Seminar 5837S: Complexity Theory and Cryptography · Theoretical Computer Science Prof. Dr. Ignaz...

Seminar 5837S:Complexity Theory and CryptographyTheoretical Computer ScienceProf. Dr. Ignaz Rutter

for students of all Computer Science programs

CryptographyProf. Dr. Jens Zumbrägel

Seminar 5837S:Complexity Theory and CryptographyTheoretical Computer ScienceProf. Dr. Ignaz Rutter

for students of all Computer Science programs

CryptographyProf. Dr. Jens Zumbrägel

(incl. Mathematics)

Seminar 5837S:Complexity Theory and CryptographyTheoretical Computer ScienceProf. Dr. Ignaz Rutter

for students of all Computer Science programs

CryptographyProf. Dr. Jens Zumbrägel

(incl. Mathematics)Mathematics Computer Science

Seminar 5837S:Complexity Theory and CryptographyTheoretical Computer ScienceProf. Dr. Ignaz Rutter

for students of all Computer Science programs

Kick-off meetings:

CryptographyProf. Dr. Jens Zumbrägel

(incl. Mathematics)Mathematics Computer Science

30.01.2019, 18:00–19:00, distribution of first topics25.04.2019 Introduction, distribution of remaining topics

Seminar: Complexity Theory and Cryptography | Prof. Rutter und Prof. Zumbrägel | 23.01.2019

Motivation

Complexity Theory:Classifies problems according to the required resources forsolving them (e.g., running time, storage)

Algorithmic point of view:If I cannot solve it, I do at least show that is (probably)unsolvable.e.g., NP-complete problems → negative results

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Seminar: Complexity Theory and Cryptography | Prof. Rutter und Prof. Zumbrägel | 23.01.2019

Motivation

Complexity Theory:Classifies problems according to the required resources forsolving them (e.g., running time, storage)

Algorithmic point of view:If I cannot solve it, I do at least show that is (probably)unsolvable.e.g., NP-complete problems → negative results

Cryptography:Based on the existence of computationally difficult problems:decrypting a message without the corresponding keymust be difficultImpossibility results as a resource

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Seminar: Complexity Theory and Cryptography | Prof. Rutter und Prof. Zumbrägel | 23.01.2019

Motivation

Complexity Theory:Classifies problems according to the required resources forsolving them (e.g., running time, storage)

Algorithmic point of view:If I cannot solve it, I do at least show that is (probably)unsolvable.e.g., NP-complete problems → negative results

Cryptography:Based on the existence of computationally difficult problems:decrypting a message without the corresponding keymust be difficultImpossibility results as a resource

Interesting interplay:Complexity Theory ↔ Cryptography

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Seminar: Complexity Theory and Cryptography | Prof. Rutter und Prof. Zumbrägel | 23.01.2019

Prerequisites

You should not be afraid of formal definitions, statements and proofsTheoretical Computer Science (in particular complexity theory)

Example: one-way functionseasy to computehard to invert

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Seminar: Complexity Theory and Cryptography | Prof. Rutter und Prof. Zumbrägel | 23.01.2019

Prerequisites

You should not be afraid of formal definitions, statements and proofsTheoretical Computer Science (in particular complexity theory)

Example: one-way functionseasy to computehard to invert

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Seminar: Complexity Theory and Cryptography | Prof. Rutter und Prof. Zumbrägel | 23.01.2019

Overviewall Math and CS programsTopic: Complexity Theory and CryptographyOne-way FunctionsRandomness and Pseudo-RandomnessDerandomization of AlgorithmsZero-Knowledge Proofs. . .

Lecturers: Prof. Dr. Ignaz Rutter and Prof. Dr. Jens ZumbrägelTime: Thursdays, 14–16 Uhr, HS 12Requirementspresentationseminar paperattendance

Literature:O. Goldreich, Foundations of Cryptography: Volume I Basic ToolsO. Goldreich, Foundations of Cryptography: Volume II Basic ApplicationsS. Arora, B. Barak, Computational Complexity: A Modern Approach,Cambridge University Press, 2009

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Seminar: Complexity Theory and Cryptography | Prof. Rutter und Prof. Zumbrägel | 23.01.2019

Next Steps

Two kick-off meetings:

1) Wednesday, 30. January, 18.00–19.00, SR 033

2) Thursday, 25. April, 14.00–16.00, HS 12

Afterwards Access via Stud.IP

→ first assignment of topics

→ remaining topics

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