Alice forms a public key for the "textbook" El Gamal public-key encryption and signature schemes, where p = 1187 and g = 2, by choosing her private key as a = 234. 1. What is Alice's public key? 2. Encrypt the message M = 3 for Alice. 3. Generate a signature on the message M = 1234567 using the following simple hash function H: {0,1} → Z, such that H(M) = 3M +5 (mod p). 4. Verify that the signature you generated in the previous step is a valid signature.
Alice forms a public key for the "textbook" El Gamal public-key encryption and signature schemes, where p = 1187 and g = 2, by choosing her private key as a = 234. 1. What is Alice's public key? 2. Encrypt the message M = 3 for Alice. 3. Generate a signature on the message M = 1234567 using the following simple hash function H: {0,1} → Z, such that H(M) = 3M +5 (mod p). 4. Verify that the signature you generated in the previous step is a valid signature.
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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![**El Gamal Public-Key Encryption and Signature Scheme**
Alice forms a public key for the “textbook” El Gamal public-key encryption and signature schemes, where \( p = 1187 \) and \( g = 2 \), by choosing her private key as \( a = 234 \).
1. **What is Alice’s public key?**
2. **Encrypt the message \( M = 3 \) for Alice.**
3. **Generate a signature on the message \( M = 1234567 \) using the following simple hash function**
\[ H : \{0, 1\} \to \mathbb{Z}_p \text{ such that } H(M) = 3M + 5 \pmod{p}. \]
4. **Verify that the signature you generated in the previous step is a valid signature.**
*You are not allowed to use computational algebra system/software for this problem. The purpose of this problem is to make sure that you understand the basic El Gamal operations. You have to show every step in your calculations for full credit.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34c2a7c6-20d8-45e7-8c90-b1c224068cda%2Fa1c2c11e-eac9-42e8-8fdc-a7b4d3548ae4%2Fby53lk7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**El Gamal Public-Key Encryption and Signature Scheme**
Alice forms a public key for the “textbook” El Gamal public-key encryption and signature schemes, where \( p = 1187 \) and \( g = 2 \), by choosing her private key as \( a = 234 \).
1. **What is Alice’s public key?**
2. **Encrypt the message \( M = 3 \) for Alice.**
3. **Generate a signature on the message \( M = 1234567 \) using the following simple hash function**
\[ H : \{0, 1\} \to \mathbb{Z}_p \text{ such that } H(M) = 3M + 5 \pmod{p}. \]
4. **Verify that the signature you generated in the previous step is a valid signature.**
*You are not allowed to use computational algebra system/software for this problem. The purpose of this problem is to make sure that you understand the basic El Gamal operations. You have to show every step in your calculations for full credit.*
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