Cryptography is the study of techniques for securing communication and information. The document provides an introduction to cryptography, including definitions of encryption, decryption, plaintext and ciphertext. It discusses classical ciphers like the Caesar cipher, monoalphabetic and polyalphabetic ciphers, the Playfair cipher, Vigenère cipher and the one-time pad cipher. It also covers cryptanalysis techniques and introduces concepts in modern cryptography like symmetric and asymmetric key cryptography.

1. Cryptography
1

2. Introduction
What is cryptography ?
 Cryptography is the study of
Encryption
◦ Greek kryptos means “hidden” and
graphia means “writtings”
 Encryption is an ancient form of
information protection. … dates back
4,000 years.
◦ process by which plaintext is converted into
ciphertext.
 Decryption is the inverse of
Encryption. 2

3. Introduction …
 A sender S wanting to transmit message
M to a receiver R
 To protect the message M, the sender first
encrypts it into meaningless message M’
 After receipt of M’, R decrypts the
message to obtain M
 M is called the plaintext
◦ What we want to encrypt
 M’ is called the ciphertext
◦ The encrypted output
3

4. Introduction…
 Notation
Given
P=Plaintext
C=CipherText
 C = EK (P) Encryption
 P = DK ( C)
Decryption
4

5. Terminologies
 Cryptography: Schemes for encryption and
decryption
 Encryption algorithm: technique or rules
selected for encryption.
 Key: is secret value used to encrypt and/or
decrypt the text.
 Cryptanalysis: The study of “breaking the
code”.
 Cryptology: Cryptography and
cryptanalysis together constitute the area of
cryptology. 5

6. Encryption vs. C-I-A
Encryption provides :
◦ Confidentiality/Secrecy
 keeps our data secret.
◦ Integrity
 protect against forgery or tampering
6

7. Cryptographic systems
are characterized along three dimensions
 operations used for transforming
◦ Substitution: Replace (bit, letter, group of bits
letters
◦ Transposition: Rearrange the order
◦ Product :use multiple stages of both
 number of keys used
◦ Symmetric: same key , secret-key, private-key
◦ Asymmetric: different key , public-key
 way in which the plaintext is processed
◦ block cipher 7

8.  . For any encryption approach, there
are two major challenges:
 Key distribution: how do we convey
keys to those who need them to
establish secure communication.
 Key management: given a large
number of keys, how do we preserve
their safety and make them available
as needed.
8

9. Transposition and
Substitution
 Simple Simple Substitution
Transposition
security
cusetyri
Encryption
security
Encryption
tfdvsjuz
security
Encryption
19 5 3 20 18 9 19
25
9

10. Classical Substitution
 Caesar Cipher: used by Julius
Caesar's military
◦ substitutes each letter of the alphabet
with the letter standing three places
further down the alphabet
10

11. Caesar cipher
11

12. Activity
 Convert it ....to Caesar Ciphertext?
 Plaintext: are you ready
 Ciphertext: duh brx uhdgb
12
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
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
z
C
Plaintext
Ciphertext

13. Caesar Cipher
 the algorithm can be expressed as, for
each plaintext letter P, substitute
ciphertext letter C.
◦ C = E(3, p) = (p + 3) mod 26
 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
 General Caesar algorithm as:
c = E(k, p) = (p + k) mod (26)
p = D(k, c) = (c – k) mod (26) 13

14. Classical Transposition
 Spartans cipher , fifth century B.C.
Start the war today
Rewrite it by reading down
Srhaoytterdatwta
S t a
r t t
h e w
a r t
o d a
y
Encryption: rearrange the text in 3 columns
14

15. Cryptanalysis
 objective to recover key not just
message
 general approaches:
◦ cryptanalytic attack
 exploits the characteristics of the algorithm
◦ brute-force attack
 try every possible key on a piece of ciphertext
 involves trying each key until you find the right
one
 if either succeed all key use
15

16. 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
◦ it either takes too long, or is too expensive,
16

17. Cryptanalysis…
 given a ciphertext Caesar cipher, then
a brute-force is easy performed:
◦ simply try all the 25 possible keys.
◦ Assuming language of the plaintext is
known.
 Thus, Caesar cipher is far from secure.
17

18. 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
18

19. Brute Force Search
 always possible to simply try every key
 assume either know / recognise plaintext
 impractical if we use an algorithm that
employs a large number of keys.
 most basic attack, proportional to key size
19

20. Language Redundancy and
Cryptanalysis
 human languages are redundant
 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 20

21. English Letter Frequencies
21

22. 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
22

23. Cryptograph cont’…
 Playfair cipher
 Polyalphabetic ciphers
◦ Vigenère cipher
◦ Vernam cipher
◦ One-timepad
 More on Transposition
◦ Rail fence cipher
◦ Message in rectangle ( row transposition )
◦ Rotor machine
23

24. 24
Playfair Cipher
 A.k.a Playfair square
 A manual symmetric encryption technique
 It was the first literal digraph substitution
cipher.
◦ The scheme was invented in 1854 by Charles
Wheatstone, but bears the name of Lord
Playfair who promoted the use of the cipher.

