diff --git a/packages/crypto/src/utils.ts b/packages/crypto/src/utils.ts
index 3dce127de..a51c8f2c0 100644
--- a/packages/crypto/src/utils.ts
+++ b/packages/crypto/src/utils.ts
@@ -1,3 +1,5 @@
+import type { Jwk } from './jose/jwk.js';
+
 import { crypto } from '@noble/hashes/crypto';
 import { randomBytes as nobleRandomBytes } from '@noble/hashes/utils';
 
@@ -63,6 +65,58 @@ export function checkValidProperty(params: {
   }
 }
 
+/**
+ * Determines the JOSE algorithm identifier of the digital signature algorithm based on the `alg` or
+ * `crv` property of a {@link Jwk | JWK}.
+ *
+ * If the `alg` property is present, its value takes precedence and is returned. Otherwise, the
+ * `crv` property is used to determine the algorithm.
+ *
+ * @see {@link https://www.iana.org/assignments/jose/jose.xhtml#web-signature-encryption-algorithms | JOSE Algorithms}
+ * @see {@link https://datatracker.ietf.org/doc/draft-ietf-jose-fully-specified-algorithms/ | Fully-Specified Algorithms for JOSE and COSE}
+ *
+ * @example
+ * ```ts
+ * const publicKey: Jwk = {
+ *   "kty": "OKP",
+ *   "crv": "Ed25519",
+ *   "x": "FEJG7OakZi500EydXxuE8uMc8uaAzEJkmQeG8khXANw"
+ * }
+ * const algorithm = getJoseSignatureAlgorithmFromPublicKey(publicKey);
+ * console.log(algorithm); // Output: "EdDSA"
+ * ```
+ *
+ * @param publicKey - A JWK containing the `alg` and/or `crv` properties.
+ * @returns The name of the algorithm associated with the key.
+ * @throws Error if the algorithm cannot be determined from the provided input.
+ */
+export function getJoseSignatureAlgorithmFromPublicKey(publicKey: Jwk): string {
+  const curveToJoseAlgorithm: Record<string, string> = {
+    'Ed25519'   : 'EdDSA',
+    'P-256'     : 'ES256',
+    'P-384'     : 'ES384',
+    'P-521'     : 'ES512',
+    'secp256k1' : 'ES256K',
+  };
+
+  // If the key contains an `alg` property that matches a JOSE registered algorithm identifier,
+  // return its value.
+  if (publicKey.alg && Object.values(curveToJoseAlgorithm).includes(publicKey.alg)) {
+    return publicKey.alg;
+  }
+
+  // If the key contains a `crv` property, return the corresponding algorithm.
+  if (publicKey.crv && Object.keys(curveToJoseAlgorithm).includes(publicKey.crv)) {
+    return curveToJoseAlgorithm[publicKey.crv];
+  }
+
+  throw new Error(
+    `Unable to determine algorithm based on provided input: alg=${publicKey.alg}, crv=${publicKey.crv}. ` +
+    `Supported 'alg' values: ${Object.values(curveToJoseAlgorithm).join(', ')}. ` +
+    `Supported 'crv' values: ${Object.keys(curveToJoseAlgorithm).join(', ')}.`
+  );
+}
+
 /**
  * Checks if the Web Crypto API is supported in the current runtime environment.
  *
diff --git a/packages/crypto/tests/utils.spec.ts b/packages/crypto/tests/utils.spec.ts
index 2bdc3e555..c2d4fdfdd 100644
--- a/packages/crypto/tests/utils.spec.ts
+++ b/packages/crypto/tests/utils.spec.ts
@@ -1,12 +1,15 @@
 import { expect } from 'chai';
 import * as sinon from 'sinon';
 
+import type { Jwk } from '../src/jose/jwk.js';
+
 import {
   randomUuid,
   randomBytes,
   checkValidProperty,
   isWebCryptoSupported,
   checkRequiredProperty,
+  getJoseSignatureAlgorithmFromPublicKey,
 } from '../src/utils.js';
 
 // TODO: Remove this polyfill once Node.js v18 is no longer supported by @web5/crypto.
@@ -65,6 +68,48 @@ describe('Crypto Utils', () => {
     });
   });
 
