3.35. This exercise asks you to use the index calculus to solve a discrete logarithm problem....

 

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3.35. 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' (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, (2), log, (3), and log, (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" 19 (mod 19079). 3.35. 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' (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, (2), log, (3), and log, (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" 19 (mod 19079).

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a Verifying smoothness g3030 mod p 12870 is 5smooth 235163 g6892 mod p 900... View the full answer