25. Playfair Key Matrix
 a 5X5 matrix of letters based on a
keyword
 fill in letters of keyword (no duplicates, i &
j)
 fill rest of matrix with other letters
 eg. using the keyword (key) simple
s i/j m p l
e a b c d
f g h k n
o q r t u
v w x y z

26. 26
Playfair Cipher
 Use filler letter to separate repeated letters
◦ eg. "balloon" encrypts as "ba lx lo on" Encrypt two
letters together
 Same row– >followed letters
◦ ac--bd
 Same column–> letters under
◦ qw--wi
 Otherwise—>square’s corner at same row
◦ ar--bq

27. Activity
 Q: construct the playfair matrix using the
keyword MONARCHY ?
 Plaintext: Ethiopia
 Ciphertext:
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
klbfhvs
b

28. Security of Playfair Cipher
 security much improved over
monoalphabetic
 But, still has much of plaintext structure.
 it can be broken, given a few hundred
letters
◦ With ciphertext only, possible to analyse
frequency of occurrence of digrams (pairs of
letters)
◦ Obtaining the key is relatively
straightforward if both plaintext and
ciphertext are known.

29. Polyalphabetic ciphers
29

30. Polyalphabetic ciphers
 using multiple substitution 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
30

31. Vigenere Cipher
 simplest polyalphabetic substitution
cipher
 meaning that instead of there being a
one-to-one relationship between each
letter and its substitute, there is a one-
to-many relationship between each letter
and its substitutes.
◦ The encipherer chooses a keyword and
repeats it until it matches the length of the
plaintext
31

32. 32
Vigenère Cipher
 Basically multiple Caesar ciphers
 key is multiple letters long
◦ K = k1 k2 ... kd
◦ ith letter specifies ith alphabet to use
◦ use each alphabet in turn, repeating from
start after d letters in message
 Plaintext: THISPROCESSCANALSOBEEXPRESSED
Keyword: CIPHERCIPHERCIPHERCIPHERCIPHE
Ciphertext: VPXZTIQKTZWTCVPSWFDMTETIGAHLH

33. 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

34. Activity
 Q: encrypt the given plaintext letter
using Vigenère Cipher use keyword
deceptive
 plaintext:
wearediscoveredsaveyourself
 Key:
 Ciphertext:
34
deceptivedeceptivedeceptive
zicvtwqngrzgvtwavzhcqyglmgj

35. Security of Vigenère Ciphers
 have multiple cipher text letters for
each plaintext letter
◦ hence letter frequencies are masked
◦ but not totally lost
 start with letter frequencies
◦ see if look mono alphabetic or not
 if not, then need to determine number
of alphabets, since then can attach
each

36. 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

37. 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
 His system works on binary data (bits
rather than letters)

38. One-Time Pad
 if a truly random key as long as the
message is used, the cipher will be
secure.
 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

39. One-time Pad: Encryption
e=000 h=001 i=010 k=011 l=100 r=101 s=110 t=111
h e i l h i t l e r
001 000 010 100 001 010 111 100 000 101
111 101 110 101 111 100 000 101 110 000
110 101 100 001 110 110 111 001 110 101
s r l h s s t h s r
Encryption: Plaintext  Key = Ciphertext
Plaintext:
Key:
Ciphertext:

40. One-time Pad: Decryption
e=000 h=001 i=010 k=011 l=100 r=101 s=110 t=111
s r l h s s t h s r
110 101 100 001 110 110 111 001 110 101
111 101 110 101 111 100 000 101 110 000
001 000 010 100 001 010 111 100 000 101
h e i l h i t l e r
Decryption: Ciphertext  Key = Plaintext
Ciphertext:
Key:
Plaintext:

41. One-time Pad
e=000 h=001 i=010 k=011 l=100 r=101 s=110 t=111
s r l h s s t h s r
110 101 100 001 110 110 111 001 110 101
101 111 000 101 111 100 000 101 110 000
011 010 100 100 001 010 111 100 000 101
k i l l h i t l e r
Ciphertext:
“key”:
“Plaintext”:
Double agent claims sender used following “key”

42. One-time Pad
e=000 h=001 i=010 k=011 l=100 r=101 s=110 t=111
s r l h s s t h s r
110 101 100 001 110 110 111 001 110 101
111 101 000 011 101 110 001 011 101 101
001 000 100 010 011 000 110 010 011 000
h e l i k e s i k e
Ciphertext:
“Key”:
“Plaintext”:
Or sender is captured and claims the key is…

