The message NOT NOW (numerically 131419131422) is to be sent to a user of the EIGamal system who has public key (37, 2, 18) and private key k = 17. If the integer j used to construct the ciphertext is changed over successive four-digit blocks from j = 13 to j = 28 to j = 11, what is the encrypted message produced? %3D %3D
The message NOT NOW (numerically 131419131422) is to be sent to a user of the EIGamal system who has public key (37, 2, 18) and private key k = 17. If the integer j used to construct the ciphertext is changed over successive four-digit blocks from j = 13 to j = 28 to j = 11, what is the encrypted message produced? %3D %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problems 10.3**
1. The message "REPLY TODAY" is to be encrypted in the ElGamal cryptosystem and forwarded to a user with public key (47, 5, 10) and private key \( k = 19 \).
(a) If the random integer chosen for encryption is \( j = 13 \), determine the ciphertext.
(b) Indicate how the ciphertext can be decrypted using the recipient’s private key.
2. Suppose that the following ciphertext is received by a person with ElGamal public key (71, 7, 32) and private key \( k = 30 \):
\[
\begin{align*}
(56, 45) & \quad (56, 38) & \quad (56, 29) & \quad (56, 03) \\
(56, 67) & \quad (56, 05) & \quad (56, 27) & \quad (56, 31) \\
(56, 38) & \quad (56, 29) & \\
\end{align*}
\]
Obtain the plaintext message.
3. The message "NOT NOW" (numerically 131419131422) is to be sent to a user of the ElGamal system who has public key (37, 2, 18) and private key \( k = 17 \). If the integer \( j \) used to construct the ciphertext is changed over successive four-digit blocks from \( j = 13 \) to \( j = 28 \) to \( j = 11 \), what is the encrypted message produced?
4. Assume that a person has ElGamal public key (2633, 3, 1138) and private key \( k = 965 \). If the person selects the random integer \( j = 583 \) to encrypt the message "BEWARE OF THEM", obtain the resulting ciphertext.
*Hint:*
\[
3^{583} \equiv 1424 \, (\text{mod} \, 2633), \quad 1138^{583} \equiv 97 \, (\text{mod} \, 2633).
\]
5.
(a) A person with public key (31, 2, 22)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66c7b497-dac7-4855-b923-2e60bbc73063%2F864e1ae3-4c94-4b0a-981a-22f43b3b01c0%2Fw8b5r3.jpeg&w=3840&q=75)
Transcribed Image Text:**Problems 10.3**
1. The message "REPLY TODAY" is to be encrypted in the ElGamal cryptosystem and forwarded to a user with public key (47, 5, 10) and private key \( k = 19 \).
(a) If the random integer chosen for encryption is \( j = 13 \), determine the ciphertext.
(b) Indicate how the ciphertext can be decrypted using the recipient’s private key.
2. Suppose that the following ciphertext is received by a person with ElGamal public key (71, 7, 32) and private key \( k = 30 \):
\[
\begin{align*}
(56, 45) & \quad (56, 38) & \quad (56, 29) & \quad (56, 03) \\
(56, 67) & \quad (56, 05) & \quad (56, 27) & \quad (56, 31) \\
(56, 38) & \quad (56, 29) & \\
\end{align*}
\]
Obtain the plaintext message.
3. The message "NOT NOW" (numerically 131419131422) is to be sent to a user of the ElGamal system who has public key (37, 2, 18) and private key \( k = 17 \). If the integer \( j \) used to construct the ciphertext is changed over successive four-digit blocks from \( j = 13 \) to \( j = 28 \) to \( j = 11 \), what is the encrypted message produced?
4. Assume that a person has ElGamal public key (2633, 3, 1138) and private key \( k = 965 \). If the person selects the random integer \( j = 583 \) to encrypt the message "BEWARE OF THEM", obtain the resulting ciphertext.
*Hint:*
\[
3^{583} \equiv 1424 \, (\text{mod} \, 2633), \quad 1138^{583} \equiv 97 \, (\text{mod} \, 2633).
\]
5.
(a) A person with public key (31, 2, 22)
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