SY CSIT 2023 Batch

Advanced
Cryptography
Dr. Araddhana Deshmukh
Director School of CSIT
Reference :- Fifth Edition
by William Stallings

Lecture slides by Lawrie Brown

Editied by R. Newman
 Chapter 2 – Classical Encryption
Techniques

Many savages at the present day regard their

names as vital parts of themselves, and
therefore take great pains to conceal their real
names, lest these should give to evil-disposed
persons a handle by which to injure their owners.
—The Golden Bough, Sir James George Frazer
 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
 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
Symmetric Cipher Model
 Requirements
two requirements for secure use of
symmetric encryption:
● a strong encryption algorithm
● a secret key known only to sender / receiver
mathematically have:
Y = EK(X)
X = DK(Y)
assume encryption algorithm is known
implies a secure channel to distribute key
 Cryptography
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
 Cryptanalysis
objective to recover key not just message
general approaches:
● cryptanalytic attack
● brute-force attack
 Cryptanalytic Attacks
ciphertext only
● only know algorithm & ciphertext, is statistical,
know or can identify plaintext
known plaintext
● know/suspect plaintext & ciphertext
chosen plaintext
● select plaintext and obtain ciphertext
chosen ciphertext
● select ciphertext and obtain plaintext
chosen text
● select plaintext or ciphertext to en/decrypt
 More Definitions
unconditional security
● no matter how much computer power or time
is available, the cipher cannot be broken since
the ciphertext 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
 Brute Force Search
always possible to simply try every key
most basic attack, proportional to key size
assume either know / recognise plaintext

Key Size (bits) Number of Alternative Time required at 1 Time required at 106
Keys decryption/µs 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)
 Classical 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 ciphertext bit
patterns
 Caesar Cipher
earliest known substitution cipher
by Julius Caesar
first attested use in military affairs
replaces each letter by 3rd letter on
example:
meet me after the toga party
PHHW PH DIWHU WKH WRJD SDUWB
 Caesar Cipher
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

then have Caesar cipher as:

c = E(p) = (p + k) mod (26)
p = D(c) = (c – k) mod (26)
 Cryptanalysis of Caesar
Cipher
only have 26 possible ciphers
● A maps to A,B,..Z
could simply try each in turn
a brute force search
given ciphertext, just try all shifts of letters
do need to recognize when have plaintext
eg. break ciphertext "GCUA VQ DTGCM"
 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
 Monoalphabetic Cipher
Security
now have a total of 26! = 4 x 1026 keys
with so many keys, might think is secure
but would be !!!WRONG!!!
problem is language characteristics
 Language Redundancy and
Cryptanalysis
human languages are redundant
eg "th lrd s m shphrd shll nt wnt"
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
English Letter Frequencies
 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
if caesar cipher look for common peaks/troughs
● peaks at: A-E-I triple, NO pair, RST triple
● troughs at: JK, X-Z
for monoalphabetic must identify each letter
● tables of common double/triple letters help
 Example Cryptanalysis
given ciphertext:
UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ
VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX
EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ
count relative letter frequencies (see text)
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
 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
 Playfair Key Matrix
a 5X5 matrix of letters based on a keyword
fill in letters of keyword (sans 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
 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
 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
it can be broken, given a few hundred letters
since still has much of plaintext structure
 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
 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
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
For (i=0; s[i]!=‘\0’ ; i++) {
If (s[i] >=‘a’ && s[i] )
1.lowercase in ASCII range=‘a’(97) to
‘z’(122)
2.subtract 32
‘a’(97)-32=‘A’(65)
3.convert ASCII back to character.
 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
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, then need to determine number of
alphabets, since then can attach each
 Kasiski Method
method developed by Babbage / Kasiski
repetitions in ciphertext give clues to period
so find same plaintext an exact period apart
which results in the same ciphertext
of course, could also be random fluke
eg repeated “VTW” in previous example
suggests size of 3 or 9
then attack each monoalphabetic cipher
individually using same techniques as before
 Autokey Cipher
ideally want a key as long as the message
Vigenère proposed the autokey cipher
with keyword is prefixed to message as key
knowing keyword can recover the first few letters
use these in turn on the rest of the message
but still have frequency characteristics to attack
eg. given key deceptive
key: deceptivewearediscoveredsav
plaintext: wearediscoveredsaveyourself
ciphertext:ZICVTWQNGKZEIIGASXSTSLVVWLA
 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
 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
 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
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: 3 4 2 1 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
 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
 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
used a series of cylinders, each giving one
substitution, which rotated and changed after
each letter was encrypted
with 3 cylinders have 263=17576 alphabets
Hagelin Rotor Machine
 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
 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