Encrypt a message using the RSA encryption system

Assignment Help Computer Network Security

Reference no: EM131825890

Question - You encrypt a message using the RSA encryption system as t^e mod n, where t, e < n and t is the numerical equivalent of the message. The message is written in a 27-letter alphabet and is split into blocks with m characters each. You have a limit of 10¹² binary operations to encrypt each block. Estimate the largest possible value of m if you use the fast exponentiation algorithm and

(a) standard algorithms for division and multiplication, which we assume require 100 · log₂ a · log₂ b binary operation to find ab and to find the quotient and remainder when a is divided by b;

(b) the best known algorithms for division and multiplication, which we assume for a ≥ b require

100 · (log₂ a) (log₂ log₂ a) · (log₂ log₂ log₂ a)

binary operation to find ab and to find the quotient and remainder when a is divided by b.

You may assume that the number of operations in the fast exponentiation algorithm is twice more than the number of operations needed for all squarings.

The number of operations needed to convert the message into a number is small and can be ignored. You may also ignore the difference between n and φ(n).

In part (b) you have to solve a transcendental equation. During the calculations you can round the results of iterations to the nearest integer.

Reference no: EM131825890

Questions Cloud

How much do you have to deposit into the account : How much do you have to deposit into the account 11.00 years from today?

What is the difference in the annual inflation rates : What is the difference in the annual inflation rates for the United States and Poland over this period?

Business or an individual budget : Question: Explain how a government budget differs from a business or an individual budget.

Role investments play in your financial management : Please reflect on the role investments play in your financial management today, and what role you expect investments to play post-graduation.

Encrypt a message using the RSA encryption system : You encrypt a message using the RSA encryption system as te mod n, where t, e

Order to endow this basketball scholarship : How large of an annual deposit must you take in order to endow this basketball scholarship.

Calculate the exercise value of the option : Calculate the exercise value of the option? Why is an investor willing to pay 50 cents an option when the stock is going for $55?

Differences in how two computer companies address items : Visit Dell and Apple's Web sites and analyze the similarities and differences in how the two computer companies address the items listed.

Make the lifetime subscription the better buy : Your subscription to Investing Wisely weekly is about to expire. how many years must you live to make the lifetime subscription the better buy?

User Account

All Pages