Basic Encryption Decryption Chapter 2

Basic Encryption and
Decryption
TOPIC 2

Definitions
 Encryption: process of encoding a message so
its meaning is not obvious.
 Decryption: reverse process which means try
to bring encrypted message back to normal
form.
 Cryptosystem: encryption & decryption system
 Plaintext: original form of message
 Ciphertext: encrypted form of message

Definitions
 Cryptography: hidden writing
 Cryptanalysis: breaking of secure messages
 Cryptanalyst: studies of encryption/decryption
message with the goal of finding the hidden
message (break the encrypted message).
 Cryptology: research/study of encryption &
decryption (both cryptography + cryptanalyst)

Encryption Algorithms
Plaintext
Encryption
Ciphertext
Decryption
Original Plaintext
 Encoding: the process of translating entire words or
phrases to other words or phrases.
 Enciphering: the process of translating letters or
symbols individually.
 Encryption: is the group of term that covers both
encoding and enciphering.

 There are 2 type of encryptions:
 Symmetric Encryption: uses same key for encryption and
decryption process.
 To encrypt: C = E(P, K)
 To decrypt: P = D (E(P,K), K)
Encryption Decryption
Plaintext Ciphertext
Original
Plaintext
Key

 Asymmetric Encryption: uses different key for
encryption and decryption process.
 To encrypt: C = E (P, KE)
 To decrypt: P = D (E (P, KE), KD)
Encryption Decryption
Plaintext Ciphertext
Original
Plaintext
Encryption Key
(KE)
Decryption Key
(KD)

Substitutions
 Substitution: one letter is exchanged for another.
 Can be divided into two categories:
 Monoalphabetic Substitution
 Polyalphabetic Substitution

Monoalphabetic Substitutions
 Monoalphabetic Cipher – always uses the same letter of
the alphabet for the ciphertext letter.
A – 0 H – 7 O – 14 V – 21
B – 1 I – 8 P – 15 W – 22
C – 2 J – 9 Q – 16 X – 23
D – 3 K – 10 R – 17 Y – 24
E – 4 L – 11 S – 18 Z – 25
F – 5 M – 12 T – 19
G – 6 N – 13 U – 20
 Arithmetic is done as if the alphabet table were circular.
 Encrypt: C = E (a) = (a + k) mod 26
 Decrypt: a = D (C) = (C – k) mod 26

The Caesar Cipher (Monoalphabetic Substitution)
 Named after Julius Caesar – said to be the first to use it.
 Each letter is translated to another letter.
 Ci = E (pi) = (pi + x) mod 26
 Example: (x = 19)
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
T U V W X Y Z A B C D E F G H I J K L M N O P Q R S
 Plaintext = “SECURITY”
 Ciphertext = “LXVNKBMR”
 Advantages: easy to remember
 Disadvantages: easy to predict pattern of encryption

 Substitution using key phrase:
• Example:
If the key phrase is BOM, the shifted key are as follows:
Plaintext: A B C D E F G H I J K L M N O P...
Ciphertext: B O M A C D E F G H I J K L N P..
• Key Phrase must contain unique letters. Any redundancy need to
be excluded before encrypting.
• Have the same strength as the previous simple substitution
ciphers.

 Let’s analyze the example below:
Example:
 Key: SPECTACULAR (key must not contain redundant letters
so drop C and A), therefore key becomes SPECTAULR
 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
 S P E C T A U L R B D F G H I J K M N O Q V W X Y Z

 To strengthen, apply matrix such as below:
C I N A B D
E F G H J K
L M O P Q R
S T U V W X
Y Z
 Key Phrase is CINCIN
P : 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
C: C E L S Y I F M T Z N G O U A H P V B J Q W D K R X

Multiplication
 f(a) = ak mod n, where k and n are relatively prime so that
the letters of the alphabet produced a complete set of
residues.
 If k and n are not relatively prime, several plaintext will
encrypt to the same ciphertext letter and not all letter will
appear in the ciphertext alphabet e.g. if k = 12 and n =26.
 Example: If k = 12
Plaintext ABC DEF GHI JKL MNO PQR STU VWX YZ
Ciphertext = AMY KWI UJS EQC OAM YKW IUA SEQ CO
eg. BOM → MMO

Cryptanalysis of the Substitution Cipher
 The Arabs were the first to make significant advances in
cryptanalysis.
 An Arabic author, Qalqashandi, wrote down a technique
for solving ciphers which is still used today.
 The technique is to write down all the ciphertext letters
and count the frequency of each symbol.
 Using the average frequency of each letter of the
language, the plaintext can be written out.
 This technique is powerful enough to cryptanalyze ANY
monoalphabetic substitution cipher if enough ciphertext
is provided.

