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IRTF Crypto Forum KDF 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 Status information for this document may be found at . Source for this draft and an issue tracker can be found at .

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.
• Enhanced forward secrecy: The use of ARKG can facilitate forward secrecy in certain contexts. For instance, section 8.5.4 of RFC 9052 notes that "Since COSE is designed for a store-and-forward environment rather than an online environment, [...] forward secrecy (see ) 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.

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 when, and only when, they appear in all capitals, as shown here.

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 .
• Elliptic curve operations are written in additive notation: + denotes point addition, i.e., the curve group operation; * denotes point multiplication, i.e., repeated point addition; and + also denotes scalar addition modulo the curve order. * has higher precedence than +, i.e., a + b * C is equivalent to a + (b * C).

The 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.

Instance parameters ARKG is composed of a suite of other algorithms. The parameters of an ARKG instance are:

• BL: An asymmetric key blinding scheme , consisting of:
  • Function BL-Generate-Keypair() -> (pk, sk): Generate a blinding key pair. No input. Output consists of a blinding public key pk and a blinding private key sk.
  • Function BL-Blind-Public-Key(pk, tau, info) -> pk_tau: Deterministically compute a blinded public key. Input consists of a blinding public key pk, a blinding factor tau and a domain separation parameter info. Output consists of the blinded public key pk_tau.
  • Function BL-Blind-Private-Key(sk, tau, info) -> sk_tau: Deterministically compute a blinded private key. Input consists of a blinding private key sk, a blinding factor tau and a domain separation parameter info. Output consists of the blinded private key sk_tau.
  tau and info are an opaque octet strings of arbitrary length. The representations of pk and pk_tau are defined by the protocol that invokes ARKG. The representations of sk and sk_tau are an undefined implementation detail. See 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. 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. describes a general formula for how any KEM can be adapted to include this guarantee. discusses the reasons for this requirement. See 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.

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. (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) ]]>

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.

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. (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.

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. 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 .

Generic ARKG instantiations This section defines generic formulae for instantiating the individual ARKG parameters, which can be used to define concrete ARKG instantiations.

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  . 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 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 .

(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 ]]>

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 , 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 and HKDF 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 , 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. (pk, sk) (pk, sk) = Sub-Kem-Generate-Keypair() KEM-Encaps(pk, info) -> (k, c) info_sub = 'ARKG-KEM-HMAC.' || DST_ext || info (k', c') = Sub-Kem-Encaps(pk, info_sub) prk = HKDF-Extract with the arguments: Hash: Hash salt: not set IKM: k' mk = HKDF-Expand with the arguments: Hash: Hash PRK: prk info: 'ARKG-KEM-HMAC-mac.' || DST_ext || info L: L t = HMAC-Hash-128(K=mk, text=c') k = HKDF-Expand with the arguments: Hash: Hash PRK: prk info: 'ARKG-KEM-HMAC-shared.' || DST_ext || info L: The length of k' in octets. c = t || c' KEM-Decaps(sk, c, info) -> k t = LEFT(c, 16) c' = DROP_LEFT(c, 16) info_sub = 'ARKG-KEM-HMAC.' || DST_ext || info k' = Sub-Kem-Decaps(sk, c', info_sub) prk = HKDF-Extract with the arguments: Hash: Hash salt: not set IKM: k' mk = HKDF-Expand with the arguments: Hash: Hash PRK: prk info: 'ARKG-KEM-HMAC-mac.' || DST_ext || info L: L t' = HMAC-Hash-128(K=mk, text=c') If t = t': k = HKDF-Expand with the arguments: Hash: Hash PRK: prk info: 'ARKG-KEM-HMAC-shared.' || DST_ext || info L: The length of k' in octets. Else: Abort with an error. ]]>

Using ECDH as the KEM Instantiations of ARKG can use ECDH as the key encapsulation mechanism KEM  . 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 .
• Hash: A cryptographic hash function.
• DST_ext: A domain separation parameter.

