Symmetric Encryption Techniques

SYMMETRIC CIPHERS
By: Dr. Kapil Gupta

Symmetric Encryption
• 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

• Conventional encryption: encryption and
decryption are performed using the same key.
• Symmetric encryption transforms plaintext
into ciphertext using a secret key and an
encryption algorithm. Using the same key and
a decryption algorithm, the plaintext is
recovered from the ciphertext.

Plaintext - original message or data that is fed into the
algorithm as input.
• Encryption algorithm – performs various substitutions or
transformations on plaintext.
• Secret key –is also input to the encryption algorithm. The
exact substitutions/transformations performed by the
algorithm depend on the key .
• Ciphertext - scrambled message produced at the output.
It depends on the plaintext and secret key. For a given
message , two different keys will produce two different
ciphertexts.
• Decryption algorithm – inverse of encryption algorithm

Two requirements for secure use of symmetric encryption:
1. A Strong Encryption Algorithm: The opponent should be
unable to decrypt ciphertext or discover the key even if he or
she is in posssession of a number of ciphertexts together with
the plaintext that produced each ciphertext.
2. A Secret Key Known Only To Sender / Receiver: if
someone can discover the key and knows the algorithm, all
communication using this key is readable.
– It is impractical to decrypt a message on the basis of the
ciphertext plus knowledge of the encryption/decryption
algorithm, and hence do not need to keep the algorithm
secret; rather we only need to keep the key secret. This
feature of symmetric encryption is what makes it feasible
for widespread use. It allows easy distribution of s/w and
h/w implementations.

Encryption
algorithm
Decryption
algorithm
Message
source
Key
source
Cryptanalyst
Destination
source
Secure Channel
X Y
K
X
Ẋ
ǩ
Model of Conventional Cryptosystem

• Mathematically :
Y = E(K, X) ; this notation indicates that Y is
produced by using encryption algorithm E as a
function of the plaintext X, with the specific
function determined by the value of the key K.
At receiver, in possession of the key, is able to
invert the transformation: X = D(K, Y)

Cryptography
• cryptographic systems are characterized along
three independent dimensions:
– 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

Type of encryption operations used
• Substitution: in which each element in the
plaintext (bit, letter, group of bits or letters)
is mapped into another element.
• Transposition: in which elements in the
plaintext are rearranged. The fundamental
requirement is that no information be lost.
• Product: involve multiple stages of
substitutions and transpositions.

Number of keys used
• Single-key or private: If both sender and receiver
use the same key, the system is referred to as
symmetric, single-key, secret-key, or
conventional encryption.
• Two-key or public: If the sender and receiver use
different keys, the system is referred to as
asymmetric, two-key, or public-key encryption

Way in which plaintext is processed
• Block: A block cipher processes the input one
block of elements at a time, producing an output
block for each input block.
• Stream: A stream cipher processes the input
elements continuously, producing output one
element at a time, as it goes along.

Cryptanalysis
• Objective of attacking an encryption system is
to recover key not just message
• general approaches:
– cryptanalytic attack
– brute-force attack
• if either succeed all key use compromised

Cryptanalytic Attacks
Cryptanalytic attacks rely on the nature of the
algorithm plus some knowledge of the general
characteristics of the plaintext .
This type of attack exploits the characteristic
of the algorithm to attempt to deduce a specific
plaintext or to deduce the key being used.
Brute-force attacks
The attacker tries every possible key on piece
of cipher-text until an intelligible translation
into plaintext is obtained.

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

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(k, p) = (p + k) mod (26)
p = D(k, c) = (c – k) mod (26)

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

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 (minus 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 (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

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

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

Vernam Cipher
ultimate defense is to use a key as long as the
plaintext
with no statistical relationship to it
invented by AT&T engineer Gilbert Vernam in
1918
originally proposed using a very long but
eventually repeating key

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
is 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: 4312567
Column Out 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

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
• advantage is can obscure encryption use

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

Reference Book
Cryptography and Network Security by William
Stallings.

Symmetric Encryption Techniques

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