Character Frequencies
 Most languages letters are not equally common
 In English e is by far the most common letter
 These are different for different languages

Cryptanalysis of the Caesar Cipher
 Suppose you were trying to break the following
ciphertext message:
Wklv phvvdjh lv qrw wrr kdug wr euhdn
 It is not so difficult to break the ciphertext above by
doing some analysis on it. How?
(1) Start on the weak points: blank is translated to itself!
(2) In English there are relatively few small words like;
am, is, be, he, we, and, are, you, she etc…
Therefore, one attack can start off by substituting
known short words at appropriates places.
(3) Look for repetition and patterns.

Cryptanalysis of the Caesar Cipher
Example:
 If wrr is TOO. wr would be TO (more sense compare to
SE)
w k l v p h v v d j h l v q r w w r r k d u g w r e u h d n
T - - - - - - - - - - - - - OT TOO - - - - TO - - - - -

Polyalphabetic Substitution Ciphers
 The weakness of monoalphabetic ciphers - frequency
distribution reflects the distribution of the underlying
alphabet.
 Solution : flatten the distribution
: use polyalphabetic substitution
 How to flatten the distribution? – combine both high and
low distributions.
If E1 (T) = a and E2 (T) = b
E1 (X) = a and E2 (X) = b

Flat distribution of ciphertext ‘a’ and ‘b’

 We can also combine two distributions by using two
separate encryption alphabets – the first for all
characters in odd positions of the plaintext message and
the second for all the characters in even positions.

 Consider the two encryption algorithms below:
26mod)*3()(1 λλπ = 26mod)*3()(1 λλπ =
26mod)13)*5(()(2 += λλπ
a d g j m p s v y b e h k n q t w z c f i l o r u x
n s x c h m r w b g l q v a f k p u z e j o t y d i
Table for Odd Position
Table for Even Position

 Encrypt TREATY IMPOSSIBLE
TREAT YIMPO SSIBL E (plaintext)
f umn f dyv t f czysh h (ciphertext)
 What have you notice?

Vigenère Ciphers
 Proposed by Blaise de Vigenere from the court of Henry
III of France in the sixteenth century.
 Basically it’s a multiple Caesar Ciphers – each row of
the Vigenere table corresponds to a Caesar cipher. The
first row is a shift of 0, the second is a shift of 1 and the
last is a shift of 25.
 Vigenere cipher uses this table together with a keyword
to encipher a message.

Vigenere Tableau
Plaintext
K
e
y
Ciphertext
2
1
3

Cryptanalysis of Polyalphabetic Substitutions
 There are two ways:
 Kasiski Method
 Index of Coincidence
Kasiski Method for repeated pattens
 Named for its developer, a Prussian military officer.
 Is a way of finding the number of alphabets that were
used for encryption.
 -th, -ion, -ed, -tion, and, to, are, appear with high
frequency (regularity of English).

Kasiski Method
 For Kasiski Method, the steps are:
1. Identify repeated patterns of three or more characters.
2. For each patterns write down the position at which each
instances of the pattern begins.
3. Compute the difference between the starting points of
successive instances.
4. Determine all factors of each difference.
5. If a polyalphabetic substitution cipher was used, the key
length will be one of the factors that appears often in step 4.

- Form set of letters according to the position of key
assumed.
- Use previous monoalphabetic cryptanalysis.
Index of Coincidence
 Index of coincidence is a measure of the variation
between frequencies in a distribution.

The “Perfect” Substitution Cipher
What makes a perfect substitution cipher?
 An ideal substitution would use many alphabets for an
unrecognizable distribution and no apparent pattern for
the choice of an alphabet at a particular point.
 Let’s look at Vernam Cipher or One-Time Pad
algorithms.

Vernam Cipher (One Time Pad)
 Introduced by Gilbert Vernam (AT&T Engineer)
in 1918.
 Immune to cryptanalytic attack because the
available ciphertext does not display the pattern
of the key.
 Involves an arbitrarily long non-repeating
sequence of numbers that are combined with
the plaintext.

 Compared with most cryptosystems it is very simple.
 To use a one time pad, you need two copies of the
“pad” (also known as the key) which is a block of truly
random data at least as long as the message you wish
to encode.
 If the data on the pad is not truly random the security of
the pad is compromised.

Example:
 Assume that the alphabetic letters are combined by sum
mod 26 with a stream of random two-digit numbers.
Plaintext : V E R N A M C I P H E R
Numerical Value : 21 4 17 13 0 12 2 8 15 7 4 17
+random number : 76 48 16 82 44 3 58 11 60 5 48 88
= sum : 97 52 33 95 44 15 60 19 75 12 52 105
mod 26 : 19 0 7 17 18 15 8 19 23 12 0 1
ciphertext : T A H R S P I T X M A B

 Note:
 random number 48 happen to fall at the places of repeated
letters, accounting for repeated ciphertext A but however highly
unlikely.
 repeated letter t comes from different plaintext letter

