diff --git a/src/mega/mega.py b/src/mega/mega.py
index e125292..93b5fed 100644
--- a/src/mega/mega.py
+++ b/src/mega/mega.py
@@ -21,7 +21,8 @@ from .errors import ValidationError, RequestError
 from .crypto import (
     a32_to_base64, encrypt_key, base64_url_encode, encrypt_attr, base64_to_a32,
     base64_url_decode, decrypt_attr, a32_to_str, get_chunks, str_to_a32,
-    decrypt_key, mpi_to_int, stringhash, prepare_key, make_id, makebyte
+    decrypt_key, mpi_to_int, stringhash, prepare_key, make_id, makebyte,
+    modular_inverse
 )
 
 logger = logging.getLogger(__name__)
@@ -132,14 +133,27 @@ class Mega:
                 rsa_private_key[i] = mpi_to_int(private_key[:bytelength])
                 private_key = private_key[bytelength:]
 
-            encrypted_sid = mpi_to_int(base64_url_decode(resp['csid']))
-            rsa_decrypter = RSA.construct(
-                (
-                    rsa_private_key[0] * rsa_private_key[1], 257,
-                    rsa_private_key[2], rsa_private_key[0],
-                    rsa_private_key[1]
-                )
+            first_factor_p = rsa_private_key[0]
+            second_factor_q = rsa_private_key[1]
+            private_exponent_d = rsa_private_key[2]
+            # In MEGA's webclient javascript, they assign [3] to a variable
+            # called u, but I do not see how it corresponds to pycryptodome's
+            # RSA.construct and it does not seem to be necessary.
+            rsa_modulus_n = first_factor_p * second_factor_q
+            phi = (first_factor_p - 1) * (second_factor_q - 1)
+            public_exponent_e = modular_inverse(private_exponent_d, phi)
+
+            rsa_components = (
+                rsa_modulus_n,
+                public_exponent_e,
+                private_exponent_d,
+                first_factor_p,
+                second_factor_q,
             )
+            rsa_decrypter = RSA.construct(rsa_components)
+
+            encrypted_sid = mpi_to_int(base64_url_decode(resp['csid']))
+
             sid = '%x' % rsa_decrypter._decrypt(encrypted_sid)
             sid = binascii.unhexlify('0' + sid if len(sid) % 2 else sid)
             self.sid = base64_url_encode(sid[:43])