From ca4efb2ab8d06f711d4cc2e0dd655c2e1f5d01e2 Mon Sep 17 00:00:00 2001
From: Maxime Vorwerk <Maxime Vorwerk>
Date: Thu, 6 Jun 2024 13:03:19 +0200
Subject: [PATCH] Mind your Ps and Qs

---
 mind_your_ps_and_qs/sol.py | 55 ++++++++++++++++++++++++++++++++++++++
 mind_your_ps_and_qs/values |  7 +++++
 2 files changed, 62 insertions(+)
 create mode 100755 mind_your_ps_and_qs/sol.py
 create mode 100755 mind_your_ps_and_qs/values

diff --git a/mind_your_ps_and_qs/sol.py b/mind_your_ps_and_qs/sol.py
new file mode 100755
index 0000000..4f18b61
--- /dev/null
+++ b/mind_your_ps_and_qs/sol.py
@@ -0,0 +1,55 @@
+#!/usr/bin/python3
+import math
+
+def totient(p, q):
+    tot, rem = divmod((p-1) * (q-1), math.gcd(p-1, q-1))
+    if rem != 0:
+        raise Exception("totient calc failed")
+    return tot
+
+def egcd(a, b):
+    x0, x1, y0, y1 = 0, 1, 1, 0
+    while a != 0:
+        (q, a), b = divmod(b, a), a
+        y0, y1 = y1, y0 - q * y1
+        x0, x1 = x1, x0 - q * x1
+    return b, x0, x1
+
+# https://en.wikibooks.org/wiki/Algorithm_Implementation/Mathematics/Extended_Euclidean_algorithm
+def mod_inv(d, lambda_n):
+    g, x, _ = egcd(d, lambda_n)
+    if g != 1:
+        raise Exception("gcd(d, lambda_n != !")
+    return x % lambda_n
+
+def rsa(text, key, n):
+    return pow(text, key, n)
+
+with open("values", 'r') as f:
+    lines = f.readlines()
+
+    C = int(lines[1][3:])
+    n = int(lines[2][3:])
+    e = int(lines[3][3:])
+    p = int(lines[4][3:])
+    q = int(lines[5][3:])
+
+    if p*q == n:
+        print("factoring correct")
+    else:
+        print("factoring incorrect")
+
+    lambda_n = totient(p, q)
+
+    d = mod_inv(e, lambda_n)
+    #d = pow(d, -1, lambda_n)
+
+    res = rsa(C, d, n)
+
+    text = ''
+    while (char := (res % 256)) != 0:
+        text = chr(char) + text;
+        res >>= 8
+
+    print(text)
+
diff --git a/mind_your_ps_and_qs/values b/mind_your_ps_and_qs/values
new file mode 100755
index 0000000..2ecd5d8
--- /dev/null
+++ b/mind_your_ps_and_qs/values
@@ -0,0 +1,7 @@
+Decrypt my super sick RSA:
+c: 861270243527190895777142537838333832920579264010533029282104230006461420086153423
+n: 1311097532562595991877980619849724606784164430105441327897358800116889057763413423
+e: 65537
+p: 1955175890537890492055221842734816092141
+q: 670577792467509699665091201633524389157003
+factored using factordb.com