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Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer FIRST

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Page 1: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

Information Security of Embedded Systems

9.1.2010: Public Key Cryptosystems, Communication

Prof. Dr. Holger SchlingloffInstitut für Informatik

undFraunhofer FIRST

Page 2: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 2

Structure

1. Introductory example2.Embedded systems

engineering1. definitions and terms2. design principles

3.Foundations of security1. threats, attacks, measures2. construction of safe

systems

4.Design of secure systems1. design challenges2. safety modelling and

assessment3. cryptographic algorithms

5. Communication of embedded systems

1. remote access2. sensor networks

6. Algorithms and measures

1. digital signatures2. key management3. authentification4. authorization

7. Formal methods for security

1. protocol verification2. logics and proof

methods

Page 3: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 3

Public Key Cryptosystems

Page 4: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 4

General Idea

Page 5: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 5

Asymmetric Cryptosystems

Page 6: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 6

Danger of Spoofing!

Page 7: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 7

RSA (1978)

http://people.csail.mit.edu/rivest/Rsapaper.pdf

Page 8: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 8

RSA Preliminaries

Page 9: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 9

Page 10: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 10

RSA Key Generation

Page 11: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 11

Page 12: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 12

Keys in RSA

Page 13: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 13

Sending Messages from A to B

Page 14: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 14

Page 15: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 15

Correctness of RSA

Page 16: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 16

Euler’s theorem

Page 17: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 17

Lemmas for Euler’s Theorem

Page 18: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 18

Proof of Lemma3

Page 19: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 19

Proof of Euler’s Theorem

Page 20: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 20

Page 21: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 21

Algorithms for the Implementation

Page 22: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 22

Primality Test: Rabin-Miller

Page 23: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 23

Encoding / Decoding

Page 24: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 24

Security of RSA

Page 25: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 25

Latest News

http://de.wikinews.org/wiki/RSA-Veschl%C3%BCsselung_mit_768_Bit_geknackt

Page 26: Information Security of Embedded Systems 9.1.2010: Public Key Cryptosystems, Communication Prof. Dr. Holger Schlingloff Institut für Informatik und Fraunhofer

13.1.2010Embedded Security © Prof. Dr. H. Schlingloff 2010 26

Latest News

http://de.wikinews.org/wiki/RSA-Veschl%C3%BCsselung_mit_768_Bit_geknackt


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