2020 Day 25

Author: Programator2

2020/25a.py

@@ -0,0 +1,48 @@
+from math import ceil, sqrt
+
+
+# Baby-Step-Giant-Step implementation by 0xTowel
+# https://gist.github.com/0xTowel/b4e7233fc86d8bb49698e4f1318a5a73
+def bsgs(g, h, p):
+    '''
+    Solve for x in h = g^x mod p given a prime p.
+    If p is not prime, you shouldn't use BSGS anyway.
+    '''
+    N = ceil(sqrt(p - 1))  # phi(p) is p-1 if p is prime
+
+    # Store hashmap of g^{1...m} (mod p). Baby step.
+    tbl = {pow(g, i, p): i for i in range(N)}
+
+    # Precompute via Fermat's Little Theorem
+    c = pow(g, N * (p - 2), p)
+
+    # Search for an equivalence in the table. Giant step.
+    for j in range(N):
+        y = (h * pow(c, j, p)) % p
+        if y in tbl:
+            return j * N + tbl[y]
+
+    # Solution not found
+    return None
+
+
+def main():
+    mod = 20201227
+    card_pub = 3418282
+    door_pub = 8719412
+
+    card_loop = bsgs(7, card_pub, mod)
+    door_loop = bsgs(7, door_pub, mod)
+    print(card_loop)
+    print(door_loop)
+
+    # Check if the computation was correct
+    print(pow(7, card_loop, mod))
+    print(pow(7, door_loop, mod))
+
+    # This is the answer
+    print(pow(door_pub, card_loop, mod))
+    print(pow(card_pub, door_loop, mod))
+
+
+main()

README.org

@@ -3,7 +3,7 @@
   my answers.
 * Personal Stats 2020
   | Day |     Time |  Rank | Score |     Time |  Rank | Score |
-  |  25 |          |       |       |          |       |       |
+  |  25 | 00:32:11 |  2354 |     0 | 00:32:44 |  1968 |     0 |
   |  24 | 00:23:36 |  1362 |     0 | 01:21:19 |  2287 |     0 |
   |  23 | 00:53:56 |  2265 |     0 | 02:09:18 |  1579 |     0 |
   |  22 | 00:17:33 |  2337 |     0 | 01:50:06 |  2972 |     0 |