gaspersic/freeCodeCamp
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

Feat: add new Markdown parser (#39800)

Browse Source 
and change all the challenges to new `md` format.
This commit is contained in:
Oliver Eyton-Williams
2020-11-27 19:02:05 +01:00
committed by GitHub
parent a07f84c8ec
commit 0bd52f8bd1
2580 changed files with 113436 additions and 111979 deletions
Download Patch File Download Diff File Expand all files Collapse all files

54
curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-182-rsa-encryption.md
View File

@ -1,50 +1,29 @@
---
id: 5900f4231000cf542c50ff35
challengeType: 5
title: 'Problem 182: RSA encryption'
challengeType: 5
forumTopicId: 301818
---
## Description
<section id='description'>
# --description--
The RSA encryption is based on the following procedure:
Generate two distinct primes p and q.Compute n=pq 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=me 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=cd mod n.
There exist values of e and m such that me mod n=m.We call messages m for which me 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 messagesm (0≤m≤n-1) are unconcealed when calculating me 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.
Choose p=1009 and q=3643.
Find the sum of all values of e, 1<e<φ(1009,3643) and gcd(e,φ)=1, so that the number of unconcealed messages for this value of e is at a minimum.
</section>
## Instructions
<section id='instructions'>
Find an integer e, 1&lt;e&lt;φ, such='' that='' gcd(e,φ)='1.' a='' message='' in='' this='' system='' is='' number='' the='' interval='' \[0,n-1].='' text='' to='' be='' encrypted='' then='' somehow='' converted='' messages='' (numbers='' \[0,n-1]).='' encrypt='' text,='' for='' each='' message,='' m,='' c='me' mod='' n='' calculated.='' decrypt='' following='' procedure='' needed:='' calculate='' d='' ed='1' φ,='' c,='' m='cd' n.='' there='' exist='' values='' of='' e='' and='' me='' call='' which='' unconcealed='' messages.='' an='' issue='' when='' choosing='' should='' not='' too='' many='' instance,='' let='' p='19' q='37.' φ='18\*36=648.' if='' we='' choose='' then,='' although='' gcd(181,648)='1' it='' turns='' out='' all='' possible='' messagesm='' (0≤m≤n-1)='' are='' calculating='' any='' valid='' choice='' some='' it's='' important='' at='' minimum.='' find='' sum='' e,='' 1&lt;e&lt;φ(1009,3643)='' so='' value='' &lt;='' section=''>&lt;/e&lt;φ,>
</section>
# --hints--
## Tests
<section id='tests'>
```yml
tests:
- text: <code>euler182()</code> should return 399788195976.
testString: assert.strictEqual(euler182(), 399788195976);
`euler182()` should return 399788195976.
```js
assert.strictEqual(euler182(), 399788195976);
```
</section>
# --seed--
## Challenge Seed
<section id='challengeSeed'>
<div id='js-seed'>
## --seed-contents--
```js
function euler182() {
@ -55,17 +34,8 @@ function euler182() {
euler182();
```
</div>
</section>
## Solution
<section id='solution'>
# --solutions--
```js
// solution required
```
</section>