@noble/curves
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Audited & minimal JS implementation of elliptic curve cryptography
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text/typescript
/**
* Friendly wrapper over elliptic curves from built-in WebCrypto. Experimental: API may change.
# WebCrypto issues
## No way to get public keys
- Export of raw secret key is prohibited by spec:
- https://w3c.github.io/webcrypto/#ecdsa-operations-export-key
-> "If format is "raw":" -> "If the [[type]] internal slot of key is not "public",
then throw an InvalidAccessError."
- Import of raw secret keys is prohibited by spec:
- https://w3c.github.io/webcrypto/#ecdsa-operations-import-key
-> "If format is "raw":" -> "If usages contains a value which is not "verify"
then throw a SyntaxError."
- SPKI (Simple public-key infrastructure) is public-key-only
- PKCS8 is secret-key-only
- No way to get public key from secret key, but we convert to JWK and then
create it manually, since a JWK secret key includes both private and public
parts.
- Noble supports generating keys for both sign, verify & getSharedSecret,
but JWK key includes usage, which forces us to patch it (non-JWK is ok)
- We have import/export for 'raw', but it doesn't work in Firefox / Safari
## Point encoding
- Raw export of public points returns uncompressed points,
but this is implementation specific and not much we can do there.
- `getSharedSecret` differs for p256, p384, p521:
Noble returns 33-byte output (y-parity + x coordinate),
while in WebCrypto returns 32-byte output (x coordinate).
This is intentional: noble keeps the full encoded shared point, and x-only
callers can slice it down themselves.
- `getSharedSecret` identical for X25519, X448
## Availability
Node.js additionally supports ed448.
There seems no reasonable way to check for availability, other than actually calling methods.
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import type { TArg, TRet } from './utils.ts';
/** Raw type */
const TYPE_RAW = 'raw';
const TYPE_JWK = 'jwk';
const TYPE_SPKI = 'spki';
const TYPE_PKCS = 'pkcs8';
/** Key serialization formats supported by the WebCrypto wrappers. */
export type WebCryptoFormat =
| typeof TYPE_RAW
| typeof TYPE_JWK
| typeof TYPE_SPKI
| typeof TYPE_PKCS;
/** WebCrypto keys can be in raw, jwk, pkcs8/spki formats. Raw is internal and fragile. */
export type WebCryptoOpts = {
/** Preferred secret-key serialization format. */
formatSec?: WebCryptoFormat;
/** Preferred public-key serialization format. */
formatPub?: WebCryptoFormat;
};
// default formats
const dfsec = TYPE_PKCS;
const dfpub = TYPE_SPKI;
function getSubtle(): any {
const s: any = globalThis?.crypto?.subtle;
if (typeof s === 'object' && s != null) return s;
throw new Error('crypto.subtle must be defined');
}
function createKeygenA(
randomSecretKey: any,
getPublicKey: any
): TRet<(seed?: Uint8Array) => Promise<{ secretKey: Uint8Array; publicKey: Uint8Array }>> {
// Runtime accepts an accidental `keygen(seed)` argument for parity with other wrappers, but the
// seed is intentionally ignored because WebCrypto keygen here always goes through fresh keygen.
return async function keygenA(_seed?: TArg<Uint8Array>) {
const secretKey = (await randomSecretKey()) as TRet<Uint8Array>;
return { secretKey, publicKey: (await getPublicKey(secretKey)) as TRet<Uint8Array> };
};
}
// Internal helper only: strict hex parser for the local hardcoded PKCS8 header constants.
