UGC NET CSE | August 2016 | Part 3 | Question: 30

Question

The plain text message $BAHI$ encrypted with $RSA$ algorithm using $e = 3, d = 7$ and $n = 33$ and the characters of the message are encoded using the values $00$ to $25$ for letters A to Z. Suppose character by character encryption was implemented. Then, the Cipher Text message is _____.

• A. ABHI
• B. HAQC
• C. IHBA
• D. BHQC

Answer 1

RSA
Encryption

1. Obtains the recipient B's public key (n, e).
2. Represents the plaintext message as a positive integer m, 1 < m < n
3. Computes the ciphertext c = m^e mod n.
4. Sends the ciphertext c to RECEIVER

Deryption

1. Uses his private key (n, d) to compute m = c^d mod n.
2. Extracts the plaintext from the message representative m.

For BAHI
A-1 ,B-2, C-3 , D-4,E-5,.... etc  (Message  Encoded Using 01-26)

B=>2=> 2⁷ mod 33 = 8 =>H
A => 1=>1⁷ mod 33 = 1 =>A
H =>8=> 8⁷ mod 33 = 17 =>Q
I=> 9=>9⁷ mod 33 = 3 => C
Cipher Text Message : HAQC

A-0 ,B-1, C-2 , D-3,E-4,.... etc  ( Message Encoded Using 00-25 as per question)

B=>1=> 1⁷ mod 33 = 0 =>B
A => 0=>0⁷ mod 33 = 1 =>A
H =>7=> 7⁷ mod 33 = 13 =>N
I=> 8=>8⁷ mod 33 = 17 => R
Cipher Text Message : BANR 

[ No options will be matched taking encoding scheme 00-25 as per the question ]

Comments

In public Key cryptography massage encryption is done with public key and in RSA public key is represented by symbol 'e' and private key as 'd'. in given question e=3 and d=7 so power of plaintext massage would be 3 not 7. C=P^3mod33

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it's wrong the right option is explained below see my comment there. B.t.w. 2⁷ mod 33 = 8 => .. who told so 128 Mod 33 =29(direct from calculator) 

='c'

Answer 2

question needs some minor correction (  A-Z  values must be from 1-26  )   else no option is correct 

formula for ciphertext is 

C=P^e mod n

where P=plain text (here its value is =2  as B is 2nd  alphabet )  here n=33 is given 

now e=3 is also given so

for B =2

C=2³ mod33 =8

now  alphabet with value 8 is  so B is mapped to H

for A =1

 C=1³ mod33 =1

so  A with value =1 is  mapped to A

for H  =8 

C=8³ mod33 => 512mod33=17  which corresponds to Q

and finally I with value 9 is 

C=9³ mod 33 =729 mod33 =3 map to C 

so ans will be option B  HAQC 

Comments

U r very much correct but not for the "question needs some minor correction (  A-Z  values must be from 1-26  ) " question is absolutely correct. They din't say that 00 is for A i.e. 'respectively'. Actually 00 is for Z which's by god's grace untouched. But A has '01' & 26 is unused value also remember it's modular calc. so 0 is must & 26 is just another value.