . . . . . . . . . . . . . . 19 4.5. ARKG-curve25519ADD-X25519 . . . . . . . . . . . . . . . . 19 4.6. ARKG-curve448ADD-X448 . . . . . . . . . . . . . . . . . . 20 4.7. ARKG-edwards25519ADD-X25519 . . . . . . . . . . . . . . . 21 4.8. ARKG-edwards448ADD-X448 . . . . . . . . . . . . . . . . . 22 5. COSE bindings . . . . . . . . . . . . . . . . . . . . . . . . 23 Lundberg & Bradley Expires 29 November 2024 [Page 2] Internet-Draft ARKG May 2024 5.1. COSE key type: ARKG public seed . . . . . . . . . . . . . 23 5.2. COSE key reference types . . . . . . . . . . . . . . . . 24 6. Security Considerations . . . . . . . . . . . . . . . . . . . 25 7. Privacy Considerations . . . . . . . . . . . . . . . . . . . 25 8. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 25 8.1. COSE Key Types Registrations . . . . . . . . . . . . . . 25 8.2. COSE Key Type Parameters Registrations . . . . . . . . . 26 8.3. COSE Algorithms Registrations . . . . . . . . . . . . . . 27 9. Design rationale . . . . . . . . . . . . . . . . . . . . . . 29 9.1. Using a MAC . . . . . . . . . . . . . . . . . . . . . . . 29 9.2. Implementation Status . . . . . . . . . . . . . . . . . . 30 10. References . . . . . . . . . . . . . . . . . . . . . . . . . 30 10.1. Normative References . . . . . . . . . . . . . . . . . . 30 10.2. Informative References . . . . . . . . . . . . . . . . . 31 Appendix A. Acknowledgements . . . . . . . . . . . . . . . . . . 32 Appendix B. Test Vectors . . . . . . . . . . . . . . . . . . . . 33 Appendix C. Document History . . . . . . . . . . . . . . . . . . 33 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 33 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- 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. Lundberg & Bradley Expires 29 November 2024 [Page 3] Internet-Draft ARKG May 2024 * *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 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] Lundberg & Bradley Expires 29 November 2024 [Page 4] Internet-Draft ARKG May 2024 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). 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. The following subsections define the abstract instance parameters used to construct the three ARKG functions, followed by the definitions of the three ARKG functions. 2.1. Instance parameters ARKG is composed of a suite of other algorithms. The parameters of an ARKG instance are: * BL: An asymmetric key blinding scheme [Wilson], consisting of: - Function BL-Generate-Keypair() -> (pk, sk): Generate a blinding key pair. Lundberg & Bradley Expires 29 November 2024 [Page 5] Internet-Draft ARKG May 2024 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, 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. Lundberg & Bradley Expires 29 November 2024 [Page 6] Internet-Draft ARKG May 2024 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. 2.2. The function ARKG-Generate-Seed This function is performed by the delegating party. The delegating party generates the ARKG seed pair (pk, sk) and keeps the private seed sk secret, while the public seed pk is provided to the subordinate party. The subordinate party will then be able to generate public keys on behalf of the delegating party. Lundberg & Bradley Expires 29 November 2024 [Page 7] Internet-Draft ARKG May 2024 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) 2.2.1. Deterministic key generation 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. 2.3. The function ARKG-Derive-Public-Key This function is performed by the subordinate party, which holds the ARKG public seed pk = (pk_kem, pk_bl). The resulting public key pk' can be provided to external parties to use in asymmetric cryptography protocols, and the resulting key handle kh can be used by the delegating party to derive the private key corresponding to pk'. This function may be invoked any number of times with the same public seed, in order to generate any number of public keys. Lundberg & Bradley Expires 29 November 2024 [Page 8] Internet-Draft ARKG May 2024 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. 2.4. The function ARKG-Derive-Private-Key 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. Lundberg & Bradley Expires 29 November 2024 [Page 9] Internet-Draft ARKG May 2024 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. 