crypto/mind_your_ps_and_qs

crypto/mind_your_ps_and_qs/solve.py

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+#!/usr/bin/env nix-shell
+#!nix-shell -i sage -p sage
+
+from sage.all import *
+import time
+import sys
+
+c = 8533139361076999596208540806559574687666062896040360148742851107661304651861689
+n = 769457290801263793712740792519696786147248001937382943813345728685422050738403253
+e = 65537
+
+if len(sys.argv) >= 2 and sys.argv[1] == 'CACHE':
+  print('Using precalculated p & q')
+  p = 1617549722683965197900599011412144490161
+  q = 475693130177488446807040098678772442581573
+else:
+  print('Factorizing N')
+  # Takes about 7-8 minutes on my own pc
+  start = time.time()
+  factorization = ZZ(n).factor(algorithm='qsieve')
+  stop = time.time()
+  print(f"Took: {stop - start}")
+
+  p, q = [x[0] for x in list(factorization)]
+
+phi = (p - 1) * (q - 1)
+d = inverse_mod(e, phi)
+m = power_mod(c, d, n)
+
+print(m.to_bytes((m.bit_length() + 7) // 8, 'big').decode())

crypto/mind_your_ps_and_qs/values

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+Decrypt my super sick RSA:
+c: 8533139361076999596208540806559574687666062896040360148742851107661304651861689
+n: 769457290801263793712740792519696786147248001937382943813345728685422050738403253
+e: 65537