function hexToBytesLocal(hex: string): TRet<Uint8Array> {
const pairs = hex.match(/[0-9a-f]{2}/gi);
if (!pairs || pairs.length * 2 !== hex.length) throw new Error('invalid hex');
return Uint8Array.from(pairs, (b) => Number.parseInt(b, 16)) as TRet<Uint8Array>;
}
export const __TEST: { hexToBytesLocal: typeof hexToBytesLocal } = /* @__PURE__ */ Object.freeze({
hexToBytesLocal,
});
// Trying to do generics here creates hell on conversion and usage
type JsonWebKey = {
crv?: string;
d?: string;
kty?: string;
x?: string;
y?: string;
[key: string]: unknown;
};
type Key = JsonWebKey | Uint8Array;
type CryptoKey = Awaited<ReturnType<typeof crypto.subtle.importKey>>;
type KeyUsage = 'deriveBits' | 'deriveKey' | 'sign' | 'verify';
type Algo = string | { name: string; namedCurve: string };
type SigAlgo = string | { name: string; hash?: { name: string } };
type KeyUtils = {
import(key: TArg<Key>, format?: WebCryptoFormat): Promise<CryptoKey>;
export(key: CryptoKey, format?: WebCryptoFormat): TRet<Promise<Key>>;
convert(
key: TArg<Key>,
inFormat?: WebCryptoFormat,
outFormat?: WebCryptoFormat
): TRet<Promise<Key>>;
};
function assertType(type: 'private' | 'public', key: any) {
// Callers are expected to pass a non-null key-like object; `null` / `undefined` still fail first
// via property access before reaching the explicit wrapper error.
if (key.type !== type) throw new Error(`invalid key type, expected ${type}`);
}
function createKeyUtils(algo: Algo, derive: boolean, keyLen: number, pkcs8header: string) {
const secUsage: KeyUsage[] = derive ? ['deriveBits'] : ['sign'];
const pubUsage: KeyUsage[] = derive ? [] : ['verify'];
// Return Uint8Array instead of ArrayBuffer
const arrBufToU8 = (res: TArg<Key>, format: WebCryptoFormat): TRet<Key> =>
(format === TYPE_JWK
? (res as JsonWebKey)
: new Uint8Array(res as unknown as ArrayBuffer)) as TRet<Key>;
const pub: KeyUtils = {
async import(key: TArg<Key>, format: WebCryptoFormat): Promise<CryptoKey> {
// For sign/verify wrappers we pass caller-provided JWK metadata through unchanged and let
// WebCrypto enforce mismatched `key_ops` / extractability instead of normalizing it here.
const keyi: CryptoKey = await getSubtle().importKey(format, key, algo, true, pubUsage);
assertType('public', keyi);
return keyi;
},
async export(key: CryptoKey, format: WebCryptoFormat): Promise<TRet<Key>> {
assertType('public', key);
const keyi = await getSubtle().exportKey(format, key);
return arrBufToU8(keyi, format);
},
async convert(
key: TArg<Key>,
inFormat: WebCryptoFormat,
outFormat: WebCryptoFormat
): Promise<TRet<Key>> {
return pub.export(await pub.import(key, inFormat), outFormat);
},
};
const priv: KeyUtils = {
async import(key: TArg<Key>, format: WebCryptoFormat): Promise<CryptoKey> {
const crypto = getSubtle();
let keyi: CryptoKey;
if (format === TYPE_RAW) {
// Chrome, node, bun, deno: works
// Safari, Firefox: Data provided to an operation does not meet requirements
// This is the best one can do. JWK can't be used: it contains public key component inside.
const k = key as Uint8Array;
const head = hexToBytesLocal(pkcs8header);
const all = new Uint8Array(head.length + k.length);
all.set(head, 0);
all.set(k, head.length);
keyi = await crypto.importKey(TYPE_PKCS, all, algo, true, secUsage);
} else {
// Sign/verify wrappers keep caller JWK metadata as-is and assume the supplied `key_ops`
// already match the requested operation. ECDH is different: noble treats the same key
// material as usable for both sign and derive, so JWK imported through the derive path
// must rewrite `key_ops` or WebCrypto refuses otherwise-correct keys exported by keygen.
if (derive && format === TYPE_JWK) key = { ...key, key_ops: secUsage };
keyi = await crypto.importKey(format, key, algo, true, secUsage);
}
assertType('private', keyi);
return keyi;
},
async export(key: CryptoKey, format: WebCryptoFormat): Promise<TRet<Key>> {
const crypto = getSubtle();
assertType('private', key);
if (format === TYPE_RAW) {
// scure-base base64urlnopad could have been used, but we can't add more deps.
