Foundation of Cryptography (0368-4162-01), Intoduction - PowerPoint PPT Presentation

Foundation of Cryptography (0368-4162-01), Intoduction Adminstration + Introduction Iftach Haitner, Tel Aviv University Tel Aviv University. February 18, 2014 Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 1 / 16

Part I Administration and Course Overview Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 2 / 16

Section 1 Administration Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 3 / 16

Important Details Iftach Haitner. Schriber 20, email iftachh at gmail.com 1 Reception: Sundays 9:00-10:00 (please coordinate via email in advance) Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 4 / 16

Important Details Iftach Haitner. Schriber 20, email iftachh at gmail.com 1 Reception: Sundays 9:00-10:00 (please coordinate via email in advance) Who are you? 2 Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 4 / 16

Important Details Iftach Haitner. Schriber 20, email iftachh at gmail.com 1 Reception: Sundays 9:00-10:00 (please coordinate via email in advance) Who are you? 2 Mailing list: 0368-4162-01@listserv.tau.ac.il 3 Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 4 / 16

Important Details Iftach Haitner. Schriber 20, email iftachh at gmail.com 1 Reception: Sundays 9:00-10:00 (please coordinate via email in advance) Who are you? 2 Mailing list: 0368-4162-01@listserv.tau.ac.il 3 ◮ Registered students are automatically on the list (need to activate the account by going to https://www.tau.ac.il/newuser/ ) Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 4 / 16

Important Details Iftach Haitner. Schriber 20, email iftachh at gmail.com 1 Reception: Sundays 9:00-10:00 (please coordinate via email in advance) Who are you? 2 Mailing list: 0368-4162-01@listserv.tau.ac.il 3 ◮ Registered students are automatically on the list (need to activate the account by going to https://www.tau.ac.il/newuser/ ) ◮ If you’re not registered and want to get on the list (or want to get another address on the list), send e-mail to: listserv@listserv.tau.ac.il with the line: subscribe 0368-3500-34 <Real Name> Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 4 / 16

Important Details Iftach Haitner. Schriber 20, email iftachh at gmail.com 1 Reception: Sundays 9:00-10:00 (please coordinate via email in advance) Who are you? 2 Mailing list: 0368-4162-01@listserv.tau.ac.il 3 ◮ Registered students are automatically on the list (need to activate the account by going to https://www.tau.ac.il/newuser/ ) ◮ If you’re not registered and want to get on the list (or want to get another address on the list), send e-mail to: listserv@listserv.tau.ac.il with the line: subscribe 0368-3500-34 <Real Name> Course website: 4 http: //www.cs.tau.ac.il/~iftachh/Courses/FOC/Spring14 (or just Google iftach and follow the link) Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 4 / 16

Grades Class exam 80 1 Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 5 / 16

Grades Class exam 80 1 Homework 20%: 5-6 exercises. 2 Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 5 / 16

Grades Class exam 80 1 Homework 20%: 5-6 exercises. 2 ◮ Recommended to use use L A T EX (see link in course website) Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 5 / 16

Grades Class exam 80 1 Homework 20%: 5-6 exercises. 2 ◮ Recommended to use use L A T EX (see link in course website) ◮ Exercises should be sent to ? or put in mailbox ?, in time! Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 5 / 16

and.. Slides 1 Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 6 / 16

and.. Slides 1 English 2 Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 6 / 16

Course Prerequisites Some prior knowledge of cryptography (such as 0369.3049) might 1 help, but not necessarily Basic probability. 2 Basic complexity (the classes P , NP , BPP ) 3 Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 7 / 16

Course Material Books: 1 Oded Goldreich. Foundations of Cryptography. 1 Jonathan Katz and Yehuda Lindell. An Introduction to Modern 2 Cryptography. Lecture notes 2 2013 Course. 1 Ran Canetti www.cs.tau.ac.il/~canetti/f08.html 2 Yehuda Lindell 3 u.cs.biu.ac.il/~lindell/89-856/main-89-856.html Luca Trevisan www.cs.berkeley.edu/~daw/cs276/ 4 Salil Vadhan people.seas.harvard.edu/~salil/cs120/ 5 Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 8 / 16

Section 2 Course Topics Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 9 / 16

Course Topics Basic primitives in cryptography (i.e., one-way functions, pseudorandom generators and zero-knowledge proofs). Focus on formal definitions and rigorous proofs. The goal is not studying some list, but to understand cryptography. Get ready to start researching Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 10 / 16

Part II Foundation of Cryptography Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 11 / 16

Cryptography and Computational Hardness What is Cryptography? 1 Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 12 / 16

