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chore: manual translations (#42811)

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Nicholas Carrigan (he/him)
2021-07-09 21:23:54 -07:00
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curriculum/challenges/italian/10-coding-interview-prep/project-euler/problem-182-rsa-encryption.md
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@ -10,26 +10,15 @@ dashedName: problem-182-rsa-encryption
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`
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.
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.
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.
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.