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