Cryptography and Computational Hardness What is Cryptography? 1 Hardness assumptions, why do we need them? 2 Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 12 / 16

Cryptography and Computational Hardness What is Cryptography? 1 Hardness assumptions, why do we need them? 2 Does P � = NP suffice? 3 Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 12 / 16

Cryptography and Computational Hardness What is Cryptography? 1 Hardness assumptions, why do we need them? 2 Does P � = NP suffice? 3 NP : all (languages) L ⊂ { 0 , 1 } ∗ for which there exists a polynomial-time algorithm V and (a polynomial) p ∈ poly such that the following hold: Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 12 / 16

Cryptography and Computational Hardness What is Cryptography? 1 Hardness assumptions, why do we need them? 2 Does P � = NP suffice? 3 NP : all (languages) L ⊂ { 0 , 1 } ∗ for which there exists a polynomial-time algorithm V and (a polynomial) p ∈ poly such that the following hold: V ( x , w ) = 0 for any x / ∈ L and w ∈ { 0 , 1 } ∗ 1 Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 12 / 16

Cryptography and Computational Hardness What is Cryptography? 1 Hardness assumptions, why do we need them? 2 Does P � = NP suffice? 3 NP : all (languages) L ⊂ { 0 , 1 } ∗ for which there exists a polynomial-time algorithm V and (a polynomial) p ∈ poly such that the following hold: V ( x , w ) = 0 for any x / ∈ L and w ∈ { 0 , 1 } ∗ 1 for any x ∈ L , ∃ w ∈ { 0 , 1 } ∗ with | w | ≤ p ( | x | ) and 2 V ( x , w ) = 1 Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 12 / 16

Cryptography and Computational Hardness What is Cryptography? 1 Hardness assumptions, why do we need them? 2 Does P � = NP suffice? 3 NP : all (languages) L ⊂ { 0 , 1 } ∗ for which there exists a polynomial-time algorithm V and (a polynomial) p ∈ poly such that the following hold: V ( x , w ) = 0 for any x / ∈ L and w ∈ { 0 , 1 } ∗ 1 for any x ∈ L , ∃ w ∈ { 0 , 1 } ∗ with | w | ≤ p ( | x | ) and 2 V ( x , w ) = 1 P � = NP : i.e., ∃ L ∈ NP , such that for any polynomial-time algorithm A, ∃ x ∈ { 0 , 1 } ∗ with A ( x ) � = 1 L ( x ) Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 12 / 16

Cryptography and Computational Hardness What is Cryptography? 1 Hardness assumptions, why do we need them? 2 Does P � = NP suffice? 3 NP : all (languages) L ⊂ { 0 , 1 } ∗ for which there exists a polynomial-time algorithm V and (a polynomial) p ∈ poly such that the following hold: V ( x , w ) = 0 for any x / ∈ L and w ∈ { 0 , 1 } ∗ 1 for any x ∈ L , ∃ w ∈ { 0 , 1 } ∗ with | w | ≤ p ( | x | ) and 2 V ( x , w ) = 1 P � = NP : i.e., ∃ L ∈ NP , such that for any polynomial-time algorithm A, ∃ x ∈ { 0 , 1 } ∗ with A ( x ) � = 1 L ( x ) polynomial-time algorithms: an algorithm A runs in polynomial-time, if ∃ p ∈ poly such that the running time of A ( x ) is bounded by p ( | x | ) for any x ∈ { 0 , 1 } ∗ Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 12 / 16

Cryptography and Computational Hardness What is Cryptography? 1 Hardness assumptions, why do we need them? 2 Does P � = NP suffice? 3 NP : all (languages) L ⊂ { 0 , 1 } ∗ for which there exists a polynomial-time algorithm V and (a polynomial) p ∈ poly such that the following hold: V ( x , w ) = 0 for any x / ∈ L and w ∈ { 0 , 1 } ∗ 1 for any x ∈ L , ∃ w ∈ { 0 , 1 } ∗ with | w | ≤ p ( | x | ) and 2 V ( x , w ) = 1 P � = NP : i.e., ∃ L ∈ NP , such that for any polynomial-time algorithm A, ∃ x ∈ { 0 , 1 } ∗ with A ( x ) � = 1 L ( x ) polynomial-time algorithms: an algorithm A runs in polynomial-time, if ∃ p ∈ poly such that the running time of A ( x ) is bounded by p ( | x | ) for any x ∈ { 0 , 1 } ∗ Problems: hard on the average. No known solution 4 Iftach Haitner (TAU) Foundation of Cryptography February 18, 2014 12 / 16