This exercise asks you to use the index calculus to solve a discrete logarithm problem. Let p = 19079 and g = 17.

(a) Verify that g^i (mod p) is 5-smooth for each of the values i = 3030, i = 6892, and i = 18312.

(b) Use your computations in (a) and linear algebra to compute the discrete loga- rithms log_g (2), log_g (3), and log_g (5). (Note that 19078 = 2 9539 and that 9539 is prime.)

(c) Verify that 19 17^12400 is 5-smooth.

(d) Use the values from (b) and the computation in (c) to solve the discrete loga-

rithm problem

17^x 19 (mod 19079).