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After reading chapter 3, analyze the history of the Caesar Cypher and its impact on cryptography. The initial post must be completed by Thursday at 11:59 eastern. You are also required to post a response to a minimum of two other student in the class by the end of the week. You must use at least one scholarly resource. Every discussion posting must be properly APA formatted.

Cryptography and Network Security:

Principles and Practice Eighth Edition

Chapter 3

Classical Encryption Techniques

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Definitions (1 of 2)

• Plaintext

– An original message

• Ciphertext

– The coded message

• Enciphering/encryption

– The process of converting from plaintext to ciphertext

• Deciphering/decryption

– Restoring the plaintext from the ciphertext

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Definitions (2 of 2)

• Cryptography

– The area of study of the many schemes used for

encryption

• Cryptographic system/cipher

– A scheme

• Cryptanalysis

– Techniques used for deciphering a message without

any knowledge of the enciphering details

• Cryptology

– The areas of cryptography and cryptanalysis

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Figure 3.1 Simplified Model of

Symmetric Encryption

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Symmetric Cipher Model

• There are two requirements for secure use of conventional

encryption:

– A strong encryption algorithm

– Sender and receiver must have obtained copies of the

secret key in a secure fashion and must keep the key

secure

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Figure 3.2 Model of Symmetric

Cryptosystem

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Cryptographic Systems

• Characterized along three independent dimensions:

• The type of operations used for transforming plaintext to

ciphertext

– Substitution

– Transposition

• The number of keys used

– Symmetric, single-key, secret-key, conventional

encryption

– Asymmetric, two-key, or public-key encryption

• The way in which the plaintext is processed

– Block cipher

– Stream cipher

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Cryptanalysis and Brute-Force Attack

• Cryptanalysis

– Attack relies on the nature of the algorithm plus some

knowledge of the general characteristics of the

plaintext

– Attack exploits the characteristics of the algorithm to

attempt to deduce a specific plaintext or to deduce the

key being used

• Brute-force attack

– Attacker tries every possible key on a piece of

ciphertext until an intelligible translation into plaintext is

obtained

– On average, half of all possible keys must be tried to

achieve success

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Table 3.1 Types of Attacks on

Encrypted Messages

Type of Attack Known to Cryptanalyst

Ciphertext Only • Encryption algorithm

• Ciphertext

Known Plaintext • Encryption algorithm

• Ciphertext

• One or more plaintext–ciphertext pairs formed with the secret key

Chosen Plaintext • Encryption algorithm

• Ciphertext

• Plaintext message chosen by cryptanalyst, together with its corresponding

ciphertext generated with the secret key

Chosen Ciphertext • Encryption algorithm

• Ciphertext

• Ciphertext chosen by cryptanalyst, together with its corresponding decrypted

plaintext generated with the secret key

Chosen Text • Encryption algorithm

• Ciphertext

• Plaintext message chosen by cryptanalyst, together with its corresponding

ciphertext generated with the secret key

• Ciphertext chosen by cryptanalyst, together with its corresponding decrypted

plaintext generated with the secret key

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Encryption Scheme Security

• Unconditionally secure

– No matter how much time an opponent has, it is

impossible for him or her to decrypt the ciphertext

simply because the required information is not there

• Computationally secure

– The cost of breaking the cipher exceeds the value of

the encrypted information

– The time required to break the cipher exceeds the

useful lifetime of the information

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Brute-Force Attack

• Involves trying every possible key until an intelligible

translation of the ciphertext into plaintext is obtained

• On average, half of all possible keys must be tried to

achieve success

• To supplement the brute-force approach, some degree of

knowledge about the expected plaintext is needed, and

some means of automatically distinguishing plaintext from

garble is also needed

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Strong Encryption

• The term strong encryption refers to encryption schemes

that make it impractically difficult for unauthorized persons

or systems to gain access to plaintext that has been

encrypted

• Properties that make an encryption algorithm strong are:

– Appropriate choice of cryptographic algorithm

– Use of sufficiently long key lengths

– Appropriate choice of protocols

– A well-engineered implementation

– Absence of deliberately introduced hidden flaws

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Substitution Technique

• Is one in which the letters of plaintext are replaced by other

letters or by numbers or symbols

• If the plaintext is viewed as a sequence of bits, then

substitution involves replacing plaintext bit patterns with

ciphertext bit patterns

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Caesar Cipher

• Simplest and earliest known use of a substitution cipher

• Used by Julius Caesar

• Involves replacing each letter of the alphabet with the

letter standing three places further down the alphabet

• Alphabet is wrapped around so that the letter following Z

is A

plain: meet me after the toga party

cipher: PHHW PH DIWHU WKH WRJD SDUWB

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Caesar Cipher Algorithm

• Can define transformation as:

a b c d e f g h i j k l m n o p q r s t u v w x y z

D E F G H I J K L M N O P Q R S T U V W X Y Z A B C

• Mathematically give each letter a number

a b c d e f g h i j k l m n o p q r s t u v w x y z

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

• Algorithm can be expressed as:

c = E(3, p) = (p + 3) mod (26)

• A shift may be of any amount, so that the general Caesar algorithm is:

