---

generate.py

@@ -0,0 +1,51 @@
+#!/usr/bin/python
+import math
+
+from functions import primality_test
+from functions import extended_gcd
+from Cryptodome.Random.random import getrandbits
+
+
+def generate() -> tuple[int, int, int]:
+  # Step 1: Find two large prime number p and q such that their produce has length of at least 1024 bits.
+  p = None
+  q = None
+
+  # p*q will certainly be at least 1024 bits long if p and q are at least 1024 bits long each.
+  while p == None:
+    num_bits = 2048
+    random_number = getrandbits(num_bits - 1) | (1 << (num_bits - 1))  # Generate 2047 random bits and add an additional 1-bit to the left to create a random 2048-bit integer
+    if random_number >= 2**1023 and primality_test(random_number):
+      p = random_number
+
+  while q == None:
+    num_bits = 2048
+    random_number = getrandbits(num_bits - 1) | (1 << (num_bits - 1))
+    if random_number >= 2**1023 and primality_test(random_number) and p != random_number:
+      q = random_number
+
+  # Step 2: Compute n = p * q
+  n = p * q
+
+  # Step 3: Compute λ(n)
+  delta_n = math.lcm(p - 1, q - 1)
+
+  # Step 4: Choose an integer e such that 1 < e < λ(n) and gcd(e, λ(n)) = 1; that is, e and λ(n) are coprime.
+  e = 65537
+
+  # Step 5: Determine d as d ≡ e^(-1)(mod λ(n)); that is, d is the modular multiplicative inverse of e modulo λ(n).
+  _, x, _ = extended_gcd(e, delta_n)
+  d = x % delta_n
+
+  return (n, e, d)
+
+
+def main():
+  (n, e, d) = generate()
+  print(f'n: {n}')
+  print(f'e: {e}')
+  print(f'd: {d}')
+
+
+if __name__ == '__main__':
+  main()