The KEM parameter of ARKG may be instantiated as described in section 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 , without point compression.
  • ECDH(pk, sk) represents the compact output of ECDH 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.
  (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) ]]>

Using X25519 or X448 as the KEM Instantiations of ARKG can use X25519 or X448 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 .
• DST_ext: A domain separation parameter.

The KEM parameter of ARKG may be instantiated as described in section 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.
  (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) ]]>

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 and ECDH is used as the KEM as described in - 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.

Concrete ARKG instantiations This section defines an initial set of concrete ARKG instantiations. TODO: IANA registry? COSE/JOSE?

ARKG-P256ADD-ECDH The identifier ARKG-P256ADD-ECDH represents the following ARKG instance:

• BL: Elliptic curve addition as described in with the parameters:
  • crv: The NIST curve secp256r1 .
  • hash-to-crv-suite: P256_XMD:SHA-256_SSWU_RO_ .
  • DST_ext: 'ARKG-P256ADD-ECDH'.
• KEM: ECDH as described in with the parameters:
  • crv: The NIST curve secp256r1 .
  • Hash: SHA-256 [FIPS 180-4].
  • DST_ext: 'ARKG-P256ADD-ECDH'.

ARKG-P384ADD-ECDH The identifier ARKG-P384ADD-ECDH represents the following ARKG instance:

• BL: Elliptic curve addition as described in with the parameters:
  • crv: The NIST curve secp384r1 .
  • hash-to-crv-suite: P384_XMD:SHA-384_SSWU_RO_ .
  • DST_ext: 'ARKG-P384ADD-ECDH'.
• KEM: ECDH as described in with the parameters:
  • crv: The NIST curve secp384r1 .
  • Hash: SHA-384 [FIPS 180-4].
  • DST_ext: 'ARKG-P384ADD-ECDH'.

ARKG-P521ADD-ECDH The identifier ARKG-P521ADD-ECDH represents the following ARKG instance:

• BL: Elliptic curve addition as described in with the parameters:
  • crv: The NIST curve secp521r1 .
  • hash-to-crv-suite: P521_XMD:SHA-512_SSWU_RO_ .
  • DST_ext: 'ARKG-P521ADD-ECDH'.
• KEM: ECDH as described in with the parameters:
  • crv: The NIST curve secp521r1 .
  • Hash: SHA-512 [FIPS 180-4].
  • DST_ext: 'ARKG-P521ADD-ECDH'.

ARKG-P256kADD-ECDH The identifier ARKG-P256kADD-ECDH represents the following ARKG instance:

• BL: Elliptic curve addition as described in with the parameters:
  • crv: The SECG curve secp256k1 .
  • hash-to-crv-suite: secp256k1_XMD:SHA-256_SSWU_RO_ .
  • DST_ext: 'ARKG-P256kADD-ECDH'.
• KEM: ECDH as described in with the parameters:
  • crv: The SECG curve secp256k1 .
  • Hash: SHA-256 [FIPS 180-4].
  • DST_ext: 'ARKG-P256kADD-ECDH'.

ARKG-curve25519ADD-X25519 The identifier ARKG-curve25519ADD-X25519 represents the following ARKG instance:

• BL: Elliptic curve addition as described in with the parameters:
  • crv: The curve curve25519 .
  • hash-to-crv-suite: curve25519_XMD:SHA-512_ELL2_RO_ .
  • DST_ext: 'ARKG-curve25519ADD-X25519'.
  WARNING: Some algorithms on curve25519, including X25519 , construct private key scalars within a particular range to enable optimizations and constant-time guarantees. This BL scheme does not guarantee that blinded private scalars remain in that range, so implementations using this ARKG instance MUST NOT rely on such a guarantee. Note: Input and output keys of this BL scheme are curve scalars and curve points. Some algorithms on curve25519, including X25519 , 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 with the parameters:
  • DH-Function: X25519 .
  • DST_ext: 'ARKG-curve25519ADD-X25519'.

