1. M. en C. Nidia Asunción Cortez Duarte
INSTITUTO POLITÉCNICO NACIONAL ESCUELA SUPERIOR DE CÓMPUTO  
Cryptography
M. en C. Nidia Asunción Cortez Duarte

2. Maestría en Ciencias (Criptografía) CINVESTAV-IPN
Ingeniería Sistemas Computacionales
ESCOM-IPN (10ma generación)
Departamento de Ingeniería en Sistemas Computacionales
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3. Why did you choose this optative class?
Name
Why did you choose this optative class?
What do you know about cryptography?
What’s the difference between cryptography and security information?
Do you like program in HW or SW? Why?
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4. 2015-2016/02 Group 3CM3 Monday, Thursday 7:00 - 8:30
Friday 8:30 – 10:00
Laboratory LS3 (tolerance of 10 min)
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5. AIM OF THE LEARNING UNIT: The student designs primitives and cryptographic applications using existant algorithms, techniques and existant tools.
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6. Alice
Bob
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7. Alice
Bob
Candy
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8. Security Shell Model
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9. CONTENTS: U1: Cryptography Fundamentals. U2: Symmetric Cryptography.
Definition and importance of cryptography
Cryptographic services.
Cryptographic system characteristics 
Attacks
U2: Symmetric Cryptography.
Symmetric cryptography characteristics  
Perfect secrecy
Classical cryptosystems
Modern cryptography algorithms
Modes of operation
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10. CONTENTS: U3: Public key Cryptography. U4: Digital Signatures.
Public key cryptography characteristics.
Integers modulo n.
Number theory
Public key algorithms
U4: Digital Signatures.
Hash functions
Message authentication codes: MAC
Digital signatures.
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11. REFERENCES
Trappe, W. Washington, L. (2006). Introduction to Cryptography with Coding Theory (2ª Ed.). United States of America: Ed. Prentice Hall. ISBN-13: Stallings, W. (2010). Cryptography and network security (5ª Ed.). United States of America: Ed. Prentice Hall. ISBN-13: Stinson, D. R. (2005). Cryptography: theory and practice (3ª Ed.). United States of America: Ed. Chapman&Hall/CRC. ISBN-13: Konheim, A. G. (2007). Computer Security and cryptography. United States of America: Ed. John Wiley & Sons. ISBN-13: Paar, C. Pelzl, J. Preneel B. (2009). Understanding Cryptography: A textbook for students and practitioners. United States of America: Ed. Springer Verlag. ISBN-13:
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12. LEARNING EVALUATION
Assessment Portfolio of Evidences: Exercise-solving (class or hw) 30% 20% Laboratory Practices 20% 30% Learning Evidence 40% 40% 30% Quiz(s) 10% 10% Project 10% 70%
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13. HW1
Read the story "The Gold Bug" In teams of 5 next Monday expose the story in English! 
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14. Class
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15. Since humans began sending each other secret
messages, they have been writing in code.
Those messages were
Military plans
Sensitive blueprints
Love letters
Encrypting the communication can
protect it from prying eyes.
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16. The search for the unbreakable code continues!
For thousands of years we have been inventing codes, and when those were broken we set about inventing better codes.
The search for the unbreakable code continues!
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17. Cryptography Since a dictionary Kriptos = hide and graphos = write,
the art to write in an enigmatic mode. .
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18. Cryptography Classical Modern Transposition Substitution Symmetric
Asymmetrical
Block
Flows
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19. Exersice
Encrypt your first name with all the classic ciphers we will see
Cipher n i d i a key
Caesars QLGLD Shift-3
… … …
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20. Exercise
Suppose someone uses the Shift-19 cipher and sends the message LHXTLR to you, find the original message.
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21. Encrypt “cryptography class”
Let C1=3p+2
C2= 2p+5
Encrypt “cryptography class”
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22. Encrypt “cryptography class”
Let C1=3p+2
C2= 2p+5
Encrypt “cryptography class”
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23. Let Encryption function C=7p+5 Find the decryption function
C= LFICHLFIJTBIJLH
Find the plaintext
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24. Ancient Egyptian hieroglyps
Julius Caesar
100 BC Roman
Shift Cipher
Rosetta Stone
Ancient Egyptian hieroglyps
Demotic
Ancient Greek
Egyptian writing system
hieroglyph
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25. Slaves
Shift-cipher
Pig-pen
Enigma Machine
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26. Vigenere Encrypt p=cryptography class using the key=secret
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27. Cryptography
“The study of mathematical techniques related to the aspects of information security, such as confidentiality, integrity and availability of the data, authentication of entity and origin, it doesn’t includes only the media to provide information security, but to a set of techniques.” Menezes & Vanstone
Handbook of Applied Cryptography
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28. Cryptography
Text Message which will be transmited in a safe way. Cipher Message that results after an encryption of the text. Key Is the information which allows to encrypt and decrypt the message.
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29. Cryptography : the art to write in an enigmatic mode
Cryptology Discipline which studies how to achieve secure communications over ways which aren’t besides it resolves another issues. (Disciplina que estudia cómo lograr comunicaciones seguras a través de formas que no son)
Cryptography : the art to write in an enigmatic mode
Cryptoanalisys Discipline which studies how to break cryptographic schemas.
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30. Theory of the Information
In its clasification in science, cryptography comes from a branch of the mathematic, which was initiated by the mathematic Claude Elwood Shannon in 1948, denominated “Theory of the Information”.
