The algorithm was published in the 70’s by Ron Rivest, Adi Shamir, and Leonard Adleman.
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.
Steps 1. Select two prime numbers , I will pick 2 and 7 , lets call them p and q where
P = 2 and Q = 7
Step 2. Multiply P and Q to get modulus n = P * Q = 14
Step 3. Calculate L = (p-1)*(q-1) where l is count of all non common factors between 1 and 14.
L=[2,3,4,5]
Step 4: select a derived Number (e) which is Coprime with L (6) = L=[2,3,4,5] and the Modulus N= (14) , the answer is 5 , there’s no other possibility .
Step 5: Formulate the Public key
The specified pair of numbers n and e forms the RSA public key and it is made public as (e,N) i.e. (5,14).
Step 6: Formulate the Private Key
Private Key d is calculated from the numbers p, q and e. The mathematical relationship between the numbers is as follows −
ed mod (p-1) (q-1) = 1
5d mod 6 = 1
d = 11
Hence, (d,n) = (11,14)
Let’s suppose p is the plaintext and c is ciphertext then:
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
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