This document is an introduction to cryptography presented by Amir Neziri and Jurlind Budurushi. It discusses the history and goals of cryptography, as well as symmetric and asymmetric cryptographic algorithms like AES, RSA, and digital signatures. It also covers cryptographic concepts such as public key encryption, message authentication codes, digital certificates, and concludes with a demo of encryption tools.

1. English for Comp. Science I
Introduction to Cryptography
Amir Neziri & Jurlind Budurushi
2/3/2011

2. Introduction
 Let’s make the introduction...
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3. Introduction
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4. Content
 History of Cryptography
 Goals of Cryptography
 Symmetric Cryptography
 Message Authentication Codes
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5. Content
 Asymmetric Cryptography
 Public Key Encryption
 Digital Signatures
 Digital Certificates
 Demo(CrypTool)
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6. 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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7. Goals of Cryptography
 Confidentially
 Encryption
 Integrity
 MAC / Digital Signatures
 Authenticity
 MAC / Digital Signatures
 Non-Repudiation
 Digital Signatures
 Others...
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8. Symmetric Cryptography
 The key for encryption and decryption
is the same
 Key exchange problem!!!
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9. Symmetric Algorithms
 Stream ciphers
 Block ciphers
 Data Encryption Standard (DES)
 Advanced Encryption Standard (AES)
 Triple DES (3DES)
 Blowfish
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10. 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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11. Asymmetric Cryptography
 The key for encryption and
decryption are different
 Key exchange problem solved
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12. Asymmetric Algorithms
 Rivest, Shamir and Adleman (RSA)
 Elgamal
 Chor-Rivest
 Rabin
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13. 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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14. 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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15. Public key encryption
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16. Digital Signatures
 Allow to test authenticity and integrity of documents
 Non-repudiation: a third party can be convinced of
authenticity
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17. 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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18. 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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19. 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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20. Demo (CrypTool)
 Symmetric Algorithms
 XOR
 Triple DES(ECB)
 ….
 Asymmetric Algorithms
 RSA
 ….
 Others…
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21. Questions???
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22. Discussion(1)
 Q: Give some other Goals of Cryptography.
 A: Availability, Anonymity, Untraceability, Unlinkability, Being
dated…
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23. Discussion(2)
 Q: Can you give an example as a solution to the key exchange
problem for the symmetric cryptography?
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24. 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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26. 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/P
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