{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture23 - Algorithms in Systems Engineering IE170 Lecture...

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Algorithms in Systems Engineering IE170 Lecture 23 Dr. Ted Ralphs
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
IE170 Lecture 23 1 References for Today’s Lecture Required reading CLRS Chapter 31 References Koblitz, A Course in Number Theory and Cryptography , Second Edition (1999).
Image of page 2
IE170 Lecture 23 2 RSA Public Key Encryption Algorithm The RSA algorithm is used almost universally to encrypt data on the Internet. If you have ever visited a secure site on the Internet, you have used RSA encryption. Procedure for creating public and private keys. Randomly choose two large prime numbers p and q such that p 6 = q . Compute n = pq . Select an odd integer e that is relatively prime to φ ( n ) = ( p - 1)( q - 1) = n + 1 - p - q . Compute d as the multiplicative inverse of e modulo φ ( n ) . The pair ( e, n ) is the public key . The pair ( d, n ) is the private key . The encoding function is f E ( P ) = P e mod n . The decoding function is f D ( C ) = C d mod n .
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
IE170 Lecture 23 3 Some Questions Does the RSA algorithm actually yield a cryptosystem (are the encoding and encoding functions really inverses)? How secure is this system, i.e., is the encoding key really a trap door function? Can we compute the keys efficiently? Can we find large prime numbers efficiently? Does d always exist and can we compute it? Can we encode and decode efficiently?
Image of page 4
IE170 Lecture 23 4 How Secure is RSA Encryption?
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

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