Initial commit

2020/day25/day25.c

@@ -0,0 +1,51 @@
+#include <math.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+#define MODULO 20201227UL
+#define PUB1 3248366UL
+#define PUB2 4738476UL
+
+unsigned long modexp(unsigned long a, unsigned long b, unsigned long n) {
+  if (b == 0) {
+    return (n == 1) ? 0 : 1;
+  }
+  if (b == 1) {
+    return a % n;
+  }
+  if (b % 2 == 0) {
+    unsigned long c = modexp(a, b / 2, n);
+    return (c * c) % n;
+  }
+  return (a * modexp(a, b - 1, n)) % n;
+}
+
+unsigned long discrete_logarithm(unsigned long a, unsigned long b,
+                                 unsigned long n) {
+  unsigned long m = ceil(sqrt(n));
+  unsigned long *table = calloc(n, sizeof(unsigned long));
+
+  for (size_t j = 0; j < m; ++j) {
+    table[modexp(a, j, n)] = j;
+  }
+  unsigned long t = modexp(a, n - m - 1, n);
+
+  unsigned long res = 0;
+  unsigned long c = b;
+  for (size_t i = 0; i < m; ++i) {
+    if (table[c] != 0) {
+      res = table[c] + i * m;
+      break;
+    }
+    c = (c * t) % n;
+  }
+  free(table);
+  return res;
+}
+
+int main(int argc, char *argv[]) {
+  unsigned long priv1 = discrete_logarithm(7, PUB1, MODULO);
+  printf("%lu\n", modexp(PUB2, priv1, MODULO));
+
+  return EXIT_SUCCESS;
+}

2020/day25/day25.rkt

@@ -0,0 +1,36 @@
+#lang racket/base
+
+(module+ test
+  (require rackunit))
+
+(define (modular-expt a b n)
+  (if (= b 0)
+      (if (= 1 n) 0 1)
+      (let loop ([b b])
+        (cond
+          [(= b 1) (modulo a n)]
+          [(even? b) (define c (loop (quotient b 2)))
+                     (modulo (* c c) n)]
+          [else (modulo (* a (loop (sub1 b))) n)]))))
+
+;; https://en.wikipedia.org/wiki/Baby-step_giant-step
+(define (discrete-logarithm a b n)
+  (define m (inexact->exact (ceiling (sqrt n))))
+  (define h (for/hash ([j (in-range m)])
+              (values (modular-expt a j n) j)))
+  (define t (modular-expt a (- n m 1) n))
+  (let loop ([c b]
+             [i 0])
+    (if (hash-has-key? h c)
+        (+ (hash-ref h c) (* i m))
+        (loop (modulo (* c t) n) (add1 i)))))
+
+(define (part1 public1 public2)
+  (define private1 (discrete-logarithm 7 public1 20201227))
+  (modular-expt public2 private1 20201227))
+
+(module+ test
+  (check-equal? (part1 5764801 17807724) 14897079))
+
+(module+ main
+  (displayln (part1 3248366 4738476)))

2020/day25/input

@@ -0,0 +1,2 @@
+3248366
+4738476