Can you decipher the word ETP
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, Springer-Verlag].
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) = (p-1) * (q-1) 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 = re (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 = sd (modulo m).
This is the ASCII code of the original character.
- Is it a weakness to be a vengeful person?
- Theresa May will fall
- How do you breed fluffy cats
- What is Google for cell phones
- What's the best use of Vantablack
- Why do banks like Ripple crypto currency
- How can the atenolol tablet be used
- How are the sizes of the beer labels determined
- What is the green agenda
- How can I fix skin with a bad complexion?
- Can a cell be damaged?
- What is alluvial land
- How did Aizen become so powerful
- Why did John Wayne hate Clark Gable
- Are sunglasses good or bad
- Exists 1 farad capacitor
- When capitalism fails, what's next
- What is an early probation document
- Why don't Indians like the cosmos?
- How math formulas were discovered
- What do you eat on Easter Sunday
- What replaces the google inbox
- What is the slowest thing that has moved
- How can I remove facial hair naturally?