Diffie-Hellman Practice Problems Online

Solving which of the following problems would allow one to break the Diffie-Hellman protocol?

Suppose Alice and Bob choose \(p=191\) and \(g=2\). If Alice's secret number is \(12\) and Bob's is \(16\), what is the shared secret key?

Which of the following primes is most likely to be used in the Diffie-Hellman protocol?

Alice and Bob unwisely choose \(p=211\) for their Diffie-Hellman protocol, along with \(g=2\). Eve sees the transmission \(g^n \pmod p = 155\) and the transmission \(g^m \pmod p = 96\). What is the shared secret key \(g^{mn} \pmod p\)?

Which of the following modifications would NOT increase the security of the Diffie-Hellman protocol?

Doubling the number of bits in the prime \(p\) Sending the same message multiple times to prevent man-in-the-middle attacks Choosing a \(g\) with order \(\frac{p-1}{2}\), instead of a \(g\) with order \(p-1\) Using an elliptic curve group rather than the additive group formed by taking modulo \(p\)

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