diff --git a/lib/algorithms/rsa.js b/lib/algorithms/rsa.js
index 929abf8..b07cd83 100644
--- a/lib/algorithms/rsa.js
+++ b/lib/algorithms/rsa.js
@@ -37,7 +37,7 @@ function uint8ArrayToUint32(bigInteger) {
 }
 
 function uint32ToUint8Array(integer) {
-  const result = Buffer.alloc(8);
+  const result = new Uint8Array(8);
   let i = 7;
   while (integer !== 0) {
     result[i--] = integer & 0xff;
@@ -46,6 +46,33 @@ function uint32ToUint8Array(integer) {
   return result.slice(i + 1);
 }
 
+function getAlgorithmProperties(key) {
+  const der = key.export({
+    format: 'der',
+    type: 'pkcs1'
+  });
+
+  const dec = new Asn1SequenceDecoder(der);
+  if (key.type === 'private') {
+    // Skip the version field.
+    dec.unsignedInteger();
+  }
+
+  const n = dec.unsignedInteger();
+  const e = dec.unsignedInteger();
+
+  // n cannot have a leading zero byte, but leading zero bits.
+  let modulusLength = 8;
+  while ((n[0] & (1 << (modulusLength - 1))) === 0)
+    modulusLength--;
+  modulusLength += (n.length - 1) * 8;
+
+  return {
+    modulusLength,
+    publicExponent: new Uint8Array(e)
+  };
+}
+
 function jwkToDer(jwk, jwkHashMapping) {
   if (jwk.kty !== 'RSA')
     throw new DataError();
@@ -205,8 +232,13 @@ const rsaBase = {
       type: keyFormat
     });
 
-    return new CryptoKey(key.type, { name: this.name, hash },
-                         extractable, keyUsages, key);
+    const algorithm = {
+      name: this.name,
+      hash,
+      ...getAlgorithmProperties(key)
+    };
+
+    return new CryptoKey(key.type, algorithm, extractable, keyUsages, key);
   },
 
   exportKey(format, key) {
diff --git a/test/unit/algorithms/rsa.js b/test/unit/algorithms/rsa.js
index bc7055f..9eb834e 100644
--- a/test/unit/algorithms/rsa.js
+++ b/test/unit/algorithms/rsa.js
@@ -23,7 +23,7 @@ function testGenImportExport(name, pubKeyUsage, privKeyUsage) {
       assert.strictEqual(key.algorithm.name, name);
       assert.strictEqual(key.algorithm.modulusLength, 2048);
       assert.deepStrictEqual(key.algorithm.publicExponent,
-                             Buffer.from([0x01, 0x00, 0x01]));
+                             new Uint8Array([0x01, 0x00, 0x01]));
       assert.strictEqual(key.algorithm.hash.name, 'SHA-384');
     }
 
@@ -41,6 +41,14 @@ function testGenImportExport(name, pubKeyUsage, privKeyUsage) {
       hash: 'SHA-384'
     }, true, [privKeyUsage]);
 
+    for (const key of [impPublicKey, impPrivateKey]) {
+      assert.strictEqual(key.algorithm.name, name);
+      assert.strictEqual(key.algorithm.modulusLength, 2048);
+      assert.deepStrictEqual(key.algorithm.publicExponent,
+                             new Uint8Array([0x01, 0x00, 0x01]));
+      assert.strictEqual(key.algorithm.hash.name, 'SHA-384');
+    }
+
     assert.deepStrictEqual(await subtle.exportKey('spki', impPublicKey),
                            expPublicKey);
     assert.deepStrictEqual(await subtle.exportKey('pkcs8', impPrivateKey),