Cybersecurity and

Cryptography in
Fintech
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Chapter 3:
CLASSICAL ENCRYPTION TECHNIQUES
After studying this chapter, you should be able to:
❑ 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.
❑ Describe the operation of a rotor machine.

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Symmetric Encryption
▪ Or conventional / private-key / single-key
▪ Sender and recipient share a common key
▪ All classical encryption algorithms are private-key
▪ Was only type prior to invention of public-key in 1970’s
▪ And by far most widely used

Symmetric Cipher Model 3

Some Basic Terminology
▪ Plaintext - original message

▪ Ciphertext - coded message

▪ Cipher - algorithm for transforming plaintext to ciphertext

▪ Key - info used in cipher known only to sender/receiver

▪ Encipher (encrypt) - converting plaintext to ciphertext

▪ Decipher (decrypt) - recovering ciphertext from plaintext

▪ Cryptography - study of encryption principles/methods

▪ Cryptanalysis (codebreaking) - study of principles/ methods of deciphering

ciphertext without knowing key
▪ Cryptology - field of both cryptography and cryptanalysis 4
Requirements
▪ Two requirements for secure use of symmetric encryption:
▪ A strong encryption algorithm (Known)
▪ A secret key known only to sender / receiver

▪ Mathematically have:
Y = E(K, X)
X = D(K, Y)
▪ Assume encryption algorithm is known

▪ Implies a secure channel to distribute key (Weakness Point?!)

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 Cryptography
▪ Can characterize cryptographic system by:
▪ Type of encryption operations used
▪ substitution
▪ transposition
▪ product
▪ Number of keys used
▪ single-key or private
▪ two-key or public
▪ Way in which plaintext is processed
▪ block
▪ stream

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 Cryptanalysis
▪ Objective: to recover key not just a message.
▪ There are two general approaches:
▪ Cryptanalysis: relies on the
▪ nature of the algorithm
▪ perhaps some knowledge of the general characteristics of the plaintext or even some sample
plaintext- ciphertext pairs.
▪ Brute-force attacks
▪ try every possible key on a piece of cipher-text until an intelligible translation into plaintext is
obtained (Recognized ?!).
▪ On average, half of all possible keys must be tried to achieve success.

▪ If either type of attack succeeds in deducing the key, the effect is

catastrophic: All future and past messages encrypted with that key are
compromised.

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Concept Check*
▪ Unconditionally secure cipher Vs. Computationally
secure cipher

* Please check it Online now.

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 Well Done!
▪ Unconditional security

▪ No matter how much computer power or time is available, the cipher cannot be broken since the

cipher-text provides insufficient information to uniquely determine the corresponding plaintext .

▪ Computational security

▪ Given limited computing resources (eg time needed for calculations is greater than age of universe),

the cipher cannot be broken.

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Brute Force Search
▪ Always possible to simply try every key.
▪ Most basic attack, proportional to key size.
▪ Assume either know / recognize plaintext.

Key Size (bits) Number of Alternative Keys Time required at 1 decryption/µs Time required at 106
decryptions/µs*
32 232 = 4.3  109 231 µs = 35.8 minutes 2.15 milliseconds
56 256 = 7.2  1016 255 µs = 1142 years 10.01 hours
128 2128 = 3.4  1038 2127 µs = 5.4  1024 years 5.4  1018 years

168 2168 = 3.7  1050 2167 µs = 5.9  1036 years 5.9  1030 years

26 characters 26! = 4  1026 2  1026 µs = 6.4  1012 years 6.4  106 years
(permutation)

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*A desktop computer is capable of 100 million operations per second, some reach between 150 to 200 million operations per second.
The two basic building blocks of
all encryption technique are
substitution and transposition.
We examine these in the next
two sections. Finally, we discuss
a system that combine both
substitution and transposition.
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PART I: Substitution Ciphers
▪ Where letters of plaintext are replaced by other letters or by numbers or symbols.

▪ Or if plaintext is viewed as a sequence of bits, then substitution involves replacing plaintext

bit patterns with cipher-text bit patterns.

