Introduction to cryptography

English for Comp. Science I Introduction to Cryptography Amir Neziri & Jurlind Budurushi2/3/2011

Introduction

Let’s make the introduction...

2/3/2011 | Department 20 | B.IT Nieh | Introduction to Cryptography | A. Neziri & J. Budurushi 2

Introduction

2/3/2011 | Department 20 | B.IT Nieh | Introduction to Cryptography | A. Neziri & J. Budurushi 3

Content

History of Cryptography

Goals of Cryptography

Symmetric Cryptography Message Authentication Codes

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Content

Asymmetric Cryptography

Public Key Encryption

Digital Signatures

Digital Certificates

Demo(CrypTool)

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History of Cryptography

Substitution ciphers: a->Z, b->T, c->E,…

Encryption determined by Permutation of alphabet

Special case of Caesar Cipher: a->D, b->E, c->F,…

Example: amir -> DPMLU

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Goals of Cryptography

Confidentially Encryption

Integrity MAC / Digital Signatures

Authenticity MAC / Digital Signatures

Non-Repudiation Digital Signatures

Others...

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Symmetric Cryptography

The key for encryption and decryption is the same

Key exchange problem!!!

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Symmetric Algorithms

Stream ciphers

Block ciphers

Data Encryption Standard (DES)

Advanced Encryption Standard (AES)

Triple DES (3DES)

Blowfish

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Message Authentication Codes (MAC)

Allow to test the integrity of a document

3 algorithms: key generation, tagging, verification Verification is usually done by re-computing the MAC

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Asymmetric Cryptography

The key for encryption and decryption are different

Key exchange problem solved

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Asymmetric Algorithms

Rivest, Shamir and Adleman (RSA)

Elgamal

Chor-Rivest

Rabin

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RSA

Frist practical asymmetric encryption algorithm proposed by Rivest, Shamir and Adleman

Security is based on the intractability of factoring large numbers

Slower than symmetric algorithms

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RSA

Key generation: Public key: (n, e), Private key: d

Encryption: c = Enc(m, e) = m^e mod n, where m is a message

Decryption m = Dec(m, d) = c^d mod n

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Public key encryption

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Digital Signatures

Allow to test authenticity and integrity of documents Non-repudiation: a third party can be convinced of

authenticity

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RSA signatures: “signing by decryption”

RSA has a commutative encryption/decryption operations: Enc(Dec(m)) = Dec(Enc(m)) = m, where m := Message

Key generation Similar to RSA, public key: (n, e), private key: d Uses a collision-resistant hash function H

Signing s = [H(m)]^d mod n, where s := Signature

Verification Test if, H(m) ≡ s^e mod n

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Digital Certificates

How can I be sure that a public key really belongs to the right person?

Solution: Digital Certificates

A digital certificate is a message signed by a trusted party that contains the identity of a person and a public key

Contents of a digital certificate: name of issuer, date, expiration date, public key, name of a person, ...

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X.509 Digital Certificates

Centralized architecture

Hierarchical system

Each department has its own certificatioin authority

(CA)

The public key of this CA is signed by a “higher” CA

“Root certificates”

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Demo (CrypTool)

Symmetric Algorithms XOR Triple DES(ECB) ….

Asymmetric Algorithms RSA ….

Others…

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Questions???

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Discussion(1)

Q: Give some other Goals of Cryptography.

A: Availability, Anonymity, Untraceability, Unlinkability, Being dated…

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Discussion(2)

Q: Can you give an example as a solution to the key exchange problem for the symmetric cryptography?

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Discussion(3)

Q: Why do we use a collision-resistant hash function H by signing?

A: We sign the hash value of a message, because it is faster than signing the whole message and even more secure.

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References

Trusted System lecture (WS10/11) http://www.seceng.informatik.tu-darmstadt.de/ts10/

C. Eckert. IT-Sicherheit: Konzepte - Verfahren – Protokolle. Oldenbourg, 2009.

J. Buchmann. Einführung in die Kryptographie. Springer, 2010

Public Key Infrastructures lecture (SS10) http://www.cdc.informatik.tu-darmstadt.de/lehre/SS10/vorlesung/PKI/PKI_Chapter03.4pp.al.pdf

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