Binary Vernam Cipher
 Works just as well as
“alphabets”.
 Example :
 This operation is perform
on each letter in
sequence.
Plaintext: 1 0 1 1 0 1 1 0 0 1 0 1 0 1 1 1 0 0 1 0 1 1 0 1
Input Bits
Output
BitsMessage Pad
0
0
0 0
0
0
1 1
1 1
1 1

 Systems using perfect random, non-repeating keys
which is endless and senseless
 Random key used once, and only once.
 It is the only unbreakable cryptography system
 Unbreakable in theory:
 the key neither repeats, nor recurs, nor makes sense,
nor erects internal frameworks
 perfect randomness nullifies any horizontal, or
lengthwise cohesion

 Why wouldn't it be used today?
 Sender and receiver need to be perfectly synchronized
 It would not work for a T1 communication line:
 If receiver is off by a bit (bit dropped during
transmission) the plaintext will not make any sense
 If bits are altered during transmission (noise hit) those
bits will decrypt incorrectly
 It does not provides authenticity, only confidentiality

Transpositions (Permutations)
 The plaintext remains the same, but the order of characters
is shuffled around – example: shuffle secret to etcrse
 Arrangement was classically done with the aid of some
type of geometric figure, usually 2-dimensional array
(matrix).
 Transposition is not a permutation of alphabet characters
but a permutation of places:
 letters retain their identity but lose their position
 there is a permutation of the plaintext letters

Plaintext
write-in
figure
take-off
Ciphertext

Transposition Cipher: Columnar
 Encryption: Plaintext is written horizontally onto the matrix of
of fixed width and the ciphertext is read off vertically.
 Decryption: Ciphertext is written vertically onto the same
matrix of identical width and then reading the plaintext off
horizontally.
 Example : Plaintext is RENAISSANCE is written into a 3 x 4
matrix as follows
R E N A
I S S A
N C E
the resulting cipher text is RINESCNSEAA

Double Transposition Algorithm
 Involves 2 columnar transposition, with different
numbers of columns, applied one after the other.
 Example:
Single Columnar
T H (I S) I
S A (M E) S
S A (G E) T
O S (H O) W
H O (W A) C
O L (U M) N
A R (T R) A
N S (P O) S
I T (I O) N
W O (R K) S
Produces :
TSSOH OANIW HAASO LRSTO
(I(M(G(H(W (U(T(P(I(R S)E)E)O)A) M)R)O)O)K)
ISTWC NASNS

 Second transposition written in an 8 by 7 matrix:
 Can you write down the result?
T S S O H O A
N I W H A A S
O L R S T O (I
(M (G (H (W (U (T (P
(I (R S) E) E) O) A)
M) R) O) O) K) I S
T W C N A S N
S X X X X X X

 Extra position must be filled with a padding character,
eg. X
 However the X’s filling the last row stands out. Better
way is to use letters that are frequently used so that it
would not be possible to identify the padding character.

Stream vsBlock Ciphers
 Stream cipher – encrypt one symbol of plaintext
immediately into a symbol of ciphertext
 Block cipher – encrypt a group of plaintext symbols as
one block.

Stream vs Block Ciphers
Advantages of stream ciphers:
 Speed of transmission – each symbol is encrypted alone, each
symbol is encrypted as soon as it is read.
 Low error propagation – an error in the encryption process affects
only that character (each symbol is separately encoded).
Disadvantages of stream ciphers:
 Low diffusion where all information of the symbol contained in one
symbol of the ciphertext – cryptanalyst consider each ciphertext as
a separate entity.
 Susceptibility to malicious insertion & modification – interceptor who
has broken the code can splice together pieces of previous
message and transmit a spurious new message that may look
authentic.

Stream vs Block Ciphers
Advantages of block ciphers:
 Diffusion – one ciphertext block may depend on several plaintext
letters.
 Immunity to insertions – because of block of symbols are
enciphered, impossible to insert a single symbol into one block.
Disadvantages of block ciphers:
 Slowness of encryption – block cipher must wait until an entire
block of plaintext symbols has been received before starting the
encryption process.
 Error propagation – an error will affect the the transformation of
all other characters in the same block.

Characteristics of “Good” Ciphers
Shannon Characteristics
 The amount of secrecy needed should determine the amount of
labor appropriate for the encryption and decryption.
 The set of keys and the enciphering algorithm should be free
from complexity.
 The implementation of the process should be as simple as
possible.
 Errors in ciphering should not propagate and cause corruption of
further information in the message.
 The size of the enciphered text should be no larger than the text
of the original message.

Characteristics of “Good” Ciphers
 Confusion – Interceptor should not be able to predict
what changing one character in the plaintext will do to
the ciphertext.
 Diffusion – Changes in the plaintext should affect many
parts of the ciphertext. Good diffusion means that the
interceptor needs access to much ciphertext to infer the
algorithm.

Basic Encryption Decryption Chapter 2

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