// pkcs8 would be even more fragile
const jwk = await crypto.exportKey(TYPE_JWK, key);
const base64 = jwk.d.replace(/-/g, '+').replace(/_/g, '/'); // base64url
const pad = base64.length % 4 ? '='.repeat(4 - (base64.length % 4)) : ''; // add padding
const binary = atob(base64 + pad);
// This is not ASCII, and not text: this is only semi-safe with atob output
const raw = Uint8Array.from(binary, (c) => c.charCodeAt(0));
// Pad key to key len because Bun strips leading zero for P-521 only
const res = new Uint8Array(keyLen);
res.set(raw, keyLen - raw.length);
return res as TRet<Key>;
}
const keyi = await crypto.exportKey(format, key);
return arrBufToU8(keyi, format);
},
async convert(
key: TArg<Key>,
inFormat: WebCryptoFormat,
outFormat: WebCryptoFormat
): Promise<TRet<Key>> {
return priv.export(await priv.import(key, inFormat), outFormat);
},
};
async function getPublicKey(
secretKey: TArg<Key>,
opts: TArg<WebCryptoOpts> = {}
): Promise<TRet<Key>> {
const fsec = opts.formatSec ?? dfsec;
const fpub = opts.formatPub ?? dfpub;
// Export to jwk, remove private scalar and then convert to format
const jwk = (
fsec === TYPE_JWK ? { ...secretKey } : await priv.convert(secretKey, fsec, TYPE_JWK)
) as JsonWebKey;
delete jwk.d;
jwk.key_ops = pubUsage;
if (fpub === TYPE_JWK) return jwk as TRet<Key>;
return pub.convert(jwk, TYPE_JWK, fpub);
}
async function randomSecretKey(format: WebCryptoFormat = dfsec): Promise<TRet<Key>> {
const keyPair = await getSubtle().generateKey(algo, true, secUsage);
return priv.export(keyPair.privateKey, format);
}
// Key generation could be slow, so we cache result once.
let supported: boolean | undefined;
return {
pub: pub as KeyUtils,
priv: priv as KeyUtils,
async isSupported(): Promise<boolean> {
if (supported !== undefined) return supported;
try {
const crypto = getSubtle();
const key = await crypto.generateKey(algo, true, secUsage);
// Deno is broken and generates key for unsupported curves, but then fails on export
await priv.export(key.privateKey, TYPE_JWK);
// Bun fails on derive for x25519, but not x448
if (derive) {
await crypto.deriveBits(
{ name: typeof algo === 'string' ? algo : algo.name, public: key.publicKey },
key.privateKey,
8
);
}
return (supported = true);
} catch (e) {
return (supported = false);
}
},
getPublicKey,
keygen: createKeygenA(randomSecretKey, getPublicKey),
utils: Object.freeze({
randomSecretKey,
// Runtime expects both formats explicitly here; omitted formats just flow into
// `subtle.importKey(...)`, and JWK conversion also assumes extractable keys (`ext !== false`).
convertPublicKey: pub.convert as KeyUtils['convert'],
// Runtime expects both formats explicitly here; omitted formats just flow into
// `subtle.importKey(...)`, and JWK conversion also assumes extractable keys (`ext !== false`).
convertSecretKey: priv.convert as KeyUtils['convert'],
}),
};
}
function createSigner(
keys: ReturnType<typeof createKeyUtils>,
algo: SigAlgo
): TRet<WebCryptoSigner> {
return {
// Historical param name: wrappers pass message bytes here, while WebCrypto performs the
// algorithm-specific hashing itself for ECDSA. We also return provider signatures verbatim:
// this wrapper is intentionally "raw WebCrypto", so it does not parse scalars or normalize
// high-S ECDSA outputs into software noble's low-S convention.
async sign(
msgHash: TArg<Uint8Array>,
secretKey: TArg<Key>,
opts: TArg<WebCryptoOpts> = {}
): Promise<TRet<Uint8Array>> {
const key = await keys.priv.import(secretKey, opts.formatSec ?? dfsec);
const sig = await getSubtle().sign(algo, key, msgHash);
return new Uint8Array(sig) as TRet<Uint8Array>;
},
async verify(
signature: TArg<Uint8Array>,
msgHash: TArg<Uint8Array>,
publicKey: TArg<Key>,
opts: TArg<WebCryptoOpts> = {}
): Promise<boolean> {
const key = await keys.pub.import(publicKey, opts.formatPub ?? dfpub);
return await getSubtle().verify(algo, key, signature, msgHash);
},
};
}
function createECDH(
keys: ReturnType<typeof createKeyUtils>,
algo: Algo,
keyLen: number
): TRet<WebCryptoECDH> {
return {
// Runtime accepts the alternate key formats supported by `keys.import(...)`; the public type is
// still narrower than that accepted surface.
