1 / 10

Information Theory

Information Theory. Rusty Nyffler. Introduction. Entropy Example of Use Perfect Cryptosystems Common Entropy. Entropy. Measure of uncertainty Entropy of a fair coin toss = 1. Why is entropy important?.

shea
Download Presentation

Information Theory

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Information Theory Rusty Nyffler

  2. Introduction • Entropy • Example of Use • Perfect Cryptosystems • Common Entropy

  3. Entropy • Measure of uncertainty • Entropy of a fair coin toss = 1

  4. Why is entropy important? • Measures the likelihood of the eavesdropper knowing something about the key, given the ciphertext • Greater entropy usually means greater security • Entropy of a cryptosystem (K = number of possible keys (if all keys are equally likely)

  5. Example • 3 possible plaintexts: a(.5), b(.3), c(.2) • Two keys k1and k2, equally likely (.5) • Possible ciphertexts U,V,W • If someone obtains sent ciphertext, then information is known about the plaintext. • If U was received, then a was the text • If V was received, then b or c was the text

  6. Example Continued • Moreover, • p(b|V) = .6 • p(c|V) = .4 • p(b|W) = .6 • p(c|W) = .4 • Which means it’s more likely that b is the plaintext when V or W is caught • Entropy shows that the eavesdropper knows more about the plaintext when the ciphertext is intercepted

  7. Perfect Cryptosystems • In a perfect cryptosystem (i.e. unbreakable), the ciphertext should not give any more information about the plaintext or the key • H(P) = H(P|C) • H(K) = H(K|C)

  8. Common Entropy • The English language • Somewhere between 1.42 and .72 • English is around 75% redundant • In many algorithms, the longer the key, the more entropy the system has • Vigenere

  9. Common Entropy • RSA • Entropy = 0 • All the info you need is in n, e, and c … except it’ll take a while to factor n

  10. References • MacKay, David J.C. Information Theory, Inference, and Learning Algorithms. 18 April 2003. http://www.inference.phy.cam.ac.uk/itprnn/book.l.pdf • North Carolina State University. Cryptography FAQ. 21 March 2003. http://isc.faqs.org/faqs/cryptography-faq/part01/ • Raynal, Frederick. Weak Algorithms. 2002. http://www.owasp.org/asac/cryptographic/algorithms.shtml • Trappe, Wade and Lawrence C. Washington. Introduction to Cryptography with Coding Theory. Upper Saddle River, New Jersey: Prentice-Hall, Inc., 2002.

More Related