Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

3: Please clearly show how to compute 2144 mod 101 (without applying Fermat's Little Theorem or Euler's Theorem, if you already know them) using

3: Please clearly show how to compute 2144 mod 101 (without applying Fermat’s Little Theorem or Eulers Theorem, if you alrea 

3: Please clearly show how to compute 2144 mod 101 (without applying Fermat's Little Theorem or Euler's Theorem, if you already know them) using no more than 8 multiplications in Z/(101). Hint: It will turn out to be helpful to know the base 2 expansion of 101. Also, you might want to warm up with count how many squarings you need to compute 22, 24, and 28... 4: Consider the function : (Z/(43)) (Z/(43)) defined by f(x) = 7x + 3. (Such a function is an example of a method of encryption called an affine cipher, combining the simpler ideas of adding or multiplying mod n.) For the example at hand, what function g would yield g(f(x)) = x for all x = {0,..., 42}? Hint: If you were over the rational numbers then this would be very easy. Perhaps you can do the same algebra over Z/(43), since you know fractions can sometimes be well-defined in Z/(N)?

Step by Step Solution

3.39 Rating (155 Votes )

There are 3 Steps involved in it

Step: 1

3To answer the first question we can use the base 2 expansion of 101 to compute 2144 mod 101 with fe... blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

A First Course In Probability

Authors: Sheldon Ross

9th Edition

978-9332519077, 9332519072

More Books

Students also viewed these Economics questions

Question

Describe the criteria for an effective budget.

Answered: 1 week ago