1. Describe the Diffie-Hellman algorithm b. Consider a Diffie-Hellman scheme with a common prime q = 11 and a primitive root of α = 2. Show that 2 is a primitive root of 11. If user A has public key YA = 10, what is A’s private key XA? If user B has public key YB = 7, what is the secret key K shared with A?
1. Describe the Diffie-Hellman algorithm
b. Consider a Diffie-Hellman scheme with a common prime q = 11 and a primitive root of α = 2.
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Show that 2 is a primitive root of 11.
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If user A has public key YA = 10, what is A’s private key XA?
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If user B has public key YB = 7, what is the secret key K shared with A?
The Diffie-Hellman key exchange algorithm is a cryptographic method that allows two parties to securely exchange cryptographic keys over an insecure communication channel without prior communication. Here's an overview of the algorithm and the specific scenario provided:
Diffie-Hellman Algorithm:
Setup: Both parties agree on two public parameters:
- A large prime number, denoted as "q."
- A primitive root modulo "q," denoted as "α" (alpha).
Key Generation:
- Each user selects their private key:
- User A chooses "XA."
- User B chooses "XB."
- Each user selects their private key:
Public Key Calculation:
- Each user calculates their public key:
- User A calculates "YA = α^XA mod q."
- User B calculates "YB = α^XB mod q."
- Each user calculates their public key:
Key Exchange:
- Users exchange their public keys over the insecure channel.
Secret Key Calculation:
- User A computes the shared secret key:
- K = YB^XA mod q.
- User B computes the shared secret key:
- K = YA^XB mod q.
- User A computes the shared secret key:
Both users now have the same secret key "K," which can be used for secure communication using symmetric encryption algorithms.
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