The document provides an introduction to cryptography and cryptanalysis. It defines basic terminology like plaintext, ciphertext, encryption, and decryption. Encryption is the process of translating plaintext into ciphertext, while decryption is the reverse process. The document also discusses concepts like character sets, keys, alphabets, word lengths, blocks, and the requirements for a successful cryptanalysis attack. The overall document serves as a high-level overview of cryptography fundamentals and concepts.

1. WORK IN PROGRESS | PRIVATE USE ONLY
Basics of Cryptography
An Introduction to Theory of
Cryptography
10/29/2012 © 2012, C.J. Dedduwage, University of Colombo 1

2. Section I
BASIC TERMINOLOGY AND CONCEPTS
© 2012, C.J. Dedduwage, University of
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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)
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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
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5. Main Types of Attack
1. 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 M
2. Interruption / Blocking
– Prevents R from getting message M
– Causes loss of availability of message M
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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 M
Closely related but different scenario is denial of M by S—called repudiation
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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 these
Method–Opportunity–Motivation: MOM
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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
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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
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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
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11. Section II
MATHEMATICS OF CRYPTOGRAPHY
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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
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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))
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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*
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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:
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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 Nulls
Homophones and Nulls help to mask character and word frequencies.
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17. Cryptosystem
• A cryptosystem M is an N-tuple formed by
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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
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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
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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.
encryption
The most basic encryption types are Substitution and Permutation (Transposition)
© 2012, C.J. Dedduwage, University of
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21. Section III
CRYPTANALYSIS
© 2012, C.J. Dedduwage, University of
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Colombo