# Understanding RSA Algorithm

RSA algorithm is a public key encryption technique and is considered as the most secure way of encryption. It was invented by Rivest, Shamir and Adleman in year 1978 and hence name RSA algorithm.

## Algorithm

The RSA algorithm holds the following features −

• RSA algorithm is a popular exponentiation in a finite field over integers including prime numbers.

• The integers used by this method are sufficiently large making it difficult to solve.

• There are two sets of keys in this algorithm: private key and public key.

You will have to go through the following steps to work on RSA algorithm −

### Step 1: Generate the RSA modulus

The initial procedure begins with selection of two prime numbers namely p and q, and then calculating their product N, as shown −

N=p*q


Here, let N be the specified large number.

### Step 2: Derived Number (e)

Consider number e as a derived number which should be greater than 1 and less than (p-1) and (q-1). The primary condition will be that there should be no common factor of (p-1) and (q-1) except 1

### Step 3: Public key

The specified pair of numbers n and e forms the RSA public key and it is made public.

### Step 4: Private Key

Private Key d is calculated from the numbers p, q and e. The mathematical relationship between the numbers is as follows −

ed = 1 mod (p-1) (q-1)


The above formula is the basic formula for Extended Euclidean Algorithm, which takes p and q as the input parameters.

## Encryption Formula

Consider a sender who sends the plain text message to someone whose public key is (n,e). To encrypt the plain text message in the given scenario, use the following syntax −

C = Pe mod n


## Decryption Formula

The decryption process is very straightforward and includes analytics for calculation in a systematic approach. Considering receiver C has the private key d, the result modulus will be calculated as −

Plaintext = Cd mod n