async getSharedSecret(
secretKeyA: TArg<Uint8Array>,
publicKeyB: TArg<Uint8Array>,
opts: TArg<WebCryptoOpts> = {}
): Promise<TRet<Uint8Array>> {
// if (_isCompressed !== true) throw new Error('WebCrypto only supports compressed keys');
const secKey = await keys.priv.import(
secretKeyA,
opts.formatSec === undefined ? dfsec : opts.formatSec
);
const pubKey = await keys.pub.import(
publicKeyB,
opts.formatPub === undefined ? dfpub : opts.formatPub
);
const shared = await getSubtle().deriveBits(
{ name: typeof algo === 'string' ? algo : algo.name, public: pubKey },
secKey,
8 * keyLen
);
return new Uint8Array(shared) as TRet<Uint8Array>;
},
};
}
type WebCryptoBaseCurve = {
name: string;
isSupported(): Promise<boolean>;
keygen(): TRet<Promise<{ secretKey: Uint8Array; publicKey: Uint8Array }>>;
getPublicKey(secretKey: TArg<Key>, opts?: TArg<WebCryptoOpts>): TRet<Promise<Key>>;
utils: {
randomSecretKey: (format?: WebCryptoFormat) => TRet<Promise<Key>>;
convertSecretKey: (
key: TArg<Key>,
inFormat?: WebCryptoFormat,
outFormat?: WebCryptoFormat
) => TRet<Promise<Key>>;
convertPublicKey: (
key: TArg<Key>,
inFormat?: WebCryptoFormat,
outFormat?: WebCryptoFormat
) => TRet<Promise<Key>>;
};
};
// Specific per-curve methods - no reason to export them; we can't "add" a new curve
/** WebCrypto signing interface shared by ECDSA and EdDSA helpers. */
export type WebCryptoSigner = {
/**
* Sign one message with a WebCrypto-backed private key.
* @param message - Message bytes to sign.
* @param secretKey - Secret key in one supported format.
* @param opts - Optional key-format overrides. See {@link WebCryptoOpts}.
* @returns Signature bytes.
*/
sign(
message: TArg<Uint8Array>,
secretKey: TArg<Key>,
opts?: TArg<WebCryptoOpts>
): TRet<Promise<Uint8Array>>;
/**
* Verify one signature with a WebCrypto-backed public key.
* @param signature - Signature bytes.
* @param message - Signed message bytes.
* @param publicKey - Public key in one supported format.
* @param opts - Optional key-format overrides. See {@link WebCryptoOpts}.
* @returns `true` when the signature is valid.
*/
verify(
signature: TArg<Uint8Array>,
message: TArg<Uint8Array>,
publicKey: TArg<Key>,
opts?: TArg<WebCryptoOpts>
): Promise<boolean>;
};
/** WebCrypto ECDH interface for shared-secret derivation. */
export type WebCryptoECDH = {
/**
* Derive one shared secret from a local secret key and peer public key.
* Short-Weierstrass wrappers return the raw x-coordinate here, not noble's parity-prefixed
* shared-point encoding. Runtime also accepts alternate key formats through `opts`, even though
* this public type is still narrowed to byte arrays.
* @param secA - Local secret key in one supported format.
* @param pubB - Peer public key in one supported format.
* @param opts - Optional key-format overrides. See {@link WebCryptoOpts}.
* @returns Shared secret bytes.
*/
getSharedSecret(
secA: TArg<Uint8Array>,
pubB: TArg<Uint8Array>,
opts?: TArg<WebCryptoOpts>
): TRet<Promise<Uint8Array>>;
};
/** WebCrypto ECDSA interface with keygen, signing, and ECDH helpers. */
export type WebCryptoECDSA = WebCryptoBaseCurve & WebCryptoSigner & WebCryptoECDH;
/** WebCrypto EdDSA interface with keygen and signing helpers. */
export type WebCryptoEdDSA = WebCryptoBaseCurve & WebCryptoSigner;
/** WebCrypto Montgomery interface with keygen and ECDH helpers. */
export type WebCryptoMontgomery = WebCryptoBaseCurve & WebCryptoECDH;
function wrapECDSA(
curve: 'P-256' | 'P-384' | 'P-521',
hash: string,
keyLen: number,
pkcs8header: string
): TRet<WebCryptoECDSA> {
const ECDH_ALGO = { name: 'ECDH', namedCurve: curve };
const keys = createKeyUtils({ name: 'ECDSA', namedCurve: curve }, false, keyLen, pkcs8header);
const keysEcdh = createKeyUtils(ECDH_ALGO, true, keyLen, pkcs8header);
return Object.freeze({
name: curve,
// Support probing comes from the sign-side wrapper only; ECDH availability is not checked
// independently here even though the public wrapper also exposes `getSharedSecret(...)`.