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Caesar Cipher
▪ Earliest known substitution cipher.
▪ By Julius Caesar.
▪ First attested use in military affairs.
▪ Replaces each letter by 3rd letter on (The Key).
▪ 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
▪ Example:
meet me after the toga party
PHHW PH DIWHU WKH WRJD SDUWB
▪ https://www.nayuki.io/page/caesar-cipher-javascript
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Caesar Cipher
▪ 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

▪ Then have Caesar cipher as:

c = E(p) = (p + k) mod (26)

p = D(c) = (c – k) mod (26)

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Cryptanalysis of Caesar Cipher
▪ Only have 26 possible ciphers (practically just 25)
▪ A maps to A,B,..Z

▪ Could simply try each in turn - a brute force search

▪ Given ciphertext, just try all shifts of letters

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Monoalphabetic Cipher
▪ Rather than just shifting the alphabet
▪ Could shuffle (jumble) the letters arbitrarily
▪ Each plaintext letter maps to a different random ciphertext
letter
▪ hence key is 26 letters long

Plain: abcdefghijklmnopqrstuvwxyz
Cipher: DKVQFIBJWPESCXHTMYAUOLRGZN

Plaintext: ifwewishtoreplaceletters
Ciphertext: WIRFRWAJUHYFTSDVFSFUUFYA
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Monoalphabetic Cipher
Security
▪ now have a total of 26!
▪ with so many keys, might think is secure
▪ being 10 orders of magnitude greater than the key space for DES

▪ but would be !!!WRONG!!!

▪ problem is language characteristics
▪ because it does not sufficiently obscure the underlying language characteristics.

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Language Redundancy and
Cryptanalysis
▪ human languages are redundant
▪ eg "th ing sh ph sh ll nt“--digrams
▪ letters are not equally commonly used
▪ in English E is by far the most common letter
▪ followed by T,R,N,I,O,A,S

▪ other letters like Z,J,K,Q,X are fairly rare

▪ have tables of single, double & triple letter frequencies for
various languages
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English Letter Frequencies

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Use in Cryptanalysis
▪ key concept - monoalphabetic substitution ciphers do not change
relative letter frequencies
▪ discovered by Arabian scientists in 9th century
▪ calculate letter frequencies for ciphertext
▪ compare counts/plots against known values

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Example Cryptanalysis
▪ given ciphertext:
UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ
VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX
EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ
▪ count relative letter frequencies
▪ guess P & Z are e and t
▪ guess ZW is th and hence ZWP is the
▪ proceeding with trial and error finally get:
it was disclosed yesterday that several informal but
direct contacts have been made with political
representatives of the viet cong in moscow
▪ https://www.dcode.fr/monoalphabetic-substitution

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Playfair Cipher
▪ not even the large number of keys in a monoalphabetic cipher provides security
▪ one approach to improving security was to encrypt multiple letters
▪ the Playfair Cipher is an example
▪ invented by Charles Wheatstone in 1854, but named after his friend Baron Playfair

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 Playfair Key Matrix
▪a 5X5 matrix of letters based on a keyword
▪ fill in letters of keyword (without duplicates)
▪ fill rest of matrix with other letters
▪ eg. 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

▪ https://planetcalc.com/7751/ 23
Encrypting and Decrypting
▪ plaintext is encrypted two letters at a time
1. if a pair is a repeated letter, insert filler like 'X’
2. if both letters fall in the same row, replace each
with letter to right (wrapping back to start from
end)
3. if both letters fall in the same column, replace each
with the letter below it (again wrapping to top from
bottom)
4. otherwise each letter is replaced by the letter in the
same row and in the column of the other letter of
the pair

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Security of Playfair Cipher
▪ security much improved over monoalphabetic
▪ since have 26 x 26 = 676 digrams
▪ would need a 676 entry frequency table to analyse (verses 26 for
a monoalphabetic)
▪ and correspondingly more ciphertext
▪ was widely used for many years
▪ eg. by US & British military in WW1 and still enjoyed considerable use by the U.S. Army and
other Allied forces during World War II.