ARKG-curve448ADD-X448 The identifier ARKG-curve448ADD-X448 represents the following ARKG instance:

• BL: Elliptic curve addition as described in with the parameters:
  • crv: The curve curve448 .
  • hash-to-crv-suite: curve448_XOF:SHAKE256_ELL2_RO_ .
  • DST_ext: 'ARKG-curve448ADD-X448'.
  WARNING: Some algorithms on curve25519, including X448 , 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 , 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 with the parameters:
  • DH-Function: X448 .
  • DST_ext: 'ARKG-curve448ADD-X448'.

ARKG-edwards25519ADD-X25519 The identifier ARKG-edwards25519ADD-X25519 represents the following ARKG instance:

• BL: Elliptic curve addition as described in with the parameters:
  • crv: The curve edwards25519 .
  • hash-to-crv-suite: edwards25519_XMD:SHA-512_ELL2_RO_ .
  • DST_ext: 'ARKG-edwards25519ADD-X25519'.
  WARNING: Some algorithms on edwards25519, including EdDSA , 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 , 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 with the parameters:
  • DH-Function: X25519 .
  • DST_ext: 'ARKG-edwards25519ADD-X25519'.

ARKG-edwards448ADD-X448 The identifier ARKG-edwards448ADD-X448 represents the following ARKG instance:

• BL: Elliptic curve addition as described in with the parameters:
  • crv: The curve edwards448 .
  • hash-to-crv-suite: edwards448_XOF:SHAKE256_ELL2_RO_ .
  • DST_ext: 'ARKG-edwards448ADD-X448'.
  WARNING: Some algorithms on edwards25519, including EdDSA , 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 , 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 with the parameters:
  • DH-Function: X448 .
  • DST_ext: 'ARKG-edwards448ADD-X448'.

COSE bindings This section proposes additions to COSE 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.

COSE key type: ARKG public seed An ARKG public seed is represented as a COSE_Key structure with kty value TBD (placeholder value -65537). This key type defines key type parameters -1 and -2 for the BL and KEM public key, respectively. The alg parameter, when present, defines the alg parameter of ARKG derived public keys derived from this ARKG public seed. The following CDDL example represents an ARKG-P256ADD-ECDH public seed restricted to generating derived public keys for use with the ESP256 signature algorithm: The following is the same example encoded as CBOR:

COSE key reference types TODO: This should eventually move to a separate "algoritm IDs for two-party signing" spec, see: While keys used by many other algorithms can usually be referenced by a single atomic identifier, such as that used in the kid parameter in a COSE_Key object or in the unprotected header of a COSE_Recipient, users of the function ARKG-Derive-Secret-Key need to represent a reference to an ARKG private seed along with a key handle for a derived private key. A COSE key reference is a COSE_Key object whose kty value is defined to represent a reference to a key. The kid parameter MUST be present when kty is a key reference type. These requirements are encoded in the CDDL type COSE_Key_Ref: $COSE_kty_ref ; kty: Any reference type 2 ^ => any, ; kid is required any => any, ; Any other entries allowed by COSE_Key } ]]> The following CDDL example represents a reference to a key derived by ARKG-P256ADD-ECDH and restricted for use with the ESP256 signature algorithm: The following is the same example encoded as CBOR:

Security Considerations TODO

Privacy Considerations TODO

IANA Considerations

COSE Key Types Registrations This section registers the following values in the IANA "COSE Key Types" registry .

