Question

Alice is sending message “HIDE” to Bob. Perform encryption and decryption using RSA algorithm, with the following information: parameters p=11,q=5, e=7

Present all the information that you will need to encrypt and decrypt only the first letter from text

Answer 1

To perform encryption we have formula as

c = m^e mod n

Where n = pq = 55

Now Lets Encrypt the message first letter i.e. H

We write letters as number i.e. map A as 0 , B as 1 , C as 2 ............ Z as 25 .

So we have H = 8

Now lets apply the formula

8⁷ mod 55= 2 = B

Similarly we can do all other

I = 9 so we get 9⁷ mod 55 = 4 = E

Hence we get Encrypted text as = BEQX

Now lets Decrypt the message

To do so we need to get Private key d

To. Compute the secret exponent d, 1<d<ϕ, such that e*d ≡ 1 mod ϕ

where ϕ = (p-1) ( q-1) = 40

We get d = 23

Then we have to use the this formula for decryption m = C^d mod n

So Lets see the that we get decrypted message as HIDE or not

d = 2²³ mod 55 = 8 = H

4²³ mod 55 = 9 = I

Similarly we get decrypted message as HIDE which is same as original message

This is how we can do encryption and decryption in RSA algorithm

Thank You

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