Can you decipher the word ETP
 
Step 2: The sender encrypts his message with the public key and sends the encrypted text back.  

The keys are generated with the following algorithm, which is based on number theory [more ... You can find an elementary proof in the book Barth, algorithms for beginners, SpringerVerlag].
First, two prime numbers p and q are chosen, which should have several hundred digits for a secure system. One multiplies this and forms m = p * q. From number theory we know that Euler's function φ (m) = (p1) * (q1) is the number of coprime numbers for m (a, b are coprime if the greatest common divisor gcd (a, b) = 1).
Next one chooses a number e that is smaller than φ and relatively prime to φ. The public key has already been created, it consists of the pair of numbers:
Public key: [m, e]
Here is an example with the small prime numbers p = 73 and q = 151:
m = 73 * 151 = 11023, & # 966 = 72 * 150 = 10800, e = 11 (chosen coprime to & # 966)
Public key: [m, e] = [11023, 11]
The private key then consists of the pair of numbers:
Private key: [m, d]
where for the number d must apply: (d * e) mod & # 966 = 1
(Since e and φ are relatively prime, Bézout's lemma from number theory says that the equation has at least one solution).
With your values for e and & # 966 you can determine the number d with a simple program by trying 100,000 values for d in a for loop.
You will receive several solutions (5891, 16691, 27491, 49091, etc.). In principle, you only need the first one to set the private key.
Private key: [m, d] = [11023, 5891]
The calculation of the private key is only so easy here because you know the numbers p and q and thus also the number & # 966. Without knowing these numbers, the private key can only be calculated with great effort
Be using the RSA algorithm numbers encrypted. To encrypt a text, you use the ASCII code of each character and use the public key [m, e] to form the encryption value s for the ciphertext according to the formula
s = r^{e} (modulo m).
You write these encryption numbers line by line in the file secret.txt.
In the decoder you read the numbers from the file secret.txt first in a list. To decrypt, use the private key to calculate the original number from the encryption number s according to the formula
r = s^{d} (modulo m).
This is the ASCII code of the original character.
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