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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?

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.7: Introduction To Coding Theory (optional)
Problem 6E: Suppose the probability of erroneously transmitting a single digit is P=0.03. Compute the...
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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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