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Dec 18, 2014

- 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 TransmissionMedium (T) Usually this involves a Computer System (or System), composed ofhardware, 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 Integritymust beunchangedfrom S to R Once received Non-repudiationM 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 wasoriginated by S Causes loss of integrity of message MClosely related but different scenario is denial of M by Scalled 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 theseMethodOpportunityMotivation: MOM10/29/2012 2012, C.J. Dedduwage, University of Colombo 7 8. Control of Attacks Control is the means by which an attack isstopped / prevented Stops a vulnerability from becoming an attack Control is a part of the system and is under ourinfluence10/29/2012 2012, C.J. Dedduwage, University of Colombo 8 9. Cryptology, Cryptography & Cryptanalysis Cryptography is the science of (overt) secretwriting, and its unauthorized decryption Cryptology = cryptography + cryptanalysis Cryptography is the science of overt secretwriting Cryptanalysis is the science of unauthorizeddecryption of an encrypted message10/29/2012 2012, C.J. Dedduwage, University of Colombo 9 10. Cryptography Cryptography Steganography is covert SteganographyCryptography secret writingonly R and S know that M is Proper Technical Linguisticbeing passed SemagramsOpen Code Cryptography proper is Jargon Code Concealmentcipher about overt secret writingnot only R and S know that an M is Cue Null cipher The Grillebeing passed 2012, C.J. Dedduwage, University of 10/29/201210 Colombo 11. Section II MATHEMATICS OF CRYPTOGRAPHY 2012, C.J. Dedduwage, University of10/29/201211Colombo 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 = C = Usually P is written in lowercase while C is written inuppercase10/29/2012 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 toformulate plaintext P, or set of characters, W, used toformulate C Length of a word is usually denoted in superscript V* set of words constructed from V W* set of words constructed from W the empty (null) word Zn the set of all words of length n, where, Zn = {}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 : ( ) is defined where = } If ( ) > 1 then each is called a Homophone (same x, many ys) If ( : ), that is, non-empty for empty word 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 asubset 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 = 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 asits 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 1Monographic Unipartite / that is subjected to one stepMonopartite from M 2Digraphic Bipartite 3TrigraphicTripartite If block length is 1 it is a etc. Polygraphic Polypartite stream cipher, otherwise it is a block cipher Note that in a suitableAll the above assumes that each encryption vocabulary of character n-step X is injunctive. If not, more than onetuples, a block encryption isword from V would encrypt to the same W. simplified to a monographicThis, 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 20Colombo 21. Section III CRYPTANALYSIS 2012, C.J. Dedduwage, University of10/29/2012 21 Colombo

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