d) What is the probability that a random element of Zy is not in Z,? e) Do you think there can be an efficient way to find an element x € Z, such that x € Z;?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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i need d,e Part solution

Suppose that N = pq, where p, q are primes of roughly the same size.
%3!
a) Show that (N) can be efficiently computed from p, q.
b) Show that given N, 4(N), one can compute p, q.
c) Do you think there is an efficient algorithm that can find @(N) given N?
d) What is the probability that a random element of ZN is not in Z,?
e) Do you think there can be an efficient way to find an element x € Z, such that x € Z;?
(Hint for c),d): there is no known efficient factoring algorithm for N of this form).
Transcribed Image Text:Suppose that N = pq, where p, q are primes of roughly the same size. %3! a) Show that (N) can be efficiently computed from p, q. b) Show that given N, 4(N), one can compute p, q. c) Do you think there is an efficient algorithm that can find @(N) given N? d) What is the probability that a random element of ZN is not in Z,? e) Do you think there can be an efficient way to find an element x € Z, such that x € Z;? (Hint for c),d): there is no known efficient factoring algorithm for N of this form).
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