diff --git a/scripts/generate_bignum_tests.py b/scripts/generate_bignum_tests.py
index 74ad934a8..cfafc5658 100755
--- a/scripts/generate_bignum_tests.py
+++ b/scripts/generate_bignum_tests.py
@@ -122,6 +122,71 @@ class BignumOperation(bignum_common.OperationCommon, BignumTarget,
         return tmp
 
 
+class BignumGCDInvModOperation(BignumOperation):
+    #pylint: disable=abstract-method
+    """Common features for testing GCD and Invmod functions."""
+    def __init__(self, val_a: str, val_b: str) -> None:
+        super().__init__(val_a=val_a, val_b=val_b)
+
+    def description_suffix(self) -> str:
+        comparison_symbol = '='
+        if abs(self.int_a) > abs(self.int_b):
+            comparison_symbol = '>'
+        elif abs(self.int_a) < abs(self.int_b):
+            comparison_symbol = '<'
+        suffix_parts = [
+            f"|A|{comparison_symbol}|N|",
+            *(["A<0"] if self.int_a < 0 else []),
+            *(["N<0"] if self.int_b < 0 else []),
+            "A=0" if self.int_a == 0 else f"A {'even' if self.int_a % 2 == 0 else 'odd'}",
+            "N=0" if self.int_b == 0 else f"B {'even' if self.int_b % 2 == 0 else 'odd'}"
+        ]
+        return ": " + ", ".join(suffix_parts)
+
+    # The default values from BignumOperation are not useful, so overwrite them.
+    input_values = [
+        "c79e27fc71c69a08b3e85bd48b9cd3be9aa8e2e56df39f4ed8",
+        "299dd34be98436729eb10f690f8d2bfc5bee21984b775e1e75",
+        "-ecbb3a4e986d488172ecd54f7bd71bd18050c4ed",
+        "7da9ec44f42e6311c56a",
+        "cdbcce3f763819345cfb",
+        "100000000", "300000000", "500000000",
+        "50000", "30000",
+        "1", "2", "3", "", "00", "-1"
+    ]
+    input_cases = [
+        ("bc7fa9fb389618302e8b", "d49730e586607d42269f"),
+        ("28bcc01a2d54b174532e", "d1915057d829a934c25d"),
+        ("d56b50834719280dfa1d", "f007b78f6278ebcccd57"),
+        ("8c327d1d8743c89d4483", "aa20b0c1f97a428311b5"),
+        ("e905382f38", "c844b4f9bdaa5ed0002df3dbd2991cd9b9d"),
+        ("e4623ef13d", "f2a4894ede013e354e481fe8974e67"),
+        ("9f6afa8bdb", "b50aa03a7066df6f27bd6267b"),
+        ("95f99b7122", "e8c74031ec75839f7539"),
+        ("32", "948fbec067"),
+        ("7445", "948fbec067"),
+        ("31850e", "948fbec067"),
+        ("421c2cc8", "948fbec067"),
+        ("32a69", "71e107"),
+        ("36d4e9", "3e05d1"),
+        ("babf01", "1bf699d1"),
+        ("7", "31"),
+    ]
+
+    def get_return_code_gcd_modinv_odd_gcd_only(self) -> str:
+        code = "0"
+        if (self.int_a > self.int_b) or \
+           (self.int_a < 0) or \
+           (self.int_b % 2 == 0):
+            code = "MBEDTLS_ERR_MPI_BAD_INPUT_DATA"
+        return code
+
+    def get_return_code_gcd_modinv_odd(self) -> str:
+        if self.int_b < 2:
+            return "MBEDTLS_ERR_MPI_BAD_INPUT_DATA"
+        return self.get_return_code_gcd_modinv_odd_gcd_only()
+
+
 class BignumCmp(BignumOperation):
     """Test cases for bignum value comparison."""
     count = 0
@@ -260,6 +325,81 @@ class BignumGCD(BignumOperation):
         return [bignum_common.quote_str("{:x}".format(self._result))]
 
 
+class BignumGCDModInvOdd(BignumGCDInvModOperation):
+    """Test cases for both modular inverse and greatest common divisor."""
+    count = 0
+    symbol = "GCD & ^-1 mod"
+    test_function = "mpi_gcd_modinv_odd_both"
+    test_name = "GCD & mod inv"
+
+    def __init__(self, val_a: str, val_b: str) -> None:
+        super().__init__(val_a, val_b)
+        self._result_code = self.get_return_code_gcd_modinv_odd()
+        self._result_gcd = math.gcd(self.int_a, self.int_b)
+        # Only compute the modular inverse if we will get a result - negative
+        # and zero Ns are also present in the test data so skip them too.
+        if self._result_gcd == 1 and self.int_b > 1:
+            self._result_invmod = \
+            bignum_common.invmod_positive(self.int_a, self.int_b) # type: int | None
+        else:
+            self._result_invmod = None # No inverse
+
+    def result(self) -> List[str]:
+        # The test requires us to tell it if there is no modular inverse.
+        if self._result_invmod is None:
+            result_invmod = "no_inverse"
+        else:
+            result_invmod = "{:x}".format(self._result_invmod)
+        return [
+            self.format_result(self._result_gcd),
+            bignum_common.quote_str(result_invmod),
+            self._result_code,
+        ]
+
+
+class BignumGCDModInvOddOnlyGCD(BignumGCDInvModOperation):
+    """Test cases for greatest common divisor only."""
+    count = 0
+    symbol = "GCD"
+    test_function = "mpi_gcd_modinv_odd_only_gcd"
+    test_name = "GCD only"
+
+    def __init__(self, val_a: str, val_b: str) -> None:
+        super().__init__(val_a, val_b)
+        self._result_code = self.get_return_code_gcd_modinv_odd_gcd_only()
+        # We always expect a positive result as the function should reject
+        # negative inputs.
+        self._result_gcd = math.gcd(self.int_a, self.int_b)
+
+    def result(self) -> List[str]:
+        return [self.format_result(self._result_gcd), self._result_code]
+
+
+class BignumGCDModInvOddOnlyModInv(BignumGCDInvModOperation):
+    """Test cases for modular inverse only."""
+    count = 0
+    symbol = "^-1 mod"
+    test_function = "mpi_gcd_modinv_odd_only_modinv"
+    test_name = "Mod inv only"
+
+    def __init__(self, val_a: str, val_b: str) -> None:
+        super().__init__(val_a, val_b)
+        self._result_code = self.get_return_code_gcd_modinv_odd()
+        # Only compute the modular inverse if we will get a result - negative
+        # and zero Ns are also present in the test data so skip them too.
+        if math.gcd(self.int_a, self.int_b) == 1 and self.int_b > 1:
+            self._result_invmod = \
+            bignum_common.invmod_positive(self.int_a, self.int_b) # type: int | None
+        else:
+            self._result_invmod = None # No inverse
+
+    def result(self) -> List[str]:
+        # The test requires us to tell it if there is no modular inverse.
+        if self._result_invmod is None:
+            return [bignum_common.quote_str("no_inverse"), self._result_code]
+        return [self.format_result(self._result_invmod), self._result_code]
+
+
 class BignumAdd(BignumOperation):
     """Test cases for bignum value addition."""
     count = 0