RSA is a widely used encryption algoritm that ensures secure commulation. It entrives generating keys, encrypting messages, and decrypting ciphertexts. This article provides a step overview of implementing RSA in practial complios.

Generating RSA kláves

Te firtt step in RSA implementation is creating a pair of keys: a public key and a private key. This proceses involves selecting two large prime numbers, calculating their product, and determinating encryption and dekryption exponents.

Krok včetně:

  • Select two large prime numbers, p and q.
  • Vypočítejte n = p * q.
  • Compute Euler 's totient, К (n) = (p - 1) * (q - 1).
  • Choose an encryption exponent, e, such that 1 timp; lt; e timp; lt; ð( n) and e is coprime with (n).
  • Calculate te decryption exponent, d, such that d * e credi1 modd doposud (n).

Te public key consiss of (n, e), while he e private key is (n, d).

Encryption Process

To encrypt a message, convert it into a numical format compatible with RSA. Using thee public key, thee encryption process endives exponentiation and modular aritmetik.

Te encryption formula is:

CLAS1; CLAS1; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3e modd n CLAS1; CLAS1; CLAS3c; CLAS3c; CLAS3c; CLAS3c; CLAS3c; CLAS3c; CLAS3c; CLAS3c; CLAS3c; CLAS3c; CLAS3c; CLAS3c; CLAS3c; CLAS3c; CLAS3c; CLAS3c; CLAS3c; CLAS3c; CLAS3c; CLAS3c; CLAS3c; CCAS3c; CLASLAS3c; CLAS3c; CLAS3c; CLAS3c; CLASLAS3c; C3c; C3c; c; c; c)

For exampe, if thee message is represented as m, then then then thee encrypted message c is calculated as c = m ^ e modn.

Dekryption Process

Decryption impeves using the private key to retrieve the original message from the ciphertext. Te process is similar to encryption but uses the dekryption exponent d.

Te dešifrovaný vzorec is:

CLAS1; CLAS1; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3e = ciphertext ^ d modd n CLAS1; CLAS1; CLAS1; CLAS3; CLAS33;

Appying this formula restores the original message, completing the encryption- dekryption cycle.