isSupported: keys.isSupported,
getPublicKey: keys.getPublicKey,
keygen: createKeygenA(keys.utils.randomSecretKey, keys.getPublicKey),
...createSigner(keys, { name: 'ECDSA', hash: { name: hash } }),
...createECDH(keysEcdh, ECDH_ALGO, keyLen),
utils: Object.freeze({
...keys.utils,
async convertSecretKey(
key: TArg<Key>,
inFormat?: WebCryptoFormat,
outFormat?: WebCryptoFormat
): Promise<TRet<Key>> {
const jwk = inFormat === TYPE_JWK ? (key as JsonWebKey) : undefined;
// `wrapECDSA(...)` exposes the same key material for both sign and derive, so an ECDH-flavored
// JWK secret key from `getSharedSecret(...)` should still round-trip through `utils`.
if (
Array.isArray(jwk?.key_ops) &&
jwk.key_ops.length === 1 &&
jwk.key_ops[0] === 'deriveBits'
)
return keysEcdh.utils.convertSecretKey(key, inFormat, outFormat);
return keys.utils.convertSecretKey(key, inFormat, outFormat);
},
}),
});
}
function wrapEdDSA(
curve: 'Ed25519' | 'Ed448',
keyLen: number,
pkcs8header: string
): TRet<WebCryptoEdDSA> {
const keys = createKeyUtils(curve, false, keyLen, pkcs8header);
return Object.freeze({
name: curve,
isSupported: keys.isSupported,
// This wrapper intentionally re-exports the generic WebCrypto key-conversion/signing behavior
// without adding extra JWK-metadata or extractability guardrails of its own.
getPublicKey: keys.getPublicKey,
keygen: createKeygenA(keys.utils.randomSecretKey, keys.getPublicKey),
...createSigner(keys, { name: curve }),
utils: keys.utils,
});
}
function wrapMontgomery(
curve: 'X25519' | 'X448',
keyLen: number,
pkcs8header: string
): TRet<WebCryptoMontgomery> {
const keys = createKeyUtils(curve, true, keyLen, pkcs8header);
return Object.freeze({
name: curve,
isSupported: keys.isSupported,
// This wrapper intentionally re-exports the generic ECDH key-format behavior without widening
// the narrow public `Uint8Array` key types.
getPublicKey: keys.getPublicKey,
keygen: createKeygenA(keys.utils.randomSecretKey, keys.getPublicKey),
...createECDH(keys, curve, keyLen),
utils: keys.utils,
});
}
/**
* Friendly wrapper over built-in WebCrypto NIST P-256 (secp256r1).
* Inherits the generic WebCrypto ECDSA caveats: `isSupported()` only probes the sign-side API, and
* the conversion/signing helpers keep the shared `createKeyUtils(...)` / `createSigner(...)` quirks,
* including raw WebCrypto ECDSA signatures without low-S normalization.
* @example
* Check support, then sign and verify once with WebCrypto P-256.
*
* ```ts
* if (await p256.isSupported()) {
* const { secretKey, publicKey } = await p256.keygen();
* const msg = new TextEncoder().encode('hello noble');
* const sig = await p256.sign(msg, secretKey);
* const isValid = await p256.verify(sig, msg, publicKey);
* }
* ```
*/
export const p256: TRet<WebCryptoECDSA> = /* @__PURE__ */ wrapECDSA(
'P-256',
'SHA-256',
32,
'3041020100301306072a8648ce3d020106082a8648ce3d030107042730250201010420'
);
/**
* Friendly wrapper over built-in WebCrypto NIST P-384 (secp384r1).
* Inherits the generic WebCrypto ECDSA caveats around support probing and key/signing conversion.
* @example
* Check support, then sign and verify once with WebCrypto P-384.
