# 10.9. Key agreement

## 10.9.1. Key agreement algorithms

### `PSA_ALG_KEY_AGREEMENT` (macro)

Macro to build a combined algorithm that chains a key agreement with a key derivation.

```#define PSA_ALG_KEY_AGREEMENT(ka_alg, kdf_alg) \
/* specification-defined value */```

Parameters

`ka_alg`

A key agreement algorithm (`PSA_ALG_XXX` value such that `PSA_ALG_IS_KEY_AGREEMENT``(``ka_alg``)` is true).

`kdf_alg`

A key derivation algorithm (`PSA_ALG_XXX` value such that `PSA_ALG_IS_KEY_DERIVATION``(``kdf_alg``)` is true).

Returns

The corresponding key agreement and derivation algorithm.

Unspecified if `ka_alg` is not a supported key agreement algorithm or `kdf_alg` is not a supported key derivation algorithm.

Description

A combined key agreement algorithm is used with a multi-part key derivation operation, using a call to `psa_key_derivation_key_agreement()`.

The component parts of a key agreement algorithm can be extracted using `PSA_ALG_KEY_AGREEMENT_GET_BASE()` and `PSA_ALG_KEY_AGREEMENT_GET_KDF()`.

### `PSA_ALG_FFDH` (macro)

The finite-field Diffie-Hellman (DH) key agreement algorithm.

`#define PSA_ALG_FFDH ((psa_algorithm_t)0x09010000)`

This algorithm can be used directly in a call to `psa_raw_key_agreement()`, or combined with a key derivation operation using `PSA_ALG_KEY_AGREEMENT()` for use with `psa_key_derivation_key_agreement()`.

When used as part of a multi-part key derivation operation, this implements a Diffie-Hellman key agreement scheme using a single Diffie-Hellman key-pair for each participant. This includes the dhEphem, dhOneFlow, and dhStatic schemes. The input step `PSA_KEY_DERIVATION_INPUT_SECRET` is used when providing the secret and peer keys to the operation.

The shared secret produced by this key agreement algorithm is `g^{ab}` in big-endian format. It is `ceiling(m / 8)` bytes long where `m` is the size of the prime `p` in bits.

This key agreement scheme is defined by NIST Special Publication 800-56A: Recommendation for Pair-Wise Key-Establishment Schemes Using Discrete Logarithm Cryptography [SP800-56A] §5.7.1.1 under the name FFC DH.

### `PSA_ALG_ECDH` (macro)

The elliptic curve Diffie-Hellman (ECDH) key agreement algorithm.

`#define PSA_ALG_ECDH ((psa_algorithm_t)0x09020000)`

This algorithm can be used directly in a call to `psa_raw_key_agreement()`, or combined with a key derivation operation using `PSA_ALG_KEY_AGREEMENT()` for use with `psa_key_derivation_key_agreement()`.

When used as part of a multi-part key derivation operation, this implements a Diffie-Hellman key agreement scheme using a single elliptic curve key-pair for each participant. This includes the Ephemeral unified model, the Static unified model, and the One-pass Diffie-Hellman schemes. The input step `PSA_KEY_DERIVATION_INPUT_SECRET` is used when providing the secret and peer keys to the operation.

The shared secret produced by key agreement is the x-coordinate of the shared secret point. It is always `ceiling(m / 8)` bytes long where `m` is the bit size associated with the curve, i.e. the bit size of the order of the curve’s coordinate field. When `m` is not a multiple of 8, the byte containing the most significant bit of the shared secret is padded with zero bits. The byte order is either little-endian or big-endian depending on the curve type.

• For Montgomery curves (curve family `PSA_ECC_FAMILY_MONTGOMERY`), the shared secret is the x-coordinate of `Z = d_A Q_B = d_B Q_A` in little-endian byte order.

• For Curve25519, this is the X25519 function defined in Curve25519: new Diffie-Hellman speed records [Curve25519]. The bit size `m` is 255.

• For Curve448, this is the X448 function defined in Ed448-Goldilocks, a new elliptic curve [Curve448]. The bit size `m` is 448.

• For Weierstrass curves (curve families `PSA_ECC_FAMILY_SECP_XX`, `PSA_ECC_FAMILY_SECT_XX`, `PSA_ECC_FAMILY_BRAINPOOL_P_R1` and `PSA_ECC_FAMILY_FRP`) the shared secret is the x-coordinate of `Z = h d_A Q_B = h d_B Q_A` in big-endian byte order. This is the Elliptic Curve Cryptography Cofactor Diffie-Hellman primitive defined by SEC 1: Elliptic Curve Cryptography [SEC1] §3.3.2 as, and also as ECC CDH by NIST Special Publication 800-56A: Recommendation for Pair-Wise Key-Establishment Schemes Using Discrete Logarithm Cryptography [SP800-56A] §5.7.1.2.

• Over prime fields (curve families `PSA_ECC_FAMILY_SECP_XX`, `PSA_ECC_FAMILY_BRAINPOOL_P_R1` and `PSA_ECC_FAMILY_FRP`), the bit size is `m = ceiling(log_2(p))` for the field `F_p`.

• Over binary fields (curve families `PSA_ECC_FAMILY_SECT_XX`), the bit size is `m` for the field `F_{2^m}`.

Note

The cofactor Diffie-Hellman primitive is equivalent to the standard elliptic curve Diffie-Hellman calculation `Z = d_A Q_B = d_B Q_A` ([SEC1] §3.3.1) for curves where the cofactor `h` is `1`. This is true for all curves in the `PSA_ECC_FAMILY_SECP_XX`, `PSA_ECC_FAMILY_BRAINPOOL_P_R1`, and `PSA_ECC_FAMILY_FRP` families.

## 10.9.2. Standalone key agreement

### `psa_raw_key_agreement` (function)

Perform a key agreement and return the raw shared secret.

