What is RSA algorithm?

RSA(Rivest–Shamir–Adleman) is an algorithm to encrypt and decrypt messages. It is an asymmetric cryptographic algorithm. There is a pair of public, private key and algorithm, the message is encrypted with the shared public key of receiver and decrypted by the private key of the receiver.

Example:

-   EncryptionKey => (5,14)
    Suppose a text to be encrypted is letter 'B' ->  2, then  2^5(mod 14)
    = 32(mod 14) = 4 (cyphertext). Where (e,N) that is 2^e(mod N) => (5,14)
    is encryption key


    DecriptionKey: (11, 14),
    4^11(mod 14) => 2 == B, where (d,N) that is 4^d(mod N) => (11, 14) is
    decription key

-   How does it work, what is the algoritm? There is no magic it is just
    simple mathematics:
    Take two prime numbers (numbers can be hundreds & hundreds digit long),
    I choose small number (for better explanation) (2,7) where p = 2, q = 7
    -   N = p * q => N = 14

    -   choose φ(N) = (p-1)(q-1)

    -   Now choose a number for encryption e where
        { 1 < e < φ(N) and coprime with N and φ(N)}
        1 < e < 6 =  2, 3, 4, 5
        number which is coprime with 14 and 6 is 5
        so our lock is (e,N) = (5,14)

    -   Now for decryption we choose d such that {d.e(mod φ(N))}
        that is -> d.5(mod 6) = 1
        the options could be -> 1.5(mod 6), 2.5(mod 6), 3.5(mod 6),
        4.5(mod 6),5.5(mod 6), 6.5(mod 6), 7.5(mod 6), 8.5(mod 6),
        9.5(mod 6), 10.5(mod 6), 11.5(mod 6), 12.5(mod 6) and so on ...

        I choose d = 11 that is 11.5(mod 6) which gives me the value 1.
        So the key is (11, 14)