Sum-O-Primes

sum_o_primes/sol.py

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+#!python3
+from sage.all import *
+import pwn
+
+with open("output.txt", 'r') as f:
+    lines = f.readlines()
+    x = Integer(lines[0][4:], 16)
+    N = Integer(lines[1][4:], 16)
+    c = Integer(lines[2][4:], 16)
+
+pwn.log.info("x: {}".format(x))
+pwn.log.info("N: {}".format(N))
+pwn.log.info("c: {}".format(c))
+
+# n = p*q
+# x = p+q
+# -> n = p*(x-p)
+# -> n = px - p²
+# -> p² - px + n = 0
+# -> (p - x/2)² + n - x²/4 = 0
+# -> (p - x/2)² = x²/4 - n
+# -> p - x/2 = +- sqrt(x²/4 - n)
+# -> p = x/2 +- sqrt(x²/4 - n)
+
+disc = sqrt(pow(x, 2)//4 - N)
+p = x//2 + disc
+q = x//2 - disc
+# since (p, q) can be replaced by (q, p)
+assert p+q == x
+assert p*q == N
+pwn.log.success("calculated p and q")
+pwn.log.info("p: {}".format(p))
+pwn.log.info("q: {}".format(q))
+
+e = Integer(65537)
+d = pow(e, -1, (p-1)*(q-1))
+pwn.log.info("calculated d: {}".format(d))
+
+m = pow(c, d, N)
+m_literal = pwn.pack(int(m), 'all', 'big', False)
+pwn.log.success(m_literal.decode())
+