From 7eaa29680eba15b98b02c9b35f5d301fb053fd62 Mon Sep 17 00:00:00 2001
From: ware255 <ware255@076.ne.jp>
Date: Sun, 1 Jan 2023 14:27:24 +0900
Subject: [PATCH] =?UTF-8?q?''=20=E3=81=AB=E3=83=95=E3=82=A1=E3=82=A4?=
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C++で書かれています。
---
 main.cpp | 183 +++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 183 insertions(+)
 create mode 100644 main.cpp

diff --git a/main.cpp b/main.cpp
new file mode 100644
index 0000000..68c287b
--- /dev/null
+++ b/main.cpp
@@ -0,0 +1,183 @@
+#include <cstdio>
+#include <random>
+using bint = unsigned long long;
+
+class crypto {
+private:
+    bint p, q, n, l, e, d;
+    bint M, MAX;
+public:
+    void init();
+    crypto() {
+        MAX = 8000000;
+        init();
+    }
+    bint extended_euclidean(bint&, bint&);
+    bint gcd(bint, bint);
+    bint lcm(bint, bint);
+    bint modPow(bint, bint, bint);
+    bint modinv(const bint&, const bint&);
+    bint Chinese_Remainder_Theorem(bint&, bint&, bint&, bint&);
+    void start();
+};
+
+bint crypto::extended_euclidean(bint& a, bint& b) {
+    bint x = 1, y = 0, u = 0, v = 1, s = a, t = b;
+    bint k = 0, tmp = 0;
+    while (t) {
+        k = s / t;
+        s -= k * t;
+        tmp = s;
+        s = t;
+        t = tmp;
+        x -= k * u;
+        tmp = x;
+        x = u;
+        u = tmp;
+        y -= k * v;
+        tmp = y;
+        y = v;
+        v = tmp;
+    }
+    if (x > y) return y;
+    return x;
+}
+
+bint crypto::gcd(bint x, bint y) {
+    while (1) {
+        if (y == 0) return x;
+        x = x % y;
+        if (x == 0) return y;
+        y = y % x;
+    }
+}
+
+bint crypto::lcm(bint a, bint b) {
+    return a * b / gcd(a, b);
+}
+
+bint crypto::modPow(bint a, bint k, bint n) {
+    a %= n;
+
+    if (a == 0 || n == 0) return 0;
+    if (k == 0) return 1 % n;
+
+    bint i;
+    bint value = 1;
+    for(i = 0; i < k; i++) {
+        value *= a;
+        if(value >= n) {
+            value %= n;
+        }
+    }
+    return value;
+}
+
+bint crypto::modinv(const bint &a, const bint &m) {
+    bint j = 1, i = 0, b = m, c = a, x, y;
+    while (c != 0) {
+        x = b / c;
+        y = b - x*c;
+        b = c;
+        c = y;
+        y = j;
+        j = i - j*x;
+        i = y;
+    }
+    if (i < 0) i += m;
+    return i;
+}
+
+bint crypto::Chinese_Remainder_Theorem(bint &p, bint &q, bint &c, bint &d) {
+    bint m1, m2, dp, dq, qinv, m, h;
+    qinv = modinv(q, p);
+
+    dp = d % (p-1);
+    dq = d % (q-1);
+
+    m1 = modPow(c, dp, p);
+    m2 = modPow(c, dq, q);
+
+    h = qinv * (m1 - m2);
+    m = m2 + h * q;
+    return m;
+}
+
+void crypto::init() {
+    bint* sieve = new bint[MAX];
+    for (size_t i = 0; i < MAX; i++) sieve[i] = true;
+    bint tmp;
+    sieve[1] = false;
+    for(size_t i = 3; i <= MAX; i+=2) {
+        if(sieve[i]) {
+            for(size_t j = 2 * i; j <= MAX; j += i) {
+                sieve[j] = false;
+            }
+        }
+    }
+    std::random_device rnd;
+    std::mt19937_64 mt(rnd());
+    std::uniform_int_distribution<> rand(300000, MAX);
+    tmp = rand(mt);
+    while (1) {
+        if (sieve[tmp]) {
+            p = tmp;
+            break;
+        }
+        tmp += 1;
+    }
+    tmp = rand(mt);
+    while (1) {
+        if (sieve[tmp]) {
+            q = tmp;
+            break;
+        }
+        tmp += 1;
+    }
+    if (p < q) {
+        tmp = p;
+        p = q;
+        q = tmp;
+    }
+    delete [] sieve;
+}
+
+void crypto::start() {
+    while (1) {
+        n = p * q;
+
+        l = lcm(p-1, q-1);
+
+        e = 65535;
+        while (gcd(l, e) != 1) {
+            e++;
+        }
+
+        d = extended_euclidean(l, e);
+        if (((e * d) % l) == 1) break;
+        init();
+    }
+    printf("P : %lld   Q : %lld\n", p, q);
+
+    printf("N : %lld   L : %lld   E : %lld   D : %lld\n", n, l, e, d);
+
+    bint plain_num;
+    printf("plain_num : ");
+    scanf("%llu", &plain_num);
+
+    //暗号化
+    bint encrypted_num = modPow(plain_num, e, n);
+    printf("encrypted_num: %llu\n", encrypted_num);
+
+    //復号
+    M = Chinese_Remainder_Theorem(p, q, encrypted_num, d);
+    printf("decrypted_num(CRT): %llu\n", M);
+}
+
+int main() {
+    crypto* t;
+    t = new crypto();
+    t->start();
+    delete t;
+    return 0;
+}
\ No newline at end of file