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 [Frymann2020] [Wilson]. This section defines a general formula for such instantiations of BL. Lundberg & Bradley Expires 29 November 2024 [Page 10] Internet-Draft ARKG May 2024 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]. Lundberg & Bradley Expires 29 November 2024 [Page 11] Internet-Draft ARKG May 2024 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 3.2. Using HMAC to adapt a KEM without integrity protection 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 include integrity protection 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. Lundberg & Bradley Expires 29 November 2024 [Page 12] Internet-Draft ARKG May 2024 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 Lundberg & Bradley Expires 29 November 2024 [Page 13] Internet-Draft ARKG May 2024 t = HMAC-Hash-128(K=mk, text=info) 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=info) 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. 3.3. Using ECDH as the KEM 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: * crv: an elliptic curve valid for use with ECDH [RFC6090]. Lundberg & Bradley Expires 29 November 2024 [Page 14] Internet-Draft ARKG May 2024 * Hash: A cryptographic hash function. * 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: 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) Lundberg & Bradley Expires 29 November 2024 [Page 15] Internet-Draft ARKG May 2024 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: * 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. Lundberg & Bradley Expires 29 November 2024 [Page 16] Internet-Draft ARKG May 2024 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) 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 [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. 4. Concrete ARKG instantiations This section defines an initial set of concrete ARKG instantiations. TODO: IANA registry? COSE/JOSE? 4.1. ARKG-P256ADD-ECDH The identifier ARKG-P256ADD-ECDH 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-P256ADD-ECDH'. Lundberg & Bradley Expires 29 November 2024 [Page 17] Internet-Draft ARKG May 2024 * KEM: ECDH as described in Section 3.3 with the parameters: - crv: The NIST curve secp256r1 [SEC2]. - Hash: SHA-256 [FIPS 180-4]. - DST_ext: 'ARKG-P256ADD-ECDH'. 4.2. ARKG-P384ADD-ECDH The identifier ARKG-P384ADD-ECDH 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-P384ADD-ECDH'. * KEM: ECDH as described in Section 3.3 with the parameters: - crv: The NIST curve secp384r1 [SEC2]. - Hash: SHA-384 [FIPS 180-4]. - DST_ext: 'ARKG-P384ADD-ECDH'. 4.3. ARKG-P521ADD-ECDH The identifier ARKG-P521ADD-ECDH 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-P521ADD-ECDH'. * KEM: ECDH as described in Section 3.3 with the parameters: - crv: The NIST curve secp521r1 [SEC2]. Lundberg & Bradley Expires 29 November 2024 [Page 18] Internet-Draft ARKG May 2024 - Hash: SHA-512 [FIPS 180-4]. - DST_ext: 'ARKG-P521ADD-ECDH'. 4.4. ARKG-P256kADD-ECDH The identifier ARKG-P256kADD-ECDH 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]. - DST_ext: 'ARKG-P256kADD-ECDH'. * KEM: ECDH as described in Section 3.3 with the parameters: - crv: The SECG curve secp256k1 [SEC2]. - Hash: SHA-256 [FIPS 180-4]. - DST_ext: 'ARKG-P256kADD-ECDH'. 4.5. ARKG-curve25519ADD-X25519 The identifier ARKG-curve25519ADD-X25519 represents the following ARKG instance: * BL: Elliptic curve addition as described in Section 3.1 with the parameters: - crv: The curve curve25519 [RFC7748]. - 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. Lundberg & Bradley Expires 29 November 2024 [Page 19] Internet-Draft ARKG May 2024 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: - DH-Function: X25519 [RFC7748]. - DST_ext: 'ARKG-curve25519ADD-X25519'. 4.6. ARKG-curve448ADD-X448 The identifier ARKG-curve448ADD-X448 represents the following ARKG instance: * BL: Elliptic curve addition as described in Section 3.1 with the parameters: - crv: The curve curve448 [RFC7748]. - hash-to-crv-suite: curve448_XOF:SHAKE256_ELL2_RO_ [RFC9380]. - DST_ext: 'ARKG-curve448ADD-X448'. 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 Lundberg & Bradley Expires 29 November 2024 [Page 20] Internet-Draft ARKG May 2024 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: - DH-Function: X448 [RFC7748]. - DST_ext: 'ARKG-curve448ADD-X448'. 