Very Smooth

very_smooth/gen.py

@@ -0,0 +1,89 @@
+#!python3
+
+from binascii import hexlify
+from gmpy2 import *
+import math
+import os
+import sys
+
+if sys.version_info < (3, 9):
+    math.gcd = gcd
+    math.lcm = lcm
+
+_DEBUG = False
+
+FLAG  = open('flag.txt').read().strip()
+FLAG  = mpz(hexlify(FLAG.encode()), 16)
+SEED  = mpz(hexlify(os.urandom(32)).decode(), 16)
+STATE = random_state(SEED)
+
+def get_prime(state, bits):
+    return next_prime(mpz_urandomb(state, bits) | (1 << (bits - 1)))
+
+def get_smooth_prime(state, bits, smoothness=16):
+    p = mpz(2)
+    p_factors = [p]
+    while p.bit_length() < bits - 2 * smoothness:
+        factor = get_prime(state, smoothness)
+        p_factors.append(factor)
+        p *= factor
+
+    bitcnt = (bits - p.bit_length()) // 2
+
+    while True:
+        prime1 = get_prime(state, bitcnt)
+        prime2 = get_prime(state, bitcnt)
+        tmpp = p * prime1 * prime2
+        if tmpp.bit_length() < bits:
+            bitcnt += 1
+            continue
+        if tmpp.bit_length() > bits:
+            bitcnt -= 1
+            continue
+        if is_prime(tmpp + 1):
+            p_factors.append(prime1)
+            p_factors.append(prime2)
+            p = tmpp + 1
+            break
+
+    p_factors.sort()
+
+    return (p, p_factors)
+
+e = 0x10001
+
+while True:
+    p, p_factors = get_smooth_prime(STATE, 1024, 16)
+    if len(p_factors) != len(set(p_factors)):
+        continue
+    # Smoothness should be different or some might encounter issues.
+    q, q_factors = get_smooth_prime(STATE, 1024, 17)
+    if len(q_factors) != len(set(q_factors)):
+        continue
+    factors = p_factors + q_factors
+    if e not in factors:
+        break
+
+if _DEBUG:
+    import sys
+    sys.stderr.write(f'p = {p.digits(16)}\n\n')
+    sys.stderr.write(f'p_factors = [\n')
+    for factor in p_factors:
+        sys.stderr.write(f'    {factor.digits(16)},\n')
+    sys.stderr.write(f']\n\n')
+
+    sys.stderr.write(f'q = {q.digits(16)}\n\n')
+    sys.stderr.write(f'q_factors = [\n')
+    for factor in q_factors:
+        sys.stderr.write(f'    {factor.digits(16)},\n')
+    sys.stderr.write(f']\n\n')
+
+n = p * q
+
+m = math.lcm(p - 1, q - 1)
+d = pow(e, -1, m)
+
+c = pow(FLAG, e, n)
+
+print(f'n = {n.digits(16)}')
+print(f'c = {c.digits(16)}')