MIT 6.875 Lecture 5 Foundations of Cryptography
Description: MIT 6.875 Lecture 5 Foundations of Cryptography TODAY 1. Theorem: If there are PRGs, then there are PRFs. The Goldreich-Goldwasser-Micali (GGM) construction. 2. More Applications of PRFs: a. Identification Protocols c. Applications to
Related Topics
Download Presentation
"MIT 6.875 Lecture 5 Foundations of Cryptography" is the property of its rightful owner. Permission is granted to download and print the materials on this website for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Presentation Transcript
slide1. MIT 6.875 Lecture 5 Foundations of Cryptography<br>
slide2. TODAY 1. Theorem: If there are PRGs, then there are PRFs. The Goldreich-Goldwasser-Micali (GGM) construction. 2. More Applications of PRFs: a. Identification Protocols c. Applications to Learning Theory b. Authentication 0. Finish up secret-key encryption.<br>
slide3. Friend-or-Foe Identification Adversary: person-in-the-middle. Can listen to / modify the communications. Wants to impersonate Tim.<br>
slide4. A Simple Lemma about Unpredictability<br>
slide5. A Simple Lemma about Unpredictability<br>
slide6. Challenge-Response Protocol<br>
slide7. TODAY 1. Theorem: If there are PRGs, then there are PRFs. The Goldreich-Goldwasser-Micali (GGM) construction. 2. More Applications of PRFs: a. Identification Protocols c. Applications to Learning Theory b. Authentication<br>
slide8. Secure Communication Alice Bob m One-time pad (and encryption schemes in general) are malleable. Can toggle between m and m’<br>
slide9. Secure Communication Alice Bob m One-time pad (and encryption schemes in general) are malleable. Can toggle between m and m’<br>
slide10. Message Authentication Codes Alice Bob m MACs give us integrity, but not privacy.<br>
slide11. Message Authentication Codes Alice Bob m MACs give us integrity, but not privacy. Solution: Encrypt, then MAC (more in pset 2)<br>
slide12. TODAY 1. Theorem: If there are PRGs, then there are PRFs. The Goldreich-Goldwasser-Micali (GGM) construction. 2. More Applications of PRFs: a. Identification Protocols c. Applications to Learning Theory b. Authentication<br>
slide13. Negative Results in Learning Theory Theorem [Kearns and Valiant 1994]: Assuming PRFs exist, there are hypothesis classes that cannot be learned by polynomial-time algorithms.<br>
slide2. TODAY 1. Theorem: If there are PRGs, then there are PRFs. The Goldreich-Goldwasser-Micali (GGM) construction. 2. More Applications of PRFs: a. Identification Protocols c. Applications to Learning Theory b. Authentication 0. Finish up secret-key encryption.<br>
slide3. Friend-or-Foe Identification Adversary: person-in-the-middle. Can listen to / modify the communications. Wants to impersonate Tim.<br>
slide4. A Simple Lemma about Unpredictability<br>
slide5. A Simple Lemma about Unpredictability<br>
slide6. Challenge-Response Protocol<br>
slide7. TODAY 1. Theorem: If there are PRGs, then there are PRFs. The Goldreich-Goldwasser-Micali (GGM) construction. 2. More Applications of PRFs: a. Identification Protocols c. Applications to Learning Theory b. Authentication<br>
slide8. Secure Communication Alice Bob m One-time pad (and encryption schemes in general) are malleable. Can toggle between m and m’<br>
slide9. Secure Communication Alice Bob m One-time pad (and encryption schemes in general) are malleable. Can toggle between m and m’<br>
slide10. Message Authentication Codes Alice Bob m MACs give us integrity, but not privacy.<br>
slide11. Message Authentication Codes Alice Bob m MACs give us integrity, but not privacy. Solution: Encrypt, then MAC (more in pset 2)<br>
slide12. TODAY 1. Theorem: If there are PRGs, then there are PRFs. The Goldreich-Goldwasser-Micali (GGM) construction. 2. More Applications of PRFs: a. Identification Protocols c. Applications to Learning Theory b. Authentication<br>
slide13. Negative Results in Learning Theory Theorem [Kearns and Valiant 1994]: Assuming PRFs exist, there are hypothesis classes that cannot be learned by polynomial-time algorithms.<br>