4.7. ARKG-edwards25519ADD-X25519 The identifier ARKG-edwards25519ADD-X25519 represents the following ARKG instance: * BL: Elliptic curve addition as described in Section 3.1 with the parameters: - crv: The curve edwards25519 [RFC7748]. - 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. Lundberg & Bradley Expires 29 November 2024 [Page 21] Internet-Draft ARKG May 2024 * KEM: X25519 as described in Section 3.4 with the parameters: - DH-Function: X25519 [RFC7748]. - DST_ext: 'ARKG-edwards25519ADD-X25519'. 4.8. ARKG-edwards448ADD-X448 The identifier ARKG-edwards448ADD-X448 represents the following ARKG instance: * BL: Elliptic curve addition as described in Section 3.1 with the parameters: - crv: The curve edwards448 [RFC7748]. - 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: - DH-Function: X448 [RFC7748]. - DST_ext: 'ARKG-edwards448ADD-X448'. Lundberg & Bradley Expires 29 November 2024 [Page 22] Internet-Draft ARKG May 2024 5. COSE bindings 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. 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). This key type defines key type parameters -1 and -2 for the BL and KEM public key, respectively. The following CDDL 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-seed ; kid: Opaque identifier 2: h'60b6dfddd31659598ae5de49acb220d8 704949e84d484b68344340e2565337d2', 3: -65539, ; alg: ESP256-ARKG -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: Lundberg & Bradley Expires 29 November 2024 [Page 23] Internet-Draft ARKG May 2024 h'a50139fbb402582060b6dfddd31659598ae5de49acb220d8704949e84d484b68 344340e2565337d2033a0001000220a40102200121582069380fc1c3b0965213 4feefba61776f97af875ce46ca20252c4165102966ebc52258208b515831462c cb0bd55cba04bfd50da63faf18bd845433622daf97c06a10d0f121a401022001 2158205c099bec31faa581d14e208250d3ffda9ec7f543043008bc84967a8d87 5b5d78225820539d57429fcb1c138da29010a155dca14566a8f55ac2f1780810 c49d4ed72d58' 5.2. COSE key reference types 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. 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: ARKG-derived ; kid: Opaque identifier of ARKG-pub-seed 2: h'60b6dfddd31659598ae5de49acb220d8 704949e84d484b68344340e2565337d2', 3: -65539, ; alg: ESP256-ARKG ; ARKG-P256ADD-ECDH key handle ; (truncated HMAC-SHA-256 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: Lundberg & Bradley Expires 29 November 2024 [Page 24] Internet-Draft ARKG May 2024 h'a40139fbb502582060b6dfddd31659598ae5de49acb220d8704949e84d484b68 344340e2565337d2033a00010002205851ae079e9c52212860678a7cee25b6a6 d4048219d973768f8e1adb8eb84b220b0ee3a2532828b9aa65254fe3717a2949 9e9baee70cea75b5c8a2ec2eb737834f7467e37b3254776f65f4cfc81e2bc474 7a84' 6. Security Considerations TODO 7. Privacy Considerations TODO 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-seed - Value: TBD (Placeholder -65537) - Description: ARKG public seed - Capabilities: [kty(-65537), pk_bl, pk_kem] - Reference: Section 5.1 of this document * Name: 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] Lundberg & Bradley Expires 29 November 2024 [Page 25] Internet-Draft ARKG May 2024 - 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 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-seed, 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-seed, placeholder -65537) - Name: pk_kem - Label: -2 - CBOR Type: COSE_Key - Description: ARKG key encapsulation public key - Reference: Section 5.1 of this document * Key Type: TBD (ARKG-derived, placeholder -65538) - Name: kh - Label: -1 - CBOR Type: bstr Lundberg & Bradley Expires 29 November 2024 [Page 26] Internet-Draft ARKG May 2024 - Description: kh argument to ARKG-Derive-Private-Key - Reference: Section 5.2 of this document * Key Type: TBD (ARKG-derived, placeholder -65538) - Name: info - Label: -2 - CBOR Type: bstr - Description: info argument to ARKG-Derive-Private-Key - Reference: Section 5.2 of this document 8.3. COSE Algorithms Registrations 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 Lundberg & Bradley Expires 29 November 2024 [Page 27] Internet-Draft ARKG May 2024 * 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 - Value: TBD (Placeholder -65542) - Description: ES256K with key derived by ARKG-P256kADD-ECDH - Capabilities: [kty] - Change Controller: TBD - Reference: [RFC8812], Section 4.4 of this document - Recommended: Yes * 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 