The Beautiful world of Cryptography -RSA

If you are into cyber security, you probably will have know what RSA means.According to wikipedia,
RSA (Rivest–Shamir–Adleman) is one of the first public-key cryptosystems and is widely used for secure data transmission. In such a cryptosystem, the encryption key is public and it is different from the decryption key which is kept secret (private). In RSA, this asymmetry is based on the practical difficulty of the factorization of the product of two large prime numbers, the "factoring problem". The acronym RSA is made of the initial letters of the surnames of Ron Rivest, Adi Shamir, and Leonard Adleman, who first publicly described the algorithm in 1978. Clifford Cocks, an English mathematician working for the British intelligence agency Government Communications Headquarters (GCHQ), had developed an equivalent system in 1973, but this was not declassified until 1997.

The beauty of cryptography is that you don't need to hide the data,the data is visible to everyone can but only the person with the key and decipher it.

The key generation in RSA is done by
1.Choose two distinct prime numbers p and q.
2.Compute n = pq.

n is used as the modulus for both the public and private keys.

1. Choose an integer e such that 1 < e < λ(n) and gcd(e, λ(n)) = 1; i.e., e and λ(n) are coprime.
   Determine d as d ≡ e−1 (mod λ(n)); i.e., d is the modular multiplicative inverse of e modulo λ(n).

This means: solve for d the equation d⋅e ≡ 1 (mod λ(n)).

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