huge commit

2026/cscg/crypto/rsa/challenge.py

@@ -0,0 +1,48 @@
+import random
+from functools import reduce
+from math import floor, log2
+
+from params import a, b, c, d, e, f, g, h, i, j, k, m, n, o, p, q, r, u, v, w
+
+
+# a < b => b
+# (a // b) * c + (a % b)
+def wut(a, b, c):
+    def wuuuuut(z):
+        if z <= b:
+            return z
+        x, y = divmod(z, b)
+        return wuuuuut(x * c + y)
+
+    return wuuuuut(a)
+
+
+def wutwut(a, b, c, d):
+    return reduce(
+        lambda x, y: (
+            wut(x * x, c, d) if not (b >> y) & 1 else wut(wut(x * x, c, d) * a, c, d)
+        ),
+        reversed(range(floor(log2(b)))),
+        wut(a, c, d),
+    )
+
+
+def rsa_decrypt(ciphertext):
+    s = wutwut(wut(ciphertext, o, p), a * b + c * d, o, p)
+    t = wutwut(wut(ciphertext, q, r), f * g + h * i, q, r)
+
+    x = s - t
+    y = (x * j + x * k) * u
+    x = y * r
+    y = t + v + y * m
+    return (y - x - w) % n
+
+
+# check if the code works correctly :)
+for _ in range(1000):
+    # encrypt 100 random plaintexts with public key
+    random_plaintext = random.randint(0, n - 1)
+    print(random_plaintext)
+
+    # verify that the decryption works correctly
+    assert rsa_decrypt(pow(random_plaintext, e, n)) == random_plaintext