RSA Algorithm with solved Example | e-Commerce

RSA Algorithm with solved Example | e-Commerce
RSA is an algorithm used by modern computers to encrypt and decrypt messages. It is an asymmetric cryptographic algorithm. Asymmetric means that there are two different keys. This is also called public key cryptography, because one of the keys can be given to anyone. The other key must be kept private.
Since this is asymmetric, nobody else except browser can decrypt the data even if a third party has public key of browser.
I. Choose two distinct prime numbers p and q.

II. Find n such that n = pq.

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

III. Find the totient of n, ϕ(n)

ϕ(n)=(p-1)(q-1).

IV. Choose an e such that ϕ(n) share no divisors other than 1 (e and ϕ(n) are relatively prime).
e is kept as the public key exponent.

V. Determine d (using modular arithmetic) which satisfies the congruence relation

de ≡ 1 (mod ϕ(n)).

In other words, pick d such that de - 1 can be evenly divided by (p-1)(q-1), the totient, or ϕ(n).
This is often computed using the Extended Euclidean Algorithm, since e and ϕ(n) are relatively prime and d is to be the modular multiplicative inverse of e.
d is kept as the private key exponent.

The public key has modulus n and the public (or encryption) exponent e. The private key has modulus n and the private (or decryption) exponent d, which is kept secret.

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