Suppose that N = pq, where p, q are primes of roughly the same size. a) Show that o(N) can be efficiently computed from p, q. b) Show that given N, q(N), one can compute p, q. c) Do you think there is an efficient algorithm that can find p(N) given N?
Suppose that N = pq, where p, q are primes of roughly the same size. a) Show that o(N) can be efficiently computed from p, q. b) Show that given N, q(N), one can compute p, q. c) Do you think there is an efficient algorithm that can find p(N) given N?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Suppose that N = pq, where p, q are primes of roughly the same size.
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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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