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(3) Diffie-Hellman key exchange: Start with the prime p = 13 and the primitive root g = 2. (a) Alice chooses the secret key a = 5. Compute the public key Aga (mod p) Alice sends A to Bob. (b) Bob chooses the secret key b = 7. Compute the public key B = gb (mod p) Bob sends B to Alice. (c) Use Diffie-Hellman key exchange to compute the secret key that Alice and Bob share.

(3) Diffie-Hellman key exchange: Start with the prime p = 13 and the primitive root g = 2. (a) Alice chooses the secret key a = 5. Compute the public key Aga (mod p) Alice sends A to Bob. (b) Bob chooses the secret key b = 7. Compute the public key B = gb (mod p) Bob sends B to Alice. (c) Use Diffie-Hellman key exchange to compute the secret key that Alice and Bob share.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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### Diffie-Hellman Key Exchange To understand the Diffie-Hellman Key Exchange protocol, let's explore a practical example. Consider the following steps: 1. **Start with the Prime Number and Primitive Root:** - Prime \( p = 13 \) - Primitive Root \( g = 2 \) 2. **Step-by-Step Process:** **(a)** **Alice's Public Key Calculation:** - Alice selects her secret key \( a = 5 \) - She computes her public key \( A \): \[ A \equiv g^a \, (\text{mod} \, p) \] Substituting the values given: \[ A \equiv 2^5 \, (\text{mod} \, 13) \] - Alice sends \( A \) to Bob. **(b)** **Bob's Public Key Calculation:** - Bob selects his secret key \( b = 7 \) - He computes his public key \( B \): \[ B \equiv g^b \, (\text{mod} \, p) \] Substituting the values given: \[ B \equiv 2^7 \, (\text{mod} \, 13) \] - Bob sends \( B \) to Alice. **(c)** **Computing the Shared Secret Key:** - Using the Diffie-Hellman key exchange, both Alice and Bob can compute a shared secret key. This key should be the same on both sides. This example outlines the essential process of Diffie-Hellman key exchange, where the secret keys \( a \) and \( b \) are privately chosen values, and the public keys \( A \) and \( B \) are shared and used to compute the common secret key.
Transcribed Image Text:### Diffie-Hellman Key Exchange To understand the Diffie-Hellman Key Exchange protocol, let's explore a practical example. Consider the following steps: 1. **Start with the Prime Number and Primitive Root:** - Prime \( p = 13 \) - Primitive Root \( g = 2 \) 2. **Step-by-Step Process:** **(a)** **Alice's Public Key Calculation:** - Alice selects her secret key \( a = 5 \) - She computes her public key \( A \): \[ A \equiv g^a \, (\text{mod} \, p) \] Substituting the values given: \[ A \equiv 2^5 \, (\text{mod} \, 13) \] - Alice sends \( A \) to Bob. **(b)** **Bob's Public Key Calculation:** - Bob selects his secret key \( b = 7 \) - He computes his public key \( B \): \[ B \equiv g^b \, (\text{mod} \, p) \] Substituting the values given: \[ B \equiv 2^7 \, (\text{mod} \, 13) \] - Bob sends \( B \) to Alice. **(c)** **Computing the Shared Secret Key:** - Using the Diffie-Hellman key exchange, both Alice and Bob can compute a shared secret key. This key should be the same on both sides. This example outlines the essential process of Diffie-Hellman key exchange, where the secret keys \( a \) and \( b \) are privately chosen values, and the public keys \( A \) and \( B \) are shared and used to compute the common secret key.
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