```psa_status_t psa_raw_key_agreement(psa_algorithm_t alg,
psa_key_id_t private_key,
const uint8_t * peer_key,
size_t peer_key_length,
uint8_t * output,
size_t output_size,
size_t * output_length);```

Parameters

`alg`

The key agreement algorithm to compute (`PSA_ALG_XXX` value such that `PSA_ALG_IS_RAW_KEY_AGREEMENT``(``alg``)` is true).

`private_key`

Identifier of the private key to use. It must allow the usage `PSA_KEY_USAGE_DERIVE`.

`peer_key`

Public key of the peer. It must be in the same format that `psa_import_key()` accepts. The standard formats for public keys are documented in the documentation of `psa_export_public_key()`.

`peer_key_length`

Size of `peer_key` in bytes.

`output`

Buffer where the raw shared secret is to be written.

`output_size`

Size of the `output` buffer in bytes. This must be appropriate for the keys:

`output_length`

On success, the number of bytes that make up the returned output.

Returns: `psa_status_t`

`PSA_SUCCESS`

Success.

`PSA_ERROR_INVALID_HANDLE`
`PSA_ERROR_NOT_PERMITTED`

The key does not have the `PSA_KEY_USAGE_DERIVE` flag, or it does not permit the requested algorithm.

`PSA_ERROR_INVALID_ARGUMENT`

`alg` is not a key agreement algorithm

`PSA_ERROR_INVALID_ARGUMENT`

`private_key` is not compatible with `alg`, or `peer_key` is not valid for `alg` or not compatible with `private_key`.

`PSA_ERROR_BUFFER_TOO_SMALL`

The size of the `output` buffer is too small. `PSA_RAW_KEY_AGREEMENT_OUTPUT_SIZE()` or `PSA_RAW_KEY_AGREEMENT_OUTPUT_MAX_SIZE` can be used to determine the required buffer size.

`PSA_ERROR_NOT_SUPPORTED`

`alg` is not a supported key agreement algorithm.

`PSA_ERROR_INSUFFICIENT_MEMORY`
`PSA_ERROR_COMMUNICATION_FAILURE`
`PSA_ERROR_HARDWARE_FAILURE`
`PSA_ERROR_CORRUPTION_DETECTED`
`PSA_ERROR_STORAGE_FAILURE`
`PSA_ERROR_DATA_CORRUPT`
`PSA_ERROR_DATA_INVALID`
`PSA_ERROR_BAD_STATE`

The library has not been previously initialized by `psa_crypto_init()`. It is implementation-dependent whether a failure to initialize results in this error code.