▪ it can be broken, given a few hundred letters

▪ since still has much of plaintext structure
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Polyalphabetic Ciphers
▪ polyalphabetic substitution ciphers
▪ improve security using multiple cipher alphabets
▪ make cryptanalysis harder with more alphabets to guess and
flatter frequency distribution
▪ use a key to select which alphabet is used for each letter of
the message
▪ use each alphabet in turn
▪ repeat from start after end of key is reached
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Vigenère Cipher
▪ simplest polyalphabetic substitution cipher
▪ effectively multiple caesar ciphers
▪ key is multiple letters long K = k1 k2 ... kd
▪ ith letter specifies ith alphabet to use
▪ use each alphabet in turn
▪ repeat from start after d letters in message
▪ decryption simply works in reverse

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Example of Vigenère Cipher
▪ write the plaintext out
▪ write the keyword repeated above it
▪ use each key letter as a caesar cipher key
▪ encrypt the corresponding plaintext letter
▪ eg using keyword deceptive
key: deceptivedeceptivedeceptive
plaintext: wearediscoveredsaveyourself
ciphertext:ZICVTWQNGRZGVTWAVZHCQYGLMGJ
▪ A general equation of the encryption process is
Ci = (Pi + Ki mod m)mod 26

▪ http://rumkin.com/tools/cipher/vigenere.php

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Expressed numerically, we have
the following result.

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Aids
▪ simple aids can assist with en/decryption
▪ a Saint-Cyr Slide is a simple manual aid
▪ a slide with repeated alphabet
▪ line up plaintext 'A' with key letter, eg 'C'
▪ then read off any mapping for key letter

▪ can bend round into a cipher disk

▪ or expand into a Vigenère Tableau

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Vigenère Tableau

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Security of Vigenère Ciphers
▪ have multiple ciphertext letters for each plaintext letter
▪ hence letter frequencies are obscured
▪ but not totally lost
▪ start with letter frequencies
▪ see if look monoalphabetic or not

▪ if not, identify the number of translation alphabets, and then

attack each separately.
▪ https://www.dcode.fr/vigenere-cipher

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One-Time Pad
▪ if a truly random key as long as the message is used, the
cipher will be secure
▪ called a One-Time pad
▪ is unbreakable since ciphertext bears no statistical
relationship to the plaintext
▪ since for any plaintext & any ciphertext there exists a key
mapping one to other
▪ can only use the key once though
▪ problems in generation & safe distribution of key

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PART II: Transposition Ciphers
▪ now consider classical transposition or permutation ciphers
▪ these hide the message by rearranging the letter order
▪ without altering the actual letters used
▪ can recognise these since have the same frequency distribution as the original text

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Rail Fence cipher
▪ write message letters out diagonally over a number of rows
▪ then read off cipher row by row
▪ eg. write message out as:
m e m a t r h t g p r y
e t e f e t e o a a t

▪ giving ciphertext
MEMATRHTGPRYETEFETEOAAT

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Row Transposition Ciphers
▪ a more complex transposition
▪ write letters of message out in rows over a specified number of columns
▪ then reorder the columns according to some key before reading off the rows
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 m x y z
Ciphertext: TTNAAPTMTSUOAODWCOIXKNLYPETZ

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▪ The transposition cipher can be made significantly more
secure by performing
▪ more than one stage of transposition. The result is a
more complex permutation that is not easily
reconstructed.

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Product Ciphers
▪ ciphers using substitutions or transpositions are not secure
because of language characteristics
▪ hence consider using several ciphers in succession to make
harder, but:
▪ two substitutions make a more complex substitution
▪ two transpositions make more complex transposition
▪ but a substitution followed by a transposition makes a new much
harder cipher
▪ this is bridge from classical to modern ciphers

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Rotor Machines
▪ before modern ciphers, rotor machines were most common
complex ciphers in use
▪ widely used in WW2
▪ German Enigma, Allied Hagelin, Japanese Purple

▪ implemented a very complex, varying substitution cipher

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▪ used a series of cylinders, each giving one substitution, which rotated and changed
after each letter was encrypted
▪ with 3 cylinders have 263=17576 different substitution alphabets used before the
system repeats.
▪ The addition of fourth and fifth rotors results in periods of 456,976 and
11,881,376 letters, respectively.

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Hagelin Rotor Machine

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Steganography
▪ an alternative to encryption
▪ hides existence of message
▪ using only a subset of letters/words in a longer message marked in some way
▪ using invisible ink
▪ hiding in LSB in graphic image or sound file

▪ has drawbacks
▪ high overhead to hide relatively few info bits
▪ Also, once the system is discovered, it becomes virtually worthless, although
a message can be first encrypted and then hidden using steganography.

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Summary
▪ have considered:
▪ classical cipher techniques and terminology
▪ monoalphabetic substitution ciphers
▪ cryptanalysis using letter frequencies
▪ Playfair cipher
▪ polyalphabetic ciphers
▪ transposition ciphers
▪ product ciphers and rotor machines
▪ stenography

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