add RSAJwk.from_prime_factors() to initialize a RSAJwk from 2 pri…

…me numbers (and an exponent). (#16)

jwskate/jwk/rsa.py

@@ -193,6 +193,28 @@ def private(
             )
         )
 
+    @classmethod
+    def from_prime_factors(cls, p: int, q: int, e: int = 65537) -> RSAJwk:
+        """Initialise a `RSAJwk` from its prime factors and exponent.
+
+        Modulus and Private Exponent are mathematically calculated based on those factors.
+
+        Exponent is usually 65537 (default).
+
+        Args:
+            p: first prime factor
+            q: second prime factor
+            e: exponent
+
+        Returns:
+            a `RSAJwk`
+
+        """
+        n = p * q
+        phi = (p - 1) * (q - 1)
+        d = pow(e, -1, phi)
+        return cls.private(n=n, e=e, d=d)
+
     @cached_property
     def key_size(self) -> int:
         """Key size, in bits."""

tests/test_jwk/test_rsa.py

@@ -278,3 +278,16 @@ def test_public_private() -> None:
         )
         == jwk
     )
+
+
+def test_init_from_prime_factors() -> None:
+    p = 398075086424064937397125500550386491199064362342526708406385189575946388957261768583317
+    q = 472772146107435302536223071973048224632914695302097116459852171130520711256363590397527
+    jwk = RSAJwk.from_prime_factors(p, q)
+    assert jwk.first_prime_factor == p
+    assert jwk.second_prime_factor == q
+    assert (
+        jwk.modulus
+        == 188198812920607963838697239461650439807163563379417382700763356422988859715234665485319060606504743045317388011303396716199692321205734031879550656996221305168759307650257059
+    )
+    assert jwk.exponent == 65537