/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q39E Give a polynomial-time algorithm... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Q39E (page 51)

Give a polynomial-time algorithm for computing,abcmodp given a,b,c, and prime p.

Short Answer

Expert verified

An Algorithm:

Use Fermat鈥檚 little theorem

ap-1鈮�1modp

Apply onabc with twice modular exponentiation operation

abc鈮�a(bc)modp-1modp

Return a,b,c,p

The algorithm runs in On3time.

Step by step solution

01

Explain Polynomial time algorithm

If an algorithm solves the problem with the O(mk)number of steps for a given input, then the algorithm is a polynomial time algorithm.

02

Give a polynomial-time algorithm for computing,abcmod p,

Consider the Fermat鈥檚 little theorem to solve the modular exponentiation.An Algorithm:

Use Fermat鈥檚 little theorem

ap-1鈮�1modp

Apply on with twice modular exponentiation operation

abc鈮�a(bc)modp-1)modp

Return a,b,c,p

The above algorithm runs in On3time.

Therefore, a polynomial time algorithm ahs be obtained to compute abcmodp.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Prove or disprove: If a has an inverse modulo b, then b has an inverse modulo a.

Find the inverse of:.20mod79,3mod62,21mod91,5mod23

Show that log(n!)=胃(nlogn)

(Hint: To show an upper bound, compare (n!) with nn. To show a lower bound, compare it with (n2)n2).

Prove that the grade-school multiplication algorithm (page 24), when applied to binary numbers, always gives the right answer.

How many integers modulo113 have inverses?(Note:113=1331)
See all solutions

Recommended explanations on Computer Science Textbooks

Theory of Computation

Read Explanation

Problem Solving Techniques

Read Explanation

Computer Organisation and Architecture

Read Explanation

Cybersecurity in Computer Science

Read Explanation

Functional Programming

Read Explanation

Cloud Services

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.