Description

Warning

The raw result of a key agreement algorithm such as finite-field Diffie-Hellman or elliptic curve Diffie-Hellman has biases, and is not suitable for use as key material. Instead it is recommended that the result is used as input to a key derivation algorithm. To chain a key agreement with a key derivation, use `psa_key_derivation_key_agreement()` and other functions from the key derivation interface.

## 10.9.3. Combining key agreement and key derivation

### `psa_key_derivation_key_agreement` (function)

Perform a key agreement and use the shared secret as input to a key derivation.

```psa_status_t psa_key_derivation_key_agreement(psa_key_derivation_operation_t * operation,
psa_key_derivation_step_t step,
psa_key_id_t private_key,
const uint8_t * peer_key,
size_t peer_key_length);```

Parameters

`operation`

The key derivation operation object to use. It must have been set up with `psa_key_derivation_setup()` with a key agreement and derivation algorithm `alg` (`PSA_ALG_XXX` value such that `PSA_ALG_IS_KEY_AGREEMENT``(``alg``)` is true and `PSA_ALG_IS_RAW_KEY_AGREEMENT``(``alg``)` is false). The operation must be ready for an input of the type given by `step`.

`step`

Which step the input data is for.

`private_key`

Identifier of the private key to use. It must allow the usage `PSA_KEY_USAGE_DERIVE`.

`peer_key`

Public key of the peer. The peer key must be in the same format that `psa_import_key()` accepts for the public key type corresponding to the type of private_key. That is, this function performs the equivalent of `psa_import_key``(..., ``peer_key``, ``peer_key_length``)` where with key attributes indicating the public key type corresponding to the type of `private_key`. For example, for EC keys, this means that peer_key is interpreted as a point on the curve that the private key is on. The standard formats for public keys are documented in the documentation of `psa_export_public_key()`.

`peer_key_length`

Size of `peer_key` in bytes.

Returns: `psa_status_t`

`PSA_SUCCESS`

Success.

`PSA_ERROR_BAD_STATE`

The operation state is not valid for this key agreement `step`.

`PSA_ERROR_INVALID_HANDLE`
`PSA_ERROR_NOT_PERMITTED`

The key does not have the `PSA_KEY_USAGE_DERIVE` flag, or it does not permit the requested algorithm.

`PSA_ERROR_INVALID_ARGUMENT`

`private_key` is not compatible with `alg`, or `peer_key` is not valid for `alg` or not compatible with `private_key`.

`PSA_ERROR_NOT_SUPPORTED`

`alg` is not supported or is not a key derivation algorithm.

`PSA_ERROR_INVALID_ARGUMENT`

`step` does not allow an input resulting from a key agreement.

`PSA_ERROR_INSUFFICIENT_MEMORY`
`PSA_ERROR_COMMUNICATION_FAILURE`
`PSA_ERROR_HARDWARE_FAILURE`
`PSA_ERROR_CORRUPTION_DETECTED`
`PSA_ERROR_STORAGE_FAILURE`
`PSA_ERROR_DATA_CORRUPT`
`PSA_ERROR_DATA_INVALID`
`PSA_ERROR_BAD_STATE`

The library has not been previously initialized by `psa_crypto_init()`. It is implementation-dependent whether a failure to initialize results in this error code.

Description

A key agreement algorithm takes two inputs: a private key `private_key` a public key `peer_key`. The result of this function is passed as input to a key derivation. The output of this key derivation can be extracted by reading from the resulting operation to produce keys and other cryptographic material.

If this function returns an error status, the operation enters an error state and must be aborted by calling `psa_key_derivation_abort()`.

## 10.9.4. Support macros

### `PSA_ALG_KEY_AGREEMENT_GET_BASE` (macro)

Get the raw key agreement algorithm from a full key agreement algorithm.

`#define PSA_ALG_KEY_AGREEMENT_GET_BASE(alg) /* specification-defined value */`

Parameters

`alg`

A key agreement algorithm identifier (value of type `psa_algorithm_t` such that `PSA_ALG_IS_KEY_AGREEMENT``(``alg``)` is true).

Returns

The underlying raw key agreement algorithm if `alg` is a key agreement algorithm.

Unspecified if `alg` is not a key agreement algorithm or if it is not supported by the implementation.

Description

