RSA Algorithm

• Generating Key value pair with a multiple options for number of bits to choose from.
• Option to store Public and Private Key in .txt file.
• Encrypts a message (also gives option to import key stored by the same program)
• Option to store Encrypted Message in .txt file.
• Decrypts a message (also gives option to import key stored by the same program)

Implementation

I. Key Generation

Using CreateRandom Class

• Get two different large prime numbers p and q
  • Using Miller-Rabin Test

Using GenerateKeys Class

• Let n = p * q

• Let φ(n) = (p-1) * (q-1)

• Choose a small, odd integer number e, where 1 < e < φ(n) and e is a co-prime to φ(n).

  • Using Euclidean Algorithm
  • Check calculateEncryptionExponent() method

• Calculate the integer number d, where ed ≡ 1 mod φ(n) and 1 < d < φ(n).

  • Using Extended Euclidean Algorithm
  • Check calculateDecryptionExponent() method

• The public key of the RSA is the pair PK = (n, e)

• The secret key of the RSA is the pair SK = (n, e)

II. Encryption

Using FME Class

• To encrypt the message m (where m < n) using the public key PK = (n, e) following formula is used: (Fast Modular Exponent)

  c := EncPK(m) = m^e (mod n).
  

III. Decryption

Using FME Class

• To decrypt the secret message c using the secret key d following formula is used: (Fast Modular Exponent)

  m := DecSK(c) = c^d (mod n).