Rsa encryption function- cryptography, Computer Engineering

The general method for constructing the parameters of the RSA cryptosystem can be described as follows:

  • Select two primes p and q
  • Let N = pq and determine ∅ (N) = (p - 1)(q - 1)
  • Randomly choose e in the range 1 < e < ∅ N, such that gcd (e,N) = 1
  • Determine d as the solution to ed ≡ 1 mod ∅ (N)
  • Publish (e,N) as the public key

a. Show that a valid public key pair can still be constructed if we use only one prime

p, such that N =p and ∅ (N) = (p - 1).

b. If we use this "one-prime" RSA construction and publish the public key (e, N),why is it easy to recover the secret key d?

c. Let RSA(M) denote the encryption of the message M using the pair (e, N). Show that the RSA encryption function has the following property for any two messages M1 and M2

            RSA (M1 × M2) =  RSA(M1) × RSA (M2)

That is, the encryption of a product is equal to the product of the encryptions.

Tasks:

a. Show that "one-prime" construction produces a valid public key

b. Show the steps to recover d

c. Mathematical argument to show the property

Posted Date: 3/6/2013 3:18:42 AM | Location : United States







Related Discussions:- Rsa encryption function- cryptography, Assignment Help, Ask Question on Rsa encryption function- cryptography, Get Answer, Expert's Help, Rsa encryption function- cryptography Discussions

Write discussion on Rsa encryption function- cryptography
Your posts are moderated
Related Questions
Define Mercantile Process Model from the Merchant’s perspective along with a suitable diagram. This model consists of three activities into the purchase consummation phase: Aut

At the bottom of the toolbar there is a box with two lesser boxes and an arrow. The uppermost box displays the present foreground color; the lowermost box shows the present backgro

Q. Shared-memory programming model? In shared-memory programming model tasks share a common address space that they read and write asynchronously. Several mechanisms like semap

Arc Consistency: There have been many advances in how constraint solvers search for solutions (remember this means an assignment of a value to each variable in such a way that

A program is to be developed to simulate the operations of a scientific calculator. List the facilities to be provided by this calculator. Analyze this using a DFD 0- level and 1-

Write a decision table that specifies the rules for the game of checkers

Identify at least eight milestones for this project. Write a one-page paper describing each milestone using the SMART criteria?

Give explanation about Stored Program Control. Stored Program Control: In this centralized control, all the control equipment is replaced through a single processor that must

Pruning and Sorting: This means we can test where each hypothesis explains as entails a common example that we can associate to a hypothesis a set of positive elements in whic

Q. Define the Circular shifts ? Circular shifts ROTATE RIGHT andROTATE LEFT. Bits shifted out at one end of word are not lost as in a logical shift however are circulated back