Question

Alice wants to use the ElGamal digital signature scheme with public parameters p = 47, α = 2, secret value\alpha =7 and \beta =34. She wants to sign the message M = 20 and send it to Bob. She chooses k = 5 as the secret value. Explain the procedure that Alice will use for computing the signature of the message. What information will she send Bob?

10 Mar 2024
Answer :
Word Count : 534
To compute the signature of the message using the ElGamal digital signature scheme, Alice will follow these steps: ### 1. Parameters Setup - \( p = 47 \) (prime number) - \( \alpha = 2 \) (primitive root modulo \( p \)) - Alice's secret key \( \beta = 34 \) - Alice's secret \( \alpha = 7 \) (this is the private key, which we can use to compute the public key \( \beta = \alpha^{\alpha} \mod p \)) - Message \( M = 20 \) that Alice wants to sign. - \( k = 5 \), which Alice selects as a secret value for this particular signature. ### 2. Signature Computation The signature consists of two components: \( r \) and \( s \). #### Step 2.1: Compute \( r \) _________ ___ ___ _________ _____ ____ ______ _________ ________.
___ ____ _______ _________ ________ _____ _________ ________ _____ ________ ________ ____.
_________ _________ ____ __________ ________ ____ _____ _______ ______ ______ _________ ____.
_______ ______ __________ __________ _________ _____.
_____ _______ _________ _______ _________ ____ _________ ____ _____ ___ _________.
_____ _______ ________ ___ ______ ___ __________ __________ ____ _____.
____ ___ ___ ___ ___ _______ _________ ________ ______ ________ ______ _____.
______ _________ ________ ____ ____ _________ ______ _______ _____.
__________ _____ _______ _____ ____.
_________ ____ ________ _____ _____ _________.
________ _______ __________ _____ _____ __________ _________ ______ _________ _______ ___.
______ __________ ______ __________ __________ _____ _____.
________ ____ ____ ________ ____ _________ ____ _________ ____ __________.
_________ ______ _______ ________ ____ ________ ________ _______ _________.
____ __________ __________ _______ _________ ________ ______.
______ ____ ________ ___ _______ __________ _______ ________ __________ ____ ______ ________.
____ _____ _______ ___ _____ ______ ___.
________ _______ _________ ________ ___ _________ _________ ________ ______ ________ ________.
__________ ______ ___ _________ __________ ____ _________ __________.
________ ___ _______ _______ _____ _______ ________ _______ ________ _____ ____.
__________ _________ ________ _______ ____ _________ ____ ____ _________.
__________ _____ _________ _________ ___ ____ ____ _______ ______ __________ __________.
___ __________ ____ _____ ________.
______ __________ _____ ____ ___.
_____ __________ _________ ___ ___ _____.
_____ __________ _____ ________ ____ _____ ____ _____ ______ _______.
__________ _______ ____ _____ ______.
____ _______ ________ ____ _____ _______ _______.
_______ ______ ______ _______ ____ _______ ____ _____ ________ ________.
_______ ________ __________ __________ ____ ______ _______ ____ ___ ______.
________ ______ ________ ______ _______ ______ __________ _________ ______ _______ ____.
___ _____ _______ ___ __________ ___ ______ ____ __________.
_________ ______ __________ _______ ____ ___ ________ __________.
_____ _______ ________ _____ _______ _________.
__________ ______ _______ ________ __________ _______.
___ ______ _____ ___ _________ ______ _________ ___ ______ ____.
__________ _________ ___ ________ ______ ________ ______ ______ ______ _________ ___.
__________ _____ ________ ________ ______ ________ _______ _________ _______ ___ _______.
_________ _________ _______ _____ __________ _________ __________.
___ _________ ________ ___ ______ ______ ______ _________ __________ ___ _________ ____.
____ _______ ________ _______ _____ _________ ___.
_______ ____ ________ ________ ______ __________ ________.
_______ _______ __________ _______ ______ ____ _____ ________ ____.
________ ___ _____ ____ _____ ______ _________.
______ ___ __________ ______ ____ _________ __________ ______ _________.
_______ ______ ________ _____ ______ ____ _______ _________.
Get Full Answer on WhatsApp
Related Questions

Text:"KSTYZKESLNZUV", encrypted with Vigenère cipher with key "RESULT"