• Name: ARKG-pub
  • Value: TBD (Placeholder -65537)
  • Description: ARKG public seed
  • Capabilities: [kty(-65537), pk_bl, pk_kem]
  • Reference: of this document
• Name: Ref-ARKG-derived
  • Value: TBD (Placeholder -65538)
  • Description: Reference to private key derived by ARKG
  • Capabilities: [kty(-65538), kh]
  • Reference: of this document
• Name: Ref-OKP
  • Value: TBD (Requested assignment -1)
  • Description: Reference to a key pair of key type "OKP"
  • Capabilities: [kty(-1), crv]
  • Reference: 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: of this document

These registrations add the following choices to the CDDL type socket $COSE_kty_ref:

COSE Key Type Parameters Registrations TODO: These should eventually move to a separate "algoritm IDs for two-party signing" spec, see: This section registers the following values in the IANA "COSE Key Type Parameters" registry .

• Key Type: TBD (ARKG-pub, placeholder -65537)
  • Name: pk_bl
  • Label: -1
  • CBOR Type: COSE_Key
  • Description: ARKG key blinding public key
  • Reference: 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: of this document
• Key Type: TBD (Ref-ARKG-derived, placeholder -65538)
  • Name: kh
  • Label: -1
  • CBOR Type: bstr
  • Description: kh argument to ARKG-Derive-Private-Key
  • Reference: of this document
• Key Type: TBD (Ref-ARKG-derived, placeholder -65538)
  • Name: info
  • Label: -2
  • CBOR Type: bstr
  • Description: info argument to ARKG-Derive-Private-Key
  • Reference: of this document

COSE Algorithms Registrations TODO: These should eventually move to a separate "algoritm IDs for two-party signing" spec, see: This section registers the following values in the IANA "COSE Algorithms" registry .

• Name: ESP256-ARKG
  • Value: TBD (Placeholder -65539)
  • Description: ESP256 with key derived by ARKG-P256ADD-ECDH
  • Capabilities: [kty]
  • Change Controller: TBD
  • Reference: , 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: , of this document
  • Recommended: Yes
• Name: ESP512-ARKG
  • Value: TBD (Placeholder -65541)
  • Description: ESP512 with key derived by ARKG-P521ADD-ECDH
  • Capabilities: [kty]
  • Change Controller: TBD
  • Reference: , 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: , 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: , of this document
  • Recommended: Yes
• Name: Ed448-ARKG
  • Value: TBD (Placeholder -65544)
  • Description: Ed448 with key derived by ARKG-edwards448ADD-X448
  • Capabilities: [kty]
  • Change Controller: TBD
  • Reference: , of this document
  • Recommended: Yes

Design rationale

Using a MAC The ARKG construction by 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. , 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. : the construction by Frymann et al. can be reduced to the ARKG construction in this document by instantiating BL as described in and KEM as described in . The use of hash_to_field in corresponds to the KDF₁ parameter in , and the use of HMAC and HKDF in corresponds to the MAC and KDF₂ parameters in . 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.

