Chapter Questions
Solve the DL problem $3^x \equiv 693 \bmod 1823$ using the baby-step giantstep algorithm.
Use the baby-step giant-step algorithm to compute the discrete logarithm of 15 to the base $2 \bmod 239$.
Solve the DL problem $g^x \equiv 507 \bmod 1117$ for the smallest primitive root $g \bmod 1117$ with the Pohlig-Hellman algorithm.
Use the Pohlig-Hellman algorithm to compute the discrete logarithm of 2 to the base $3 \bmod 65537$.
Use the Pollard $\rho$-algorithm to solve the DL problem $g^x \equiv 15 \bmod$ 3167 for the smallest primitive root $g \bmod 3167$.
Use the variant of the Pollard $\rho$-algorithm that stores eight triplets $(\beta, x, y)$ to solve the DL problem $g^x \equiv 15 \bmod 3167$ for the smallest primitive root $g$ mod 3167 . Compare the efficiency of this computation with the efficiency of the simple Pollard $\rho$-algorithm (Exercise 9.9.5).
Use the index calculus algorithm with the factor base $\{2,3,5,7,11\}$ to solve $7^x \equiv 13 \bmod 2039$.
Determine the smallest factor base that can be used in the index calculus algorithm to solve $7^x \cong 13 \bmod 2039$.