### `PSA_ALG_KEY_AGREEMENT_GET_KDF` (macro)

Get the key derivation algorithm used in a full key agreement algorithm.

`#define PSA_ALG_KEY_AGREEMENT_GET_KDF(alg) /* specification-defined value */`

Parameters

`alg`

A key agreement algorithm identifier (value of type `psa_algorithm_t` such that `PSA_ALG_IS_KEY_AGREEMENT``(``alg``)` is true).

Returns

The underlying key derivation algorithm if `alg` is a key agreement algorithm.

Unspecified if `alg` is not a key agreement algorithm or if it is not supported by the implementation.

Description

### `PSA_ALG_IS_RAW_KEY_AGREEMENT` (macro)

Whether the specified algorithm is a raw key agreement algorithm.

`#define PSA_ALG_IS_RAW_KEY_AGREEMENT(alg) /* specification-defined value */`

Parameters

`alg`

An algorithm identifier (value of type `psa_algorithm_t`).

Returns

`1` if `alg` is a raw key agreement algorithm, `0` otherwise. This macro can return either `0` or `1` if `alg` is not a supported algorithm identifier.

Description

A raw key agreement algorithm is one that does not specify a key derivation function. Usually, raw key agreement algorithms are constructed directly with a `PSA_ALG_xxx` macro while non-raw key agreement algorithms are constructed with `PSA_ALG_KEY_AGREEMENT()`.

The raw key agreement algorithm can be extracted from a full key agreement algorithm identifier using `PSA_ALG_KEY_AGREEMENT_GET_BASE()`.

### `PSA_ALG_IS_FFDH` (macro)

Whether the specified algorithm is a finite field Diffie-Hellman algorithm.

`#define PSA_ALG_IS_FFDH(alg) /* specification-defined value */`

Parameters

`alg`

An algorithm identifier (value of type `psa_algorithm_t`).

Returns

`1` if `alg` is a finite field Diffie-Hellman algorithm, `0` otherwise. This macro can return either `0` or `1` if `alg` is not a supported key agreement algorithm identifier.

Description

This includes the raw finite field Diffie-Hellman algorithm as well as finite-field Diffie-Hellman followed by any supporter key derivation algorithm.

### `PSA_ALG_IS_ECDH` (macro)

Whether the specified algorithm is an elliptic curve Diffie-Hellman algorithm.

`#define PSA_ALG_IS_ECDH(alg) /* specification-defined value */`

Parameters

`alg`

An algorithm identifier (value of type `psa_algorithm_t`).

Returns

`1` if `alg` is an elliptic curve Diffie-Hellman algorithm, `0` otherwise. This macro can return either `0` or `1` if `alg` is not a supported key agreement algorithm identifier.

Description

This includes the raw elliptic curve Diffie-Hellman algorithm as well as elliptic curve Diffie-Hellman followed by any supporter key derivation algorithm.

### `PSA_RAW_KEY_AGREEMENT_OUTPUT_SIZE` (macro)

Sufficient output buffer size for `psa_raw_key_agreement()`.

```#define PSA_RAW_KEY_AGREEMENT_OUTPUT_SIZE(key_type, key_bits) \
/* implementation-defined value */```

Parameters

`key_type`

A supported key type.

`key_bits`

The size of the key in bits.

Returns

If the parameters are valid and supported, return a buffer size in bytes that guarantees that `psa_raw_key_agreement()` will not fail with `PSA_ERROR_BUFFER_TOO_SMALL`. If the parameters are a valid combination that is not supported by the implementation, this macro must return either a sensible size or `0`. If the parameters are not valid, the return value is unspecified.

Description

This macro returns a compile-time constant if its arguments are compile-time constants.

Warning

This function might evaluate its arguments multiple times or zero times. Providing arguments that have side effects will result in implementation-specific behavior, and is non-portable.

### `PSA_RAW_KEY_AGREEMENT_OUTPUT_MAX_SIZE` (macro)

Maximum size of the output from `psa_raw_key_agreement()`.

```#define PSA_RAW_KEY_AGREEMENT_OUTPUT_MAX_SIZE \
/* implementation-defined value */```

This macro must expand to a compile-time constant integer. It is recommended that this value is the maximum size of the output any raw key agreement algorithm supported by the implementation, in bytes. The value must not be smaller than this maximum.