Number Theory

Euler's Theorem



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

Suppose Alice and Bob choose p=191p=191 and g=2g=2. If Alice's secret number is 1212 and Bob's is 1616, 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=211p=211 for their Diffie-Hellman protocol, along with g=2g=2. Eve sees the transmission gn(modp)=155g^n \pmod p = 155 and the transmission gm(modp)=96g^m \pmod p = 96. What is the shared secret key gmn(modp)g^{mn} \pmod p?

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


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