Review

• What is security: history and definition

• Security policy, mechanisms and services
• Security models
 Outline
• Overview of Cryptography
• Classical Symmetric Cipher