readme

Author: sagi

2016/wiener-rsa-attack/vulnerable_key.py

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+import gmpy2, random
+from gmpy2 import isqrt, c_div
+# Adapted from Hack.lu 2014 CTF
+
+urandom = random.SystemRandom()
+
+def get_prime(size):
+    while True:
+        r = urandom.getrandbits(size)
+        if gmpy2.is_prime(r): # Miller-rabin
+            return r
+
+def test_key(N, e, d):
+    msg = (N - 123) >> 7
+    c = pow(msg, e, N) 
+    return pow(c, d, N) ==  msg
+
+def create_keypair(size):
+    while True:
+        p = get_prime(size // 2)
+        q = get_prime(size // 2)
+        if q < p < 2*q:   
+            break
+
+    N = p * q
+    phi_N = (p - 1) * (q - 1)
+   
+    # Recall that: d < (N^(0.25))/3
+    max_d = c_div(isqrt(isqrt(N)), 3)
+    max_d_bits = max_d.bit_length() - 1
+
+    while True:
+        d = urandom.getrandbits(max_d_bits)
+        try:
+            e = int(gmpy2.invert(d, phi_N))
+        except ZeroDivisionError:
+            continue
+        if (e * d) % phi_N == 1:
+            break
+    assert test_key(N, e, d)
+    
+    return  N, e, d, p, q

README.md

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+Code for blog entries.
+