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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