This branch of the science which is divided in: “Code Theory” and “Cryptology”. As the same way Cryptology is divided in Cryptanalisys and Cryptography, as it is shown in the next figure:
Mathematics
Theory of the Information
Code Theory
Cryptology
Cryptography
Cryptoanalisys
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31. Historically Cryptography can be clasified in two:
Clasification
Historically Cryptography can be clasified in two:
Classical Cryptography it’s the one which was used before the actual age until half XX Century.
It also can be understood as non computarized cryptography or non digitized.
The used methods were varied, some very simple and other very complex to cryptanalize for the age.
It can be said that the modern Cryptography was initiated after 3 facts:
The first was the publication of the “Theory of Information” by Shannon.
The second, the appearance in 1974 of the standard of the encryption system DES (Data Encryption Standard) and finally with the appearance of the study in 1976 made by Whitfield Diffle and Martin Hellman about the application of mathematic functions in a single way to a decrypt model named public key encrypt.
Both classical and modern cryptography are classified in accordance to the techniques or methods which are used to encrypt messages.
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32. Cryptography Classical Modern Transposition Sustitution Symmetric
Asymmetrical
Block
Flows
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33. As it was mentioned, classical cryptography is very old.
The cryptographical techniques were very clever and were used to send secret messages between people who had the power or in the war age to send instructions.
Unlike the modern cryptography, the algorythm of the cryptographic system was kept in secret.
Classical Cryptography also includes the construction of machines, which through mechanisms, commonly gear and rotors, they transform a clear message to a encrypted message, like the Enigma machine used in the World War II.
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34. Euclides: Greatestx common divisor [ 300BC]
Historical overview
Euclides: Greatestx common
divisor [ 300BC]
• Eratóstenes: Sieve to find prime numbers[ 220BC]
Fibonacci: algorithm for factoring integers[1200 AD]
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35. Fermat: Factoring and prime number theorem[ 1630 AD]
•Euler: Fermat’s general petit algorithm
[1750 AD] •
Gauss: new factoring algorithm
[1820 AD]
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36. Scytale Cesar Codes Kama Sutra Encryption method by transposition
Classical Encrypt
Scytale
Encryption method by transposition
[Sparta, 650 BC]
Cesar Codes
Encryption method by mono-alphabetical sustitution[Roman Empire, 50BC]
Kama Sutra
Hindu Technique which allowed lovers to communicate without being caught.
[550 AD]
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37. Babington’s mono-alphabetical encryption
Used by Maria I, queen of the Scots
[1542 AD]
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38. Sustitution Encrypt
The encryption alphabet consists in a rearrangement of the original text’s alphabet. Like that each letter of the original alphabet is always replaced for the same letter of the encryption alphabet
…How many different keys are in our alphabet?
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39. Edgar Allan Poe (1809-1849) THE GOLD BUG
'A good glass in the bishop's hostel in the devil's seat twenty-one
degrees and thirteen minutes northeast and by north main branch
seventh limb east side shoot from the left eye of the death's-head
a bee line from the tree through the shot fifty feet out.'
53++!305))6*;4826)4+.)4+);806*;48!8`60))85;]8*:+*8!83(88)5*!;
46(;88*96*?;8)*+(;485);5*!2:*+(;4956*2(5*-4)8`8*; );)6
!8)4++;1(+9;48081;8:8+1;48!85;4)485!528806*81(+9;48;(88;4(+?3
4;48)4+;161;:188;+?;
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40. Class 3
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41. Introduction Cryptography is a very useful tool when we want
Computer Security confidentiality and integrity
can be guaranteed, but we must know how to
use it, to achieve that it’s important to have
clear the basic concepts of the modern
cryptographyc systems.
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42. The need of Information Security in an enterprise has changed in the last decades, before the use of the computers, Information Security was provided by physical media, for example the use of safes and administrative measures, like document clasification procedures.
With the computer, and even more with the arrival of the Internet, it has been essential the use of automatized tools for the protection of files and information stored in the computers, some of this tools are firewalls, IDS (Intrution Detection System) and cryptographyc systems.
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43. Attacks
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44. Alice
John
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45. Kerckhkoff’s Principle
Eva’s objectives
1.Read the original message.
2.Get Alice’s secret key.
3.Modify the original message.
4.Usurp Alice’s identity.
Kerckhkoff’s Principle
It parts from the premise that the foe knows the used cryptographic algorithm. So, the system’s security must be based on:
• The algorithm quality (strenght).
• The key size (bit size of the key).
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46. Alice
John
Eva
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47. Alice
John
Eva
Interruption
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48. Alice
John
Eva
Interruption
Interception
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49. Alice John Eva Interruption Interception Modification
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50. Alice John Eva Interruption Interception Modification Fabrication
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51. “Yes, I do.”
Alice
“No, I don’t.”
Alice
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52. Security According to the Real Spanish Academy means:
Definitions
Security According to the Real Spanish Academy means:
Attribute of secure.
Said of a mechanism which assures a correct behavior, forseeing failures, frustration or violent.
Information Security. We can talk about it like the set of rules, plans and actions which allow the assurance of the information keeping the properties of confidentiality, integity and availability.
Confidentiality means that the information can be read only by those who are authorized.
Integrity means that the information can only be created and modified for those who are authorized, and that the information keeps it hole structure and completeness.
Avilability means that the information must be accessible for consult or modification in the time it’s needed only for those who are authorized.
Computer Security. Set of policies and mechanisms which allows us to guarantee the confidentiality, integrity and availability of the system resources (Understand system resources as the processing memory, storage in a physical device, processing time, band width and the information stored in the system).
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53. Integridad
Autenticación
No repudio
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54. HOMEWORK Consider the spanish alphabet, m=3 P=“amigoconductor”
Key=“peligroso”
find C
Find 𝑘 −1
Download RFC DES
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