C = E(k , p ) = (p + k ) mod 26

• Where k takes on a value in the range 1 to 25; the decryption algorithm is

simply:

p = D(k , C ) = (C − k ) mod 26

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Figure 3.3 Brute-Force Cryptanalysis

of Caesar Cipher

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Sample of Compressed Text

Figure 3.4 Sample of Compressed Text

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Monoalphabetic Cipher

• Permutation

– Of a finite set of elements S is an ordered sequence of

all the elements of S , with each element appearing

exactly once

• If the “cipher” line can be any permutation of the 26

alphabetic characters, then there are 26! or greater than

4 x 1026 possible keys

– This is 10 orders of magnitude greater than the key

space for DES

– Approach is referred to as a monoalphabetic

substitution cipher because a single cipher alphabet is

used per message

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Figure 3.5 Relative Frequency of

Letters in English Text

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Monoalphabetic Ciphers

• Easy to break because they

reflect the frequency data of the

original alphabet

• Countermeasure is to provide

multiple substitutes

(homophones) for a single letter

• Digram

– Two-letter combination

– Most common is th

• Trigram

– Three-letter combination

– Most frequent is the

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Playfair Cipher

• Best-known multiple-letter encryption cipher

• Treats digrams in the plaintext as single units and

translates these units into ciphertext digrams

• Based on the use of a 5 × 5 matrix of letters constructed

using a keyword

• Invented by British scientist Sir Charles Wheatstone in

1854

• Used as the standard field system by the British Army in

World War I and the U.S. Army and other Allied forces

during World War II

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Playfair Key Matrix

• Fill in letters of keyword (minus duplicates) from left to right

and from top to bottom, then fill in the remainder of the

matrix with the remaining letters in alphabetic order

• Using the keyword MONARCHY:

M O N A R

C H Y B D

E F G I/J K

L P Q S T

U V W X Z

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Figure 3.6 Relative Frequency of

Occurrence of Letters

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Hill Cipher

• Developed by the mathematician Lester Hill in 1929

• Strength is that it completely hides single-letter frequencies

– The use of a larger matrix hides more frequency

information

– A 3 x 3 Hill cipher hides not only single-letter but also

two-letter frequency information

• Strong against a ciphertext-only attack but easily broken

with a known plaintext attack

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Polyalphabetic Ciphers

• Polyalphabetic substitution cipher

– Improves on the simple monoalphabetic technique by

using different monoalphabetic substitutions as one

proceeds through the plaintext message

• All these techniques have the following features in

common:

– A set of related monoalphabetic substitution rules is

used

– A key determines which particular rule is chosen for a

given transformation

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Vigenère Cipher

• Best known and one of the simplest polyalphabetic

substitution ciphers

• In this scheme the set of related monoalphabetic

substitution rules consists of the 26 Caesar ciphers with

shifts of 0 through 25

• Each cipher is denoted by a key letter which is the

ciphertext letter that substitutes for the plaintext letter a

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Example of Vigenère Cipher

• To encrypt a message, a key is needed that is as long as

the message

• Usually, the key is a repeating keyword

• For example, if the keyword is deceptive, the message “we

are discovered save yourself” is encrypted as:

key: deceptivedeceptivedeceptive

plaintext: wearediscoveredsaveyourself

ciphertext: ZICVTWQNGRZGVTWAVZHCQYGLMGJ

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Vigenère Autokey System

• A keyword is concatenated with the plaintext itself to

provide a running key

• Example:

key: deceptivewearediscoveredsav

plaintext: wearediscoveredsaveyourself

ciphertext: ZICVTWQNGKZEIIGASXSTSLVVWLA

• Even this scheme is vulnerable to cryptanalysis

– Because the key and the plaintext share the same

frequency distribution of letters, a statistical technique

can be applied

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Vernam Cipher

Figure 3.7 Vernam Cipher

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One-Time Pad

• Improvement to Vernam cipher

proposed by an Army Signal

Corp officer, Joseph

Mauborgne

• Use a random key that is as

long as the message so that

the key need not be repeated

• Key is used to encrypt and

decrypt a single message and

then is discarded

• Each new message requires a

new key of the same length as

the new message

• Scheme is unbreakable

– Produces random output

that bears no statistical

relationship to the

plaintext

– Because the ciphertext

contains no information

whatsoever about the

plaintext, there is simply

no way to break the code

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Difficulties

• The one-time pad offers complete security but, in practice, has two

fundamental difficulties:

– There is the practical problem of making large quantities of

random keys

▪ Any heavily used system might require millions of random

characters on a regular basis

– Mammoth key distribution problem

▪ For every message to be sent, a key of equal length is needed

by both sender and receiver

• Because of these difficulties, the one-time pad is of limited utility

– Useful primarily for low-bandwidth channels requiring very high

security

• The one-time pad is the only cryptosystem that exhibits perfect

secrecy (see Appendix F)

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Rail Fence Cipher

• Simplest transposition cipher

• Plaintext is written down as a sequence of diagonals and

then read off as a sequence of rows

• To encipher the message “meet me after the toga party”

with a rail fence of depth 2, we would write:

m e m a t r h t g p r y

e t e f e t e o a a t

Encrypted message is:

MEMATRHTGPRYETEFETEOAAT

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Row Transposition Cipher

• Is a more complex transposition

• Write the message in a rectangle, row by row, and read the

message off, column by column, but permute the order of

the columns

– The order of the columns then becomes the key to the

algorithm

Key: 4 3 1 2 5 6 7

Plaintext: a t t a c k p

o s t p o n e

d u n t i l t

w o a mx y z

Ciphertext: TTNAAPTMTSUOAODWCOIXKNLYPETZ

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Summary

• Present an overview of the main concepts of symmetric

cryptography

• Explain the difference between cryptanalysis and brute-

force attack

• Understand the operation of a monoalphabetic substitution

cipher

• Understand the operation of a polyalphabetic cipher

• Present an overview of the Hill cipher

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