*
* ```ts
* if (await p384.isSupported()) {
* const { secretKey, publicKey } = await p384.keygen();
* const msg = new TextEncoder().encode('hello noble');
* const sig = await p384.sign(msg, secretKey);
* const isValid = await p384.verify(sig, msg, publicKey);
* }
* ```
*/
export const p384: TRet<WebCryptoECDSA> = /* @__PURE__ */ wrapECDSA(
'P-384',
'SHA-384',
48,
'304e020100301006072a8648ce3d020106052b81040022043730350201010430'
);
/**
* Friendly wrapper over built-in WebCrypto NIST P-521 (secp521r1).
* Inherits the generic WebCrypto ECDSA caveats around support probing and key/signing conversion.
* @example
* Check support, then sign and verify once with WebCrypto P-521.
*
* ```ts
* if (await p521.isSupported()) {
* const { secretKey, publicKey } = await p521.keygen();
* const msg = new TextEncoder().encode('hello noble');
* const sig = await p521.sign(msg, secretKey);
* const isValid = await p521.verify(sig, msg, publicKey);
* }
* ```
*/
export const p521: TRet<WebCryptoECDSA> = /* @__PURE__ */ wrapECDSA(
'P-521',
'SHA-512',
66,
'3060020100301006072a8648ce3d020106052b81040023044930470201010442'
);
/**
* Friendly wrapper over built-in WebCrypto ed25519.
* Inherits the generic WebCrypto EdDSA caveats around JWK conversion metadata and extractability.
* @example
* Check support, then sign and verify once with WebCrypto Ed25519.
*
* ```ts
* if (await ed25519.isSupported()) {
* const { secretKey, publicKey } = await ed25519.keygen();
* const msg = new TextEncoder().encode('hello noble');
* const sig = await ed25519.sign(msg, secretKey);
* const isValid = await ed25519.verify(sig, msg, publicKey);
* }
* ```
*/
export const ed25519: TRet<WebCryptoEdDSA> = /* @__PURE__ */ wrapEdDSA(
'Ed25519',
32,
'302e020100300506032b657004220420'
);
/**
* Friendly wrapper over built-in WebCrypto ed448.
* Inherits the generic WebCrypto EdDSA caveats around JWK conversion metadata and extractability.
* @example
* Check support, then sign and verify once with WebCrypto Ed448.
*
* ```ts
* if (await ed448.isSupported()) {
* const { secretKey, publicKey } = await ed448.keygen();
* const msg = new TextEncoder().encode('hello noble');
* const sig = await ed448.sign(msg, secretKey);
* const isValid = await ed448.verify(sig, msg, publicKey);
* }
* ```
*/
export const ed448: TRet<WebCryptoEdDSA> = /* @__PURE__ */ wrapEdDSA(
'Ed448',
57,
'3047020100300506032b6571043b0439'
);
/**
* Friendly wrapper over built-in WebCrypto x25519 (ECDH over Curve25519).
* Inherits the generic WebCrypto Montgomery caveat that runtime accepts more key formats than the
* narrow public `Uint8Array` argument types suggest.
* @example
* Check support, then derive one shared secret with WebCrypto X25519.
*
* ```ts
* if (await x25519.isSupported()) {
* const alice = await x25519.keygen();
* const bob = await x25519.keygen();
* const shared = await x25519.getSharedSecret(alice.secretKey, bob.publicKey);
* }
* ```
*/
export const x25519: TRet<WebCryptoMontgomery> = /* @__PURE__ */ wrapMontgomery(
'X25519',
32,
'302e020100300506032b656e04220420'
);
/**
* Friendly wrapper over built-in WebCrypto x448 (ECDH over Curve448).
* Inherits the generic WebCrypto Montgomery caveat that runtime accepts more key formats than the
* narrow public `Uint8Array` argument types suggest.
* @example
* Check support, then derive one shared secret with WebCrypto X448.
*
* ```ts
* if (await x448.isSupported()) {
* const alice = await x448.keygen();
* const bob = await x448.keygen();
* const shared = await x448.getSharedSecret(alice.secretKey, bob.publicKey);
* }
* ```
*/
export const x448: TRet<WebCryptoMontgomery> = /* @__PURE__ */ wrapMontgomery(
'X448',
56,
'3046020100300506032b656f043a0438'
);