Q2. Application of Digital Signature

The working procedure of the digital signature is illustrated in Figure-2. It is recommended that you use the concept of digital signature to answer both Q2(a) and Q2(b). 

(a) Digital signature for large text message

Suppose Bob (the sender) wants to send a large text message M to Alice (the receiver). The text message M is as follows (in bold and italic face):

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1st Prime number: p = 430620674058481288123238045697123658933

2nd Prime number: q = 124566090654136987961913344431645866767

Public key parameter: e=23

In this task, you need to show how Alice generates digital signature for a large text message and Bob verifies the signature using RSA based digital signature scheme. To do this:

i. Show how Alice would generate Public and Private keys.

ii. Show how Alice would generate the digital signature for M.

iii. Show how Bob would verify the digital signature using Alice’s public-key.

iv. Do you think that RSA based digital signature can be forged? Justify why or why not.

Use the following links:

For generating MD5 hash: http://www.miraclesalad.com/webtools/md5.php

For converting hexadecimal to decimal and vice versa:

https://www.mobilefish.com/services/big_number/big_number.php

For performing large integer operations (power mod, inverse mod, LCM, GCD, Multiplication):

https://www.mobilefish.com/services/big_number_equation/big_number_equation.php ] 

(b) ElGamal based digital signature scheme

Recently, Charlie has developed a software for Alice’s Restaurant. Alice emails the payable amount (M) to her manager Bob. To ensure the integrity and authenticity, Alice generates a digital signature for the above amount with ElGamal based digital signature scheme and sends the signed message to Bob via email. Alice chooses ElGamal public key (i.e., modulus p and generator g) and private-key (i.e., secret number x). Bob chooses a random number k. The equivalent decimal numbers as follows:

M = 2300, p = 191447, g = 425, x = 1998, k = 2813

In this task, you need to show how Alice generates digital signature and Bob verifies the payable amount using ElGamal based digital signature scheme. To do this:

i. Show how Alice would generate Public and Private keys.

ii. Show how Alice would generate the digital signature for M.

iii. Show how Bob would verify the digital signature using Alice’s public-key.

iv. Does ElGamal Signature approach prevent cheating on digital signature? Justify why or why not.

Use the following links: For performing large integer operations (power mod, inverse mod, LCM, GCD, Multiplication): https://www.mobilefish.com/services/big_number_equation/big_number_equation.php ]