Implementation Status TODO

References Normative References Self-Issued Consulting IANA This document describes HMAC, a mechanism for message authentication using cryptographic hash functions. HMAC can be used with any iterative cryptographic hash function, e.g., MD5, SHA-1, in combination with a secret shared key. The cryptographic strength of HMAC depends on the properties of the underlying hash function. This memo provides information for the Internet community. This memo does not specify an Internet standard of any kind This Glossary provides definitions, abbreviations, and explanations of terminology for information system security. The 334 pages of entries offer recommendations to improve the comprehensibility of written material that is generated in the Internet Standards Process (RFC 2026). The recommendations follow the principles that such writing should (a) use the same term or definition whenever the same concept is mentioned; (b) use terms in their plainest, dictionary sense; (c) use terms that are already well-established in open publications; and (d) avoid terms that either favor a particular vendor or favor a particular technology or mechanism over other, competing techniques that already exist or could be developed. This memo provides information for the Internet community. This document specifies a simple Hashed Message Authentication Code (HMAC)-based key derivation function (HKDF), which can be used as a building block in various protocols and applications. The key derivation function (KDF) is intended to support a wide range of applications and requirements, and is conservative in its use of cryptographic hash functions. This document is not an Internet Standards Track specification; it is published for informational purposes. This note describes the fundamental algorithms of Elliptic Curve Cryptography (ECC) as they were defined in some seminal references from 1994 and earlier. These descriptions may be useful for implementing the fundamental algorithms without using any of the specialized methods that were developed in following years. Only elliptic curves defined over fields of characteristic greater than three are in scope; these curves are those used in Suite B. This document is not an Internet Standards Track specification; it is published for informational purposes. This memo specifies two elliptic curves over prime fields that offer a high level of practical security in cryptographic applications, including Transport Layer Security (TLS). These curves are intended to operate at the ~128-bit and ~224-bit security level, respectively, and are generated deterministically based on a list of required properties. This document describes elliptic curve signature scheme Edwards-curve Digital Signature Algorithm (EdDSA). The algorithm is instantiated with recommended parameters for the edwards25519 and edwards448 curves. An example implementation and test vectors are provided. This document proposes a notational convention to express Concise Binary Object Representation (CBOR) data structures (RFC 7049). Its main goal is to provide an easy and unambiguous way to express structures for protocol messages and data formats that use CBOR or JSON. The W3C Web Authentication (WebAuthn) specification and the FIDO Alliance FIDO2 Client to Authenticator Protocol (CTAP) specification use CBOR Object Signing and Encryption (COSE) algorithm identifiers. This specification registers the following algorithms (which are used by WebAuthn and CTAP implementations) in the IANA "COSE Algorithms" registry: RSASSA-PKCS1-v1_5 using SHA-256, SHA-384, SHA-512, and SHA-1; and Elliptic Curve Digital Signature Algorithm (ECDSA) using the secp256k1 curve and SHA-256. It registers the secp256k1 elliptic curve in the IANA "COSE Elliptic Curves" registry. Also, for use with JSON Object Signing and Encryption (JOSE), it registers the algorithm ECDSA using the secp256k1 curve and SHA-256 in the IANA "JSON Web Signature and Encryption Algorithms" registry and the secp256k1 elliptic curve in the IANA "JSON Web Key Elliptic Curve" registry. Concise Binary Object Representation (CBOR) is a data format designed for small code size and small message size. There is a need to be able to define basic security services for this data format. This document defines the CBOR Object Signing and Encryption (COSE) protocol. This specification describes how to create and process signatures, message authentication codes, and encryption using CBOR for serialization. This specification additionally describes how to represent cryptographic keys using CBOR. This document, along with RFC 9053, obsoletes RFC 8152. This document specifies a number of algorithms for encoding or hashing an arbitrary string to a point on an elliptic curve. This document is a product of the Crypto Forum Research Group (CFRG) in the IRTF. Certicom Research Certicom Research In many standards track documents several words are used to signify the requirements in the specification. These words are often capitalized. This document defines these words as they should be interpreted in IETF documents. This document specifies an Internet Best Current Practices for the Internet Community, and requests discussion and suggestions for improvements. RFC 2119 specifies common key words that may be used in protocol specifications. This document aims to reduce the ambiguity by clarifying that only UPPERCASE usage of the key words have the defined special meanings. Informative References Technische Universität Darmstadt IBM Zurich Research Lab University of Waterloo,

Acknowledgements ARKG was first proposed under this name by Frymann et al. , who analyzed a proposed extension to W3C Web Authentication by Lundberg and Nilsson , which was in turn inspired by a similar construction by Wuille used to create privacy-preserving Bitcoin addresses. Frymann et al. 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 , Frymann et al. and Wilson . This document adopts the construction proposed by Wilson , modified by the inclusion of a MAC in the key handles as done in the original construction by Frymann et al. . The authors would like to thank all of these authors for their research and development work that led to the creation of this document.

Test Vectors TODO

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.
• 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.

Contributors Yubico

Agency for Digital Government

SE