Very Smooth

very_smooth/sol.py

@@ -0,0 +1,65 @@
+#!python3
+from sage.all import *
+from pwn import *
+
+with open("output.txt", 'r') as f:
+    lines = f.readlines()
+    N = Integer(lines[0][4:].strip(), 16)
+    c = Integer(lines[1][4:].strip(), 16)
+log.info(f"N: {N}")
+log.info(f"c: {c}")
+
+e = Integer(0x10001)
+log.info(f"e: {e}")
+
+smooth_bound = 16
+loopmsg = log.progress("calculating p, q")
+interval = (0, smooth_bound)
+center = 0
+while True:
+    base = Integer(2)
+    M = 1
+    for p in Primes():
+	    if p >= smooth_bound:
+	        break
+	
+	    np = p
+	    while np+p < smooth_bound:
+	        np += p
+	
+	    M *= np
+    
+    g = gcd(pow(base, M, N)-1, N)
+    
+    if g == 1 and center == 0:
+        interval = (smooth_bound, smooth_bound*2)
+        smooth_bound *= 2
+    elif g == 1 and center != 0:
+        interval = (center, interval[1])
+        center = interval[0] + (interval[1] - interval[0])/2
+        smooth_bound = center
+    elif g == N and center == 0:
+        center = interval[0] + (interval[1] - interval[0])/2
+        smooth_bound = center
+    elif g == N and center != 0:
+        interval = (interval[0], center)
+        center = interval[0] + (interval[1] - interval[0])/2
+        smooth_bound = center
+    else:
+        loopmsg.success("factoring found")
+        p = int(g)
+        q = N // p
+        break
+
+assert p*q == N
+log.info(f"p: {p}")
+log.info(f"q: {q}")
+
+d = pow(e, -1, (p-1)*(q-1))
+log.info(f"d: {d}")
+
+m = pow(c, d, N)
+log.info(f"m: {m}")
+m_literal = pack(int(m), 'all', 'big', False)
+log.success(f"solution: {m_literal}")
+