A (very) simple implementation of the RSA encryption algorithm in Dart. RSA is a widely used public-key cryptography algorithm that allows secure communication over an insecure channel.

There are several steps shown in this code in order to perform the RSA algorithm:

• Generate Public Key: The public key is generated using two prime numbers, p and q. The public key consists of the exponent e and the modulus n.
  • generatePublicKey(p, q)
• Encrypt Text: The plaintext is encrypted using the public key, resulting in the ciphertext.
  • encryptText(plainText, e, n)
• Generate Private Key: The private key is generated using the same prime numbers p and q, and the public key exponent e. The private key consists of the exponent d and the modulus n.
  • obtainPrivateKey(p, q, e)
• Decrypt Text: The ciphertext is decrypted using the private key, resulting in the original plaintext.
  • decryptText(cipherText, d, n)

The program uses two vital mathematical functions:

• findGcd(phiN, e): Finds the greatest common divisor (gcd) of two numbers using the Euclidean algorithm.
• bezout(phiN, e): Implements the Bézout's identity algorithm to find the private key exponent d. It is the reverse process of Euclid's algorithm, i.e., the findGcd function.

The main() function demonstrates the usage of the RSA algorithm by:

• Generating the public key (e, n).
• Encrypting a plainText using the public key.
• Generating the private key (d, n).
• Decrypting the cipherText using the private key.

The example values used in the main() function are:

public key <e, n> : < 7, 77 >
9 ^ 7 % 77
plain text: 9, cipherText: 37
private key <d, n>: < 9, 77 >
cipher text: 37, plain text: 9