Computer Science / Python

IT Homework Help-Shared Key Calculation

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IT Homework Help-Shared Key Calculation

Given that Alice and Bob want to communicate over a public link using Diffie Hellman algorithm and the value of p = 43 while g = 13. Alice chooses kA = 5 while Bob chooses kB= 7, determine the shared key(show working)

To determine the shared key using the Diffie-Hellman algorithm with the given parameters:

  1. Shared Prime Modulus (p): p=43
  2. Generator (g): g=13
  3. Alice’s Private Key (kA): kA=5
  4. Bob’s Private Key (kB): kB=7

The steps to compute the shared key are as follows:

Alice’s Calculation:

  1. Alice computes A=gkAmod  p A=135mod  43 A=122mod  43 A=38

Bob’s Calculation:

  1. Bob computes B=gkBmod  p B=137mod  43 B=62748517mod  43 B=24

Shared Key Calculation:

  1. Alice sends A to Bob, and Bob sends B to Alice.
  2. Alice computes the shared key: K=BkAmod  p

    K=245mod  43

    K=7962624mod  43

    K=9

    The shared key for Alice is 9.

  3. Bob computes the shared key: K=AkBmod  p

    K=387mod  43

    K=45435424mod  43

    K=9

    The shared key for Bob is also 9.

Therefore, both Alice and Bob compute the same shared key, which is K=9.

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