Write down the RSA Algorithm

RSA Algorithm :

                                         The Rivest-Shamir-Adleman(RSA) algorithm is one of the most popular and secure public-key encryption methods. The algorithms capitalizes on the fact that there is n no efficient way to factor very large(100-200) digit numbers.

using as encryption key(e,n) the algorithm is as follows

1.Represent the message as an integer between 0 and (n-1). Large messages can be broken up into a number of blocks.Each block would then be represented by an integer in the same range.

2. Encrypt the message by raising it to the eth power module n. The result is a ciphertext message C.

3. To decrypt ciphertext message C, raise it to another power d module n.

The encryption key (e,n) is made public.The decryption key(d,n) is kept private by the user.The keys for the RSA algorithm are generated the following way :

(i) Choose two different large random prime numbers p and q.

(ii) Set n equals to p*q[(n=pq)]

where n is the modules for the public and private key

(iii) Choose any large integer, d, such that GCD(d,(p-1)*(q-1)) = 1

(iv) Find e such that e8d = 1(mod((p-1)*(q-1)))

Rivest shamir and adleman provide efficient algorithms for each required operation.