feat: enable new langs (#42491)

Enable italian and portuguese

curriculum/challenges/italian/10-coding-interview-prep/project-euler/problem-182-rsa-encryption.md

@@ -0,0 +1,113 @@
+---
+id: 5900f4231000cf542c50ff35
+title: 'Problem 182: RSA encryption'
+challengeType: 5
+forumTopicId: 301818
+dashedName: problem-182-rsa-encryption
+---
+
+# --description--
+
+The RSA encryption is based on the following procedure:
+
+Generate two distinct primes `p` and `q`.
+Compute `n=p*q` and `φ=(p-1)(q-1)`.
+Find an integer `e`, `1 < e < φ`, such that `gcd(e,φ) = 1`
+
+A message in this system is a number in the interval `[0,n-1]`.
+A text to be encrypted is then somehow converted to messages (numbers in the interval `[0,n-1]`).
+To encrypt the text, for each message, `m`, c=m<sup>e</sup> mod n is calculated.
+
+To decrypt the text, the following procedure is needed: calculate `d` such that `ed=1 mod φ`, then for each encrypted message, `c`, calculate m=c<sup>d</sup> mod n.
+
+There exist values of `e` and `m` such that m<sup>e</sup> mod n = m.
+We call messages `m` for which m<sup>e</sup> mod n=m unconcealed messages.
+
+An issue when choosing `e` is that there should not be too many unconcealed messages.
+For instance, let `p=19` and `q=37`.
+Then `n=19*37=703` and `φ=18*36=648`.
+If we choose `e=181`, then, although `gcd(181,648)=1` it turns out that all possible messages
+m `(0≤m≤n-1)` are unconcealed when calculating m<sup>e</sup> mod n.
+For any valid choice of `e` there exist some unconcealed messages.
+It's important that the number of unconcealed messages is at a minimum.
+
+For any given `p` and `q`, find the sum of all values of `e`, `1 < e < φ(p,q)` and `gcd(e,φ)=1`, so that the number of unconcealed messages for this value of `e` is at a minimum.
+
+# --hints--
+
+`RSAEncryption` should be a function.
+
+```js
+assert(typeof RSAEncryption === 'function')
+```
+
+`RSAEncryption` should return a number.
+
+```js
+assert.strictEqual(typeof RSAEncryption(19, 37), 'number');
+```
+
+`RSAEncryption(19, 37)` should return `17766`.
+
+```js
+assert.strictEqual(RSAEncryption(19, 37), 17766);
+```
+
+`RSAEncryption(283, 409)` should return `466196580`.
+
+```js
+assert.strictEqual(RSAEncryption(283, 409), 466196580);
+```
+
+`RSAEncryption(1009, 3643)` should return `399788195976`.
+
+```js
+assert.strictEqual(RSAEncryption(19, 37), 17766);
+```
+
+# --seed--
+
+## --seed-contents--
+
+```js
+function RSAEncryption(p, q) {
+
+  return true;
+}
+
+RSAEncryption(19, 37);
+```
+
+# --solutions--
+
+```js
+function gcd(a, b) {
+    if (b)
+        return gcd(b, a % b);
+    else
+        return a;
+}
+
+function RSAEncryption(p, q) {
+    let phi = (p - 1) * (q - 1);
+
+    let best = Number.MAX_SAFE_INTEGER;
+    let sum = 0;
+
+    for (let e = 0; e < phi; ++e) {
+        if (!(gcd(e, phi) == 1))
+            continue;
+
+        let msg = (gcd(p - 1, e - 1) + 1) * (gcd(q - 1, e - 1) + 1);
+
+        if (best == msg) {
+            sum += e;
+        } else if (best > msg) {
+            best = msg;
+            sum = e;
+        }
+    }
+
+    return sum;
+}
+```