Lecture 4 part 2.ppt - RSA Encryption What is an RSA Number An RSA number n is a number s.t n=pq Where p and q are distinct large prime integers totient

Lecture 4 part 2.ppt - RSA Encryption What is an RSA Number...

This preview shows page 1 - 5 out of 5 pages.

RSA Encryption
Image of page 1

Subscribe to view the full document.

What is an RSA Number? An RSA number n is a number s.t. n=pq Where p and q are distinct, large, prime integers.
Image of page 2
totient function φ(n) In number theory, Euler's totient function counts the positive integers up to a given integer n that are relatively prime to n. For example, the totatives of n = 9 are the six numbers 1, 2, 4, 5, 7 and 8
Image of page 3

Subscribe to view the full document.

Let’s Make a Key, Shall We? 1. Let’s use small prime numbers for the example: p=2 q=5 n=pq=10 2. Compute the totient: φ(n) = (p-1)(q-1) = 1*4 = 4 Observe that the number of integers less than n that are coprime to n is 4: (1, 3, 7, 9) 3. Choose an integer
Image of page 4
Image of page 5

Unformatted text preview: e s.t. 1 < e < φ( n ), and e and φ( n ) are coprime (1 < e < 4) e = 3 (e is used as the public key exponent) 4. Compute d s.t. d*e = 1 + kφ(n) for some integer k (k=2,5) . d*3 = 1 + k*4 OR e*d=1 mod ø(N) 3*d=1 mod 4 d = 7 ( d is used as the private key exponent) Let’s Make a Key, Shall We? 5-So then, the public key will be: c=m e mod n c=m 3 mod 10 6-And the private key will be: m=c d mod n m=c 7 mod 10 example We use the public key to encrypt and the private key to decrypt If we want to encrypt m=8 we use c=8 3 mod 10 = 2 In order to decrypt c=2 we use m=2 7 mod 10 = 8...
View Full Document

  • Fall '17
  • Dr.hatem

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask You can ask ( soon) You can ask (will expire )
Answers in as fast as 15 minutes