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- 1. WORK IN PROGRESS | PRIVATE USE ONLY Basics of Cryptography An Introduction to Theory of Cryptography10/29/2012 © 2012, C.J. Dedduwage, University of Colombo 1
- 2. Section I BASIC TERMINOLOGY AND CONCEPTS © 2012, C.J. Dedduwage, University of10/29/2012 2 Colombo
- 3. Terminology• A Message (M) is a crucial piece of information• Sender (S) is the party that originates the message• Recipient (R) is the intended party of receipt for M• The medium through which M is sent, is called Transmission Medium (T)• Usually this involves a Computer System (or System), composed of hardware, software and data• A Vulnerability is a weakness in the security of the system• An Attack is an exploitation of a vulnerability, by an Intruder (human/machine) who perpetrates (commonly an Outsider O) 10/29/2012 © 2012, C.J. Dedduwage, University of Colombo 3
- 4. Properties of a Message • Only intended Confidentiality parties must receive M • Contents of M Integrity must be unchanged from S to R • Once received Non- repudiation M cannot be denied by R 10/29/2012 © 2012, C.J. Dedduwage, University of Colombo 4
- 5. Main Types of Attack1. Interception – Listening to the message while it passes from S to R – Does not stop R from getting the message M – Causes loss of confidentiality of message M2. Interruption / Blocking – Prevents R from getting message M – Causes loss of availability of message M 10/29/2012 © 2012, C.J. Dedduwage, University of Colombo 5
- 6. Main Types of Attack 3. Modification – Alteration of the contents of message M – R does not receive the original M sent by S – Causes loss of integrity of message M 4. Fabrication – R receives an authentic-looking message, as if it was originated by S – Causes loss of integrity of message MClosely related but different scenario is denial of M by S—called repudiation 10/29/2012 © 2012, C.J. Dedduwage, University of Colombo 6
- 7. Requirements for a Successful Attack • Method: tools, knowledge, skills • Opportunity: time and access to resources • Motivation: a reason to conduct the attack • If any of these are denied, attack would not occur • But all three lie with the intruder, not system • Not practical to target and eliminate theseMethod–Opportunity–Motivation: MOM 10/29/2012 © 2012, C.J. Dedduwage, University of Colombo 7
- 8. Control of Attacks• Control is the means by which an attack is stopped / prevented• Stops a vulnerability from becoming an attack• Control is a part of the system and is under our influence 10/29/2012 © 2012, C.J. Dedduwage, University of Colombo 8
- 9. Cryptology, Cryptography & Cryptanalysis• Cryptography is the science of (overt) secret writing, and its unauthorized decryption• Cryptology = cryptography + cryptanalysis• Cryptography is the science of overt secret writing• Cryptanalysis is the science of unauthorized decryption of an encrypted message 10/29/2012 © 2012, C.J. Dedduwage, University of Colombo 9
- 10. Cryptography Cryptography • Steganography is covert Steganography Cryptography secret writing—only R and S know that M is Proper Technical Linguistic being passed Semagrams Open Code • Cryptography proper is Jargon Code Concealment cipher about overt secret writing—not only R and S know that an M is Cue Null cipher The Grille being passed © 2012, C.J. Dedduwage, University of 10/29/2012 10 Colombo
- 11. Section II MATHEMATICS OF CRYPTOGRAPHY © 2012, C.J. Dedduwage, University of10/29/2012 11 Colombo
- 12. Plaintext & Ciphertext• Plaintext P is the original form of the message• Ciphertext C is the message in its encrypted form• P and C are sequences of characters in the form – P = <P1, P2, P3, P4, … > – C = <C1, C2, C3, C4, … >• Usually P is written in lowercase while C is written in uppercase 10/29/2012 © 2012, C.J. Dedduwage, University of Colombo 12
- 13. Encryption & Decryption• Encryption is the process of translating P into C• Decryption is the reverse process: C into P – Encryption: C = E(P) – Decryption: P = D(C) – Satisfying, P = D(E(C)) 10/29/2012 © 2012, C.J. Dedduwage, University of Colombo 13
- 14. Character Sets• A Vocabulary is a set of characters, V, used to formulate plaintext P, or set of characters, W, used to formulate C• Length of a word is usually denoted in superscript – V*– set of words constructed from V – W*– set of words constructed from W – ε – the empty (null) word – Zn – the set of all words of length n, where, – Zn = {ε}Z1 Z2 … Zn | Zn Z* 10/29/2012 © 2012, C.J. Dedduwage, University of Colombo 14
- 15. Encryption & Decryption• An encryption X is a relation / rule / algorithm – X ∶ V ∗ ⇢ W ∗ where x ↦ z ⋀ y ↦ z ⟶ (x = y) that is injective: – X −1 : V ∗ ⇠ W ∗ x ↤ z iff (x ↦ y)• The converse is written X-1: 10/29/2012 © 2012, C.J. Dedduwage, University of Colombo 15
- 16. Fiber, Homophones and Nulls • Fiber of message 𝑥: (𝑥 ∈ 𝑉 ∗ ) is defined 𝐻 𝑥 where – 𝐻 𝑥 = 𝑦 ∈ 𝑊∗ 𝑥 ↦ 𝑦 𝑢𝑢𝑢𝑢𝑢 𝑋} • If 𝑛(𝐻 𝑥 ) > 1 then each 𝑦 ∈ 𝐻 𝑥 is called a Homophone (same x, many y’s) • If (∆∈ 𝐻 𝑥 : 𝜀 ↦ ∆ 𝑢𝑢𝑢𝑢𝑢 𝑋), that is, non-empty 𝐻 𝑥 for empty word 𝜀 exist, they are called NullsHomophones and Nulls help to mask character and word frequencies. 10/29/2012 © 2012, C.J. Dedduwage, University of Colombo 16
- 17. Cryptosystem• A cryptosystem M is an N-tuple formed by 10/29/2012 © 2012, C.J. Dedduwage, University of Colombo 17
- 18. Keys• A Key is an external parameter that selects a subset of the encryption steps – C = E(P, KE): KE is the encryption key – P = D(C, KD): KD is the decryption key• If KE = KD then the cryptosystem is symmetric, otherwise asymmetric• If KE = KD = ε then M is a keyless cipher 10/29/2012 © 2012, C.J. Dedduwage, University of Colombo 18
- 19. Alphabets• Number of steps in system M = |M| is known as its cardinality• If |M|=1 then the system M is monoalphabetic, otherwise polyalphabetic 10/29/2012 © 2012, C.J. Dedduwage, University of Colombo 19
- 20. Word Lengths and Blocks Word Length Encryption Decryption • A Block is a word from 𝑉 𝑛 1 Monographic Unipartite / that is subjected to one step Monopartite from M 2 Digraphic Bipartite 3 Trigraphic Tripartite • If block length is 1 it is a etc. Polygraphic Polypartite stream cipher, otherwise it is a block cipher • Note that in a suitable All the above assumes that each encryption vocabulary of character n- step X is injunctive. If not, more than one tuples, a block encryption is word from V would encrypt to the same W. simplified to a monographic This, known as polyphony, is rarely seen. encryptionThe most basic encryption types are Substitution and Permutation (Transposition) © 2012, C.J. Dedduwage, University of 10/29/2012 20 Colombo
- 21. Section III CRYPTANALYSIS © 2012, C.J. Dedduwage, University of10/29/2012 21 Colombo

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