+  describe('getJoseSignatureAlgorithmFromPublicKey()', () => {
+    it('returns the algorithm specified by the alg property regardless of the crv property', () => {
+      const publicKey: Jwk = { kty: 'OKP', alg: 'EdDSA', crv: 'P-256' };
+      expect(getJoseSignatureAlgorithmFromPublicKey(publicKey)).to.equal('EdDSA');
+    });
+
+    it('returns the correct algorithm for Ed25519 curve', () => {
+      const publicKey: Jwk = { kty: 'OKP', crv: 'Ed25519' };
+      expect(getJoseSignatureAlgorithmFromPublicKey(publicKey)).to.equal('EdDSA');
+    });
+
+    it('returns the correct algorithm for P-256 curve', () => {
+      const publicKey: Jwk = { kty: 'EC', crv: 'P-256' };
+      expect(getJoseSignatureAlgorithmFromPublicKey(publicKey)).to.equal('ES256');
+    });
+
+    it('returns the correct algorithm for P-384 curve', () => {
+      const publicKey: Jwk = { kty: 'EC', crv: 'P-384' };
+      expect(getJoseSignatureAlgorithmFromPublicKey(publicKey)).to.equal('ES384');
+    });
+
+    it('returns the correct algorithm for P-521 curve', () => {
+      const publicKey: Jwk = { kty: 'EC', crv: 'P-521' };
+      expect(getJoseSignatureAlgorithmFromPublicKey(publicKey)).to.equal('ES512');
+    });
+
+    it('throws an error for unsupported algorithms', () => {
+      const publicKey: Jwk = { kty: 'EC', alg: 'UnsupportedAlgorithm' };
+      expect(() => getJoseSignatureAlgorithmFromPublicKey(publicKey)).to.throw();
+    });
+
+    it('throws an error for unsupported curves', () => {
+      const publicKey: Jwk = { kty: 'EC', crv: 'UnsupportedCurve' };
+      expect(() => getJoseSignatureAlgorithmFromPublicKey(publicKey)).to.throw();
+    });
+
+    it('throws an error when neither alg nor crv is provided', () => {
+      const publicKey: Jwk = { kty: 'EC' };
+      expect(() => getJoseSignatureAlgorithmFromPublicKey(publicKey)).to.throw();
+    });
+  });
+
   describe('isWebCryptoSupported()', () => {
     afterEach(() => {
       // Restore the original state after each test
diff --git a/packages/dids/src/bearer-did.ts b/packages/dids/src/bearer-did.ts
index c9b718b22..f8f312031 100644
--- a/packages/dids/src/bearer-did.ts
+++ b/packages/dids/src/bearer-did.ts
@@ -1,4 +1,16 @@
-import { LocalKeyManager, type CryptoApi, type EnclosedSignParams, type EnclosedVerifyParams, type Jwk, type KeyIdentifier, type KeyImporterExporter, type KmsExportKeyParams, type KmsImportKeyParams, type Signer } from '@web5/crypto';
+import type {
+  Jwk,
+  Signer,
+  CryptoApi,
+  KeyIdentifier,
+  EnclosedSignParams,
+  KmsExportKeyParams,
+  KmsImportKeyParams,
+  KeyImporterExporter,
+  EnclosedVerifyParams,
+} from '@web5/crypto';
+
+import { LocalKeyManager, utils as cryptoUtils } from '@web5/crypto';
 
 import type { DidDocument } from './types/did-core.js';
 import type { DidMetadata, PortableDid } from './types/portable-did.js';
@@ -88,13 +100,15 @@ export class BearerDid {
    * `PortableDid` structure.
    *
    * @remarks
-   * This method requires that the DID's key manager supports the `exportKey` operation. If the DID
-   * document does not contain any verification methods, or if the key manager does not support key
-   * export, an error is thrown.
+   * If the DID's key manager does not allow private keys to be exported, the `PortableDid` returned
+   * will not contain a `privateKeys` property. This enables the importing and exporting DIDs that
+   * use the same underlying KMS even if the KMS does not support exporting private keys. Examples
+   * include hardware security modules (HSMs) and cloud-based KMS services like AWS KMS.
    *
-   * The resulting `PortableDid` will contain the same number of verification methods as the DID
-   * document, each with its associated public and private keys and the purposes for which the key
-   * can be used.
+   * If the DID's key manager does support exporting private keys, the resulting `PortableDid` will
+   * include a `privateKeys` property which contains the same number of entries as there are
+   * verification methods as the DID document, each with its associated private key and the
+   * purpose(s) for which the key can be used (e.g., `authentication`, `assertionMethod`, etc.).
    *
    * @example
    * ```ts
@@ -179,7 +193,7 @@ export class BearerDid {
     const keyManager = this.keyManager;
 
     // Determine the signing algorithm.
-    const algorithm = BearerDid.getAlgorithmFromPublicKey(publicKey);
+    const algorithm = cryptoUtils.getJoseSignatureAlgorithmFromPublicKey(publicKey);
 
     return {
       algorithm : algorithm,
@@ -263,45 +277,4 @@ export class BearerDid {
 
     return did;
   }
-
-  /**
-   * Determines the name of the algorithm based on the key's curve property.
-   *
-   * @remarks
-   * This method facilitates the identification of the correct algorithm for cryptographic
-   * operations based on the `alg` or `crv` properties of a {@link Jwk | JWK}.
-   *
-   * @example
-   * ```ts
-   * const publicKey = { ... }; // Public key in JWK format
-   * const algorithm = BearerDid.getAlgorithmFromPublicKey({ key: publicKey });
-   * ```
-   *
-   * @param publicKey - A JWK containing the `alg` and/or `crv` properties.
-   *
-   * @returns The name of the algorithm associated with the key.
-   *
-   * @throws Error if the algorithm cannot be determined from the provided input.
-   */
-  private static getAlgorithmFromPublicKey(publicKey: Jwk): string {
-    const registeredSigningAlgorithms: Record<string, string> = {
-      'Ed25519'   : 'EdDSA',
-      'P-256'     : 'ES256',
-      'P-384'     : 'ES384',
-      'P-521'     : 'ES512',
-      'secp256k1' : 'ES256K',
-    };
-
-    // If the key contains an `alg` property, return its value.
-    if (publicKey.alg) {
-      return publicKey.alg;
-    }
-
-    // If the key contains a `crv` property, return the corresponding algorithm.
-    if (publicKey.crv && Object.keys(registeredSigningAlgorithms).includes(publicKey.crv)) {
-      return registeredSigningAlgorithms[publicKey.crv];
-    }
-
-    throw new Error(`Unable to determine algorithm based on provided input: alg=${publicKey.alg}, crv=${publicKey.crv}`);
-  }
 }
\ No newline at end of file