43. 43
One-time pad…
 the only cryptosystem that exhibits what is
referred to as perfect secrecy
 Drawbacks
◦ it requires secure exchange of the one-time pad
material, which must be as long as the message
◦ pad disposed of correctly and never reused
 In practice
◦ Generate a large number of random keys,
◦ Exchange the key material securely between the
users before sending an one-time enciphered
message,
◦ Keep both copies of the key material for each
message securely until they are used, and
◦ Securely dispose of the key material after use,
thereby ensuring the key material is never

44. 44
 Strength
◦ Is unconditionally secure provided key is
truly random

45. 45
Key Management
 Using secret channel
 Encrypt the key
 Third trusted party
 The sender and the receiver generate
key

46. More Transposition 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

47. 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: depth 2
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
 Plain msg : "meet me after the toga party"

48. 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

49. Taxonomy of Cryptography
Modern world….
 Symmetric key
◦ Same key for encryption and decryption
◦ Two types : Stream Cipher, Block Cipher
 Public key (or asymmetric crypto)
◦ Two keys, one for encryption (public), and
one for decryption (private)
◦ Also, digital signatures…not possible
before
 Hash algorithms (Crypto hash
function)

50. Symmetric Key Crypto
 Stream cipher  like a one-time pad
◦ Except that key is relatively short
◦ Key is stretched into a long keystream
◦ Keystream is used just like a one-time pad.
◦ Employs “substitution” only
 Block cipher  based on codebook
concept
◦ Block cipher key determines a codebook
◦ Each key yields a different codebook
◦ Employs both “substitution” and “transposition”

51. Block vs. Stream Ciphers…

52. Summary
 Stream cipher  like a one-time pad
◦ Key is stretched into a long keystream then
XOR
◦ Psudorandom key stream generator
◦ Confusion only just like a one-time pad
◦ Efficient for hardware implementation (low
powered device)
 Block cipher  based on codebook
concept
◦ Block cipher key determines a codebook
◦ Employs both “confusion” and “diffusion”
◦ Faster, Good for Software implementation

53.  Data encryption standard (DES)

54. Data Encryption Standard
 Most widely used block cipher in world
 DES developed in 1970’s
 Based on IBM revised Lucifer cipher
 U.S. government standard
 DES development was controversial
◦ NSA secretly involved
◦ Design process was secret
◦ Key length reduced from 128 to 56 bits
◦ clever changes to Lucifer algorithm

55. DES Design Controversy
 although DES standard is public
 was considerable controversy over design
◦ in choice of 56-bit key (vs Lucifer 128-bit)
◦ and because design criteria were classified
 subsequent events and public analysis
show in fact design was appropriate.
 use of DES has flourished
◦ especially in financial applications
◦ still standardised for legacy application use

56. DES
 DES is a Feistel cipher with…
◦ 64 bit block length
◦ 56 bit key length
◦ 16 rounds
◦ 48 bits of key used each round (subkey)
 Each round is simple (for a block cipher)
 Security depends heavily on “S-boxes”
◦ Each S-boxes maps 6 bits to 4 bits

57. DES Encryption Overview

58. Initial Permutation IP
 IP: the first step of the encryption.
 It reorders the input data bits.
 The last step of encryption is the inverse of IP.
 IP and IP-1 are specified by tables

59. L R
expand shift
shift
key
key
S-boxes
compress
L R
28
28
28
28
28
28
48
32
48
32
32
32
32
One
Roun
d
of
DES
48
32
Ki
P box



60. DES Round Structure

61. DES Encryption Overview

62. DES review
 The left side shows the basic process for
enciphering a 64-bit data block which consists
of:
◦ - an initial permutation (IP) which shuffles the 64-bit
input block
◦ - 16 rounds of a complex key dependent round
function involving substitutions & permutations
◦ - a final permutation, being the inverse of IP
 The right side shows the handling of the 56-bit
key and consists of:
◦ - an initial permutation of the key (PC1) which
selects 56-bits out of the 64-bits input, in two 28-bit
halves
◦ - 16 stages to generate the 48-bit subkeys using a

63. Strength of DES – Key Size
 56-bit keys have 256 = 7.2 x 1016
values
 brute force search looks hard
 recent advances have shown is
possible
◦ in 1997 on Internet in a few months
◦ in 1998 on dedicated h/w (EFF) in a few
days
◦ in 1999 above combined in 22hrs!
 still must be able to recognize

64. Multiple Encryption & DES
 clear a replacement for DES was
needed
◦ theoretical attacks that can break it
◦ demonstrated exhaustive key search
attacks
 AES is a new cipher alternative
 prior to this alternative was to use
multiple encryption with DES
implementations
 Triple-DES is the chosen form

