Answered: I. Fermat's test consists of using…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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I. Fermat's test consists of using Fermat's Theorem (an¹=1 (mod n)) with prime n. Just pick any number a E {1, ..., n-1} and check if it satisfies the expression. If not, then it must be a composite number, that is, it is not prime.

II. Although Fermat's Theorem is used to check whether a number is prime or not, we can still obtain equality (an¹-1 (mod n)) even when n is not prime. E The numbers for which this situation occurs are called Carmichael numbers or pseudoprimes.

III. Both the Miller-Rabin and AKS algorithms (checking a prime number) work for any type of input and are polynomial time. However, only AKS is deterministic.

IV. The Miller-Rabin algorithm guarantees when a number is prime, but when it is composite (non-prime) it can only guarantee this characteristic in probabilistic terms.

Only the following items are correct:

	A	I, II, III
	B	I, II, IV
	C	I, III, IV
	D	II, III, IV
	E	I, II, III, IV

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