Lundberg & Bradley Expires 29 November 2024 [Page 28] Internet-Draft ARKG May 2024 - Capabilities: [kty] - Change Controller: TBD - Reference: [fully-spec-algs], Section 4.8 of this document - Recommended: Yes TODO: Add the rest 9. Design rationale 9.1. Using a MAC The ARKG construction by Wilson [Wilson] omits the MAC and instead encodes application context in the PRF labels, arguing 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 Lundberg & Bradley Expires 29 November 2024 [Page 29] Internet-Draft ARKG May 2024 use of hash_to_field in Section 3.1 corresponds to the KDF_1 parameter in [Frymann2020], and the use of HMAC and HKDF in Section 3.2 corresponds to the MAC and KDF_2 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. 9.2. Implementation Status TODO 10. References 10.1. Normative References [fully-spec-algs] Jones, M. B., "Fully-Specified Algorithms for JOSE and COSE", 2024, . [IANA.cose] IANA, "CBOR Object Signing and Encryption (COSE)", . [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, . Lundberg & Bradley Expires 29 November 2024 [Page 30] Internet-Draft ARKG May 2024 [RFC7748] Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves for Security", RFC 7748, DOI 10.17487/RFC7748, January 2016, . [RFC8032] Josefsson, S. and I. Liusvaara, "Edwards-Curve Digital Signature Algorithm (EdDSA)", RFC 8032, DOI 10.17487/RFC8032, January 2017, . [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, . [SEC1] Certicom Research, "SEC 1: Elliptic Curve Cryptography", 2009, . [SEC2] Certicom Research, "SEC 2: Recommended Elliptic Curve Domain Parameters", 2010, . 10.2. Informative References [BIP32] Wuille, P., "BIP 32 Hierarchical Deterministic Wallets", 2012, . Lundberg & Bradley Expires 29 November 2024 [Page 31] Internet-Draft ARKG May 2024 [Clermont] Clermont, S. A. and Technische Universität Darmstadt, "Post Quantum Asynchronous Remote Key Generation. Master's thesis", 2022, . [Frymann2020] Frymann, N., Gardham, D., Kiefer, F., Lundberg, E., Manulis, M., and D. Nilsson, "Asynchronous Remote Key Generation: An Analysis of Yubico's Proposal for W3C WebAuthn. CCS '20: Proceedings of the 2020 ACM SIGSAC Conference on Computer and Communications Security", 2020, . [Frymann2023] Frymann, N., Gardham, D., and M. Manulis, "Asynchronous Remote Key Generation for Post-Quantum Cryptosystems from Lattices. 2023 IEEE 8th European Symposium on Security and Privacy", 2023, . [WebAuthn-Recovery] Lundberg, E. and D. Nilsson, "WebAuthn recovery extension: Asynchronous delegated key generation without shared secrets. GitHub", 2019, . [Wilson] Wilson, S. M. and University of Waterloo,, "Post-Quantum Account Recovery for Passwordless Authentication. Master's thesis", 2023, . Appendix A. Acknowledgements ARKG was first proposed under this name by Frymann et al. [Frymann2020], who analyzed a proposed extension to W3C Web Authentication by Lundberg and Nilsson [WebAuthn-Recovery], which was in turn inspired by a similar construction by Wuille [BIP32] used to create privacy-preserving Bitcoin addresses. Frymann et al. [Frymann2020] generalized the constructions by Lundberg, Nilsson and Wuille from elliptic curves to any discrete logarithm (DL) problem, and also proved the security of arbitrary asymmetric protocols composed with ARKG. Further generalizations to include quantum- resistant instantiations were developed independently by Clermont [Clermont], Frymann et al. [Frymann2023] and Wilson [Wilson]. This document adopts the construction proposed by Wilson [Wilson], modified by the inclusion of a MAC in the key handles as done in the original construction by Frymann et al. [Frymann2020]. Lundberg & Bradley Expires 29 November 2024 [Page 32] Internet-Draft ARKG May 2024 The authors would like to thank all of these authors for their research and development work that led to the creation of this document. Appendix B. Test Vectors TODO Appendix C. Document History * 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. Contributors Dain Nilsson Yubico Peter Altmann Agency for Digital Government Sweden Authors' Addresses Lundberg & Bradley Expires 29 November 2024 [Page 33] Internet-Draft ARKG May 2024 Emil Lundberg (editor) Yubico Kungsgatan 44 Stockholm Sweden Email: emil@emlun.se John Bradley Yubico Email: ve7jtb@ve7jtb.com Lundberg & Bradley Expires 29 November 2024 [Page 34]