Course Solutions Uncategorized (Solved) : Let P 1621 Given 17 Generator Z P Let B 2 3 Factor Base Index Calculus Method Find Least Q19378320 . . . .

(Solved) : Let P 1621 Given 17 Generator Z P Let B 2 3 Factor Base Index Calculus Method Find Least Q19378320 . . . .

 

Let p 1621, it is given that 17 is a generator of (zi, (a) (10 pts) Let B {2,3 be a factor base (as in the index calculus method). Find at least two distinct equations of the form 17k e 2e3 mod p for some integers k, e, t (b) 10 pts) Let B 12, 3, 5, 7, 11, 13, 17, 23 be another factor base In this case, find at least 8 distinct equations of the form 17 213 567 11013 17 823j for some integers k, i, t, b, y, o, u, s, j (c) (10 pts) Discuss advantages and disadvantages of using larger factor base. (d) (20 pts) Note 7 in (Zp, has order 81. What do you think about using 7 instead of 17 in part a and part b?

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