65. Triple DES
 Today, 56 bit DES key is too small
◦ Exhaustive key search is feasible
 But DES is everywhere, so what to do?
 Triple DES or 3DES (112 bit key)
◦ C = E(D(E(P,K1),K2),K1)
◦ P = D(E(D(C,K1),K2),K1)
 Why Encrypt-Decrypt-Encrypt with 2 keys?
◦ Backward compatible: E(D(E(P,K),K),K) = E(P,K)
◦ And 112 bits is enough

66. Reading assignments
 Differential and linear
cryptanalysis attack
 Different block cipher modes
 Deniable encryption

67.  Advanced Encryption Standard
(AES)

68. Origins
 clear a replacement for DES was needed
◦ have theoretical attacks that can break it.
◦ have demonstrated exhaustive key search
attacks.
 can use Triple-DES – but slow, has small
blocks
◦ US NIST issued call for ciphers in 1997
◦ 15 candidates accepted in Jun 98
◦ 5 were shortlisted in Aug-99
 Rijndael was selected as the AES in Oct-
2000
◦ designed by Rijmen-Daemen in Belgium

69. The AES Cipher - Rijndael
 Iterated block cipher (like DES)
 Not a Feistel cipher (unlike DES)
◦ operates on entire data block in every round.
 Block size:128 bits (192 or 256)
 Key length: 128, 192 or 256 bits
(independent of block size)
 10 to 14 rounds (depends on key length)
 Each round uses 4 functions (3 “layers”)
◦ ByteSub (nonlinear layer)
◦ ShiftRow (linear mixing layer)
◦ MixColumn (nonlinear layer)
◦ AddRoundKey (key addition layer)

70. AES
Encryption
Process

71. AES Structure
 data block of 4 columns of 4 bytes is state(16
byte)
 key is expanded to array of words
 has 9/11/13 rounds in which state undergoes:
◦ byte substitution (1 S-box used on every byte)
◦ shift rows (permute bytes between groups/columns)
◦ mix columns (subs using matrix multiply of groups)
◦ add round key (XOR state with key material)
◦ view as alternating XOR key & scramble data bytes
 initial XOR key material & incomplete last round

72. AES Structure

73. Substitute Bytes
 AES treat 128 bit block as 4x4 byte array
 a simple byte-by-byte substitution of the
block!
 uses one table of 16x16 bytes containing a
permutation of all 256 8-bit values.
 each byte of state is replaced by byte
indexed by row (left 4-bits) & column (right 4-
bits)
◦ eg. byte {95} is replaced by byte in row 9 column 5
◦ which has value {2A}

74. Substitute Bytes

75. Substitute Bytes Example

76. AES ByteSub
 ByteSub is AES’s “S-box”
 Treat 128 bit block as 4x4 byte array

77. Shift Rows
 a circular byte shift in each
◦ 1st row is unchanged
◦ 2nd row does 1 byte circular shift to left
◦ 3rd row does 2 byte circular shift to left
◦ 4th row does 3 byte circular shift to left
 decrypt inverts using shifts to right
 since state is processed by columns, this
step permutes bytes between the columns

78. Shift Rows

79. AES MixColumn
 Implemented as a (big) lookup table
 Nonlinear, invertible operation applied to
each column

80. Mix Columns
 each column is processed separately
 each byte is replaced by a value
dependent on all 4 bytes in the column
 effectively a matrix multiplication in
GF(28) using prime poly m(x)
=x8+x4+x3+x+1

81. Mix Columns

82. Mix Columns Example

83. Mix Columns
 can express each col as 4 equations
◦ to derive each new byte in col
 decryption requires use of inverse matrix
◦ with larger coefficients, hence a little harder
 have an alternate characterisation
◦ each column a 4-term polynomial
◦ with coefficients in GF(28)
◦ and polynomials multiplied modulo (x4+1)
 coefficients based on linear code with
maximal distance between codewords

84. AES Round

85. AES Decryption
 To decrypt, process must be invertible
 Inverse of MixAddRoundKey is easy,
◦ since “”is its own inverse
 MixColumn is invertible
◦ (inverse is also implemented as a lookup table)
 Inverse of ShiftRow is easy
◦ (cyclic shift the other direction)
 ByteSub is invertible
◦ (inverse is also implemented as a lookup table)

86. AES Decryption

87. Some Comments on AES
1. an iterative rather than feistel cipher
2. key expanded into array of 32-bit words
1. four words form round key in each round
3. 4 different stages are used as shown
4. has a simple structure
5. only AddRoundKey uses key
6. AddRoundKey a form of Vernam cipher
7. each stage is easily reversible
8. decryption uses keys in reverse order
9. decryption does recover plaintext
10. final round has only 3 stages