RSA, Diffie-Hellman & analytic number theory

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Standard

   In Diffie-Hellman key exchange with public prime $p=13$ and base $g=3$, Alice's secret exponent is $a=4$ and Bob's is $b=5$. The shared secret is $g^{ab}\bmod p$. Compute its least nonnegative value.

2. Standard

   In Diffie-Hellman key exchange with public prime $p=23$ and base $g=2$, Alice's secret exponent is $a=2$ and Bob's is $b=5$. The shared secret is $g^{ab}\bmod p$. Compute its least nonnegative value.

3. Standard

   In Diffie-Hellman key exchange with public prime $p=17$ and base $g=3$, Alice's secret exponent is $a=3$ and Bob's is $b=5$. The shared secret is $g^{ab}\bmod p$. Compute its least nonnegative value.

Problems shown under their original terms: Generated (template, solver-computed).