Add Python program for Extended Euclidan Algorithm

examples/crypto/eea/gf_inverse.py

@@ -0,0 +1,81 @@
+//
+// gf_inverse.py
+// Extended Euclidean Algorithm
+// james.stine@okstate.edu 8 April 2025
+//
+
+def gf_mul(a, b, modulus):
+    result = 0
+    while b:
+        if b & 1:
+            result ^= a
+        b >>= 1
+        a <<= 1
+        if a & (1 << 8):
+            a ^= modulus
+    return result & 0xFF
+
+def gf_mul_poly(a, b):
+    result = 0
+    while b:
+        if b & 1:
+            result ^= a
+        a <<= 1
+        b >>= 1
+    return result
+
+def gf_divmod(a, b):
+    if b == 0:
+        raise ZeroDivisionError()
+    deg_a = a.bit_length() - 1
+    deg_b = b.bit_length() - 1
+    quotient = 0
+    while deg_a >= deg_b:
+        shift = deg_a - deg_b
+        quotient ^= 1 << shift
+        a ^= b << shift
+        deg_a = a.bit_length() - 1
+    return quotient, a
+
+def gf_inverse(a, modulus):
+    if a == 0:
+        raise ValueError("No inverse for 0 in GF(2^n)")
+
+    r0, r1 = modulus, a
+    s0, s1 = 0, 1
+    loop_count = 0
+
+    print(f"{'Loop':<5} {'r0':>6} {'r1':>6} {'q':>6} {'s0':>6} {'s1':>6}")
+
+    while r1 != 0:
+        q, _ = gf_divmod(r0, r1)
+        new_r = r0 ^ gf_mul_poly(q, r1)
+        new_s = s0 ^ gf_mul_poly(q, s1)
+
+        print(f"{loop_count:<5} {r0:06X} {r1:06X} {q:06X} {s0:06X} {s1:06X}")
+
+        r0, r1 = r1, new_r
+        s0, s1 = s1, new_s
+        loop_count += 1
+
+    print(f"{loop_count:<5} {r0:06X} {' '*6} {' '*6} {s0:06X}")
+
+    if r0 != 1:
+        raise ValueError(f"No inverse for {a:#02x} mod {modulus:#04x}")
+
+    return s0 & 0xFF
+
+# Example usage
+if __name__ == "__main__":
+    import sys
+    if len(sys.argv) != 3:
+        print("Usage: python gf_inverse_parametric.py <value> <modulus>")
+        print("Example: python gf_inverse_parametric.py 0x53 0x11B")
+        sys.exit(1)
+
+    value = int(sys.argv[1], 0)
+    modulus = int(sys.argv[2], 0)
+
+    inv = gf_inverse(value, modulus)
+    print(f"\nMultiplicative inverse of {value:#02x} in GF(2^8) mod {modulus:#04x} is {inv:#02x}")
+    assert gf_mul(value, inv, modulus) == 1, "Verification failed!"