Text: "CBBGYAEBBFZCFEPXYAEBB", encrypted with affine cipher with key (7,2)

Alice wants to use the Digital Signature algorithm for signing messages. She chooses p = 83, q = 41, g = 2 and a = 3. Alice wants to sign the message M = 20. She chooses the secret value k = 8. Explain the procedure that Alice will use for computing the signature. What information will she send Bob?

a) Decrypt the ciphertext 101000111001 which was encrypted with the Toy block cipher once
using the key 101010010. Show all the steps. (5)
b) A 64 bit key for the DES is given below
    11000111 10000101
    11110111 11000001
    11111011 10101011
    10011101 10010001
i) Check whether the key is error free using the parity bits.
ii) Find the keys for the second round.

Alice wants to use the ElGamal digital signature scheme with public parameters p = 47, α = 2, secret value\alpha =7 and \beta =34. She wants to sign the message M = 20 and send it to Bob. She chooses k = 5 as the secret value. Explain the procedure that Alice will use for computing the signature of the message. What information will she send Bob?

In this exercise, we introduce you to Hill cipher. In this cipher, we convert our message to numbers, just as in affine cipher. However, instead of encrypting character by character, we encrypt pairs of characters by multiplying them with an invertible matrix with co-efficients in Z_{26} .

Here is an example: Suppose we want to ENCRYPT "ALLISWELL". Since we require the plaintext to have even number of characters, we pad the message with the character ‘X’. We break up the message into pairs of characters AL, LI, SW, EL and LX. We convert each pair of characters into a pair elements in Z_{26} as follows:

                       Image ignouassignments-ignouacademy-com--p-digital-98380

Next, we choose an inveritble 2×2 matrix with coefficients in Z_{26}, for example,A=\left [ \frac{3}{7}\, \frac{1}{4} \right ].

This matrix has determinant \bar{3},\bar{4}-\bar{7},\bar{1}=\bar{5}\, and\, \bar{5} and 5 is a unit in  Z_{26} with inverse \bar{21}. We write each pair of elements in Z_{26} as a column vector and multiply it by A:

A\left [ \frac{\bar{0}}{11} \right ]=\left [ \frac{\bar{11}}{18} \right ].A\left [ \frac{\bar{11}}{8} \right ]=\left [ \frac{\bar{15}}{5} \right ]....   

We then convert each pair of numbers to a pair of characters and write them down. In this example, we get the cipher text "LSPFYGXUEN" corresponding to the plain text "ALLWELL". To decrypt, we convert pairs of characters to pairs of numbers and multiply by A^{1}=\bar{5}^{-1} \left [ \frac{\bar{4}}{-7}\:\, \: \frac{\bar{-1}}{3} \right ]=\bar{21}\left [ \frac{\bar{4}}{-7}\, \, \, \frac{\bar{-1}}{3} \right ]=\left [ \frac{\bar{6}}{9}\: \, \, \frac{\bar{5}}{11} \right ]  and we have 

\left [ \frac{\bar{6}}{9}\, \, \bar{\frac{5}{11}} \right ]\left [ \frac{\bar{11}}{18} \right ]=\left [ \frac{\bar{0}}{18} \right ].... 

Decrypt the text "TWDXHUJLUENN" which was encrypted using the Hill’s cipher with the matrix \left [ \frac{\bar{3}}{0} \, \, \, \frac{\bar1}{9}\right ]  as the encryption matrix

i) Bob uses ElGamal cyrptosystem with parameters p = 47, g = 5 and the secret value
x = 3. What values will he make public? 
ii) Alice wants to send Bob the message M = 15. She chooses k = 5. How will she compute
the cipher text? What information does she send to Bob? 
iii) Explain how Bob will decrypt the message.

IGNOU Solved Assignments Assignments Ignou Projects Project Previous Year Solved Exam Papers Notes Notes Sample Question Papers Sample Question Papers
Login Cart
IGNOU NEWS
Assignment Submission Last Date Extended Till 30 June 2026 Click Here★★★IGNOU June 2026 TEE Date Sheet Released Click Here★★★
Top
📞
Call Support Instant phone assistance Alice wants to use the ElGamal digital signature scheme with public pa
→
🟢
WhatsApp Chat Fast live messaging
→
Email Us Business enquiries & support
→