Rsa Algorithm Essay

INTRODUCTION

RSA Algorithm was discovered by a group of three scientists namely Ron Rivest,Adi Shamir and Len Adleman and was first published in 1978.

The RSA scheme is a block cipher in which the plain text and cipher text are integers between 0 and n-1 for some n.
A Typical size of n is 1024 bits or 309 decimal digits.
This is a public key encryption scheme.

In this scheme two pairs of integers {e, n} and {d, n} are used. First of them i.e. {e.n} is called the RSA public key and the other one i.e. {d, n} is called the RSA secret key.

The sender uses the public key and encrypts the message say M into cipher text as –

C = M^e mod n.
Where C is the cipher text and M is the message or the plane text
At the receiving end the receiver accept the cipher text C and decrypt the C into M using secret key {d, n}-

M = C^d mod n.

Example:
Let , e=3, d=7, n=33. Suppose the message is ‘SUN’ and we use the numeric values of the characters according to their serial in alphabets.

Plaintext Ciphertext(C) after decryption

Sym num M^3 M^3 mod33 C^7 C^7mod33 sym S 19 6859 28 13492928512 19 S U 21 9261 21 1801088541 21 U N 14 2744 5 78125 14 N

KEY GENERATION

The process of Key Generation contain the following steps

1- Select two prime numbers say p and q randomly Where p ≠ q.

2- Calculate- n = p *q. 3- Calculate Ø(n) = (p-1) (q-1) Note- What is Ø(n)?
Ø(n) is called the Euler’s Totient function. It is the no. of positive integers that are