Dachshund Attacks

dachshund_attacks/sol.py

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+#!/home/maxime/.pyvenv/bin/python3
+from sympy import Rational, Symbol, solve
+from sympy.ntheory.continued_fraction import continued_fraction, continued_fraction_convergents
+from pwn import *
+
+conn = connect("mercury.picoctf.net", 30761)
+conn.recvuntil(b':')
+e = int(conn.recvline().strip())
+conn.recvuntil(b':')
+n = int(conn.recvline().strip())
+conn.recvuntil(b':')
+c = int(conn.recvline().strip())
+conn.close()
+
+print("n =", n, '\n')
+print("e =", e, '\n')
+print("c =", c, '\n')
+
+
+cont_frac = continued_fraction(Rational(e, n))
+convergents = continued_fraction_convergents(cont_frac)
+
+
+for convergent in convergents:
+    if convergent.p == 0:
+        continue
+    pk = convergent.p
+    pd = convergent.q
+    pphi = (e*pd - 1)//pk
+
+    p = Symbol('p', integer=True)
+    roots = solve(p**2 + (pphi - n - 1)*p + n, p)
+
+    if len(roots) == 2:
+        pp, pq = roots
+        if pp*pq == n:
+            print("factorized!")
+            P = pow(c, pd, n)
+            print(P.to_bytes((P.bit_length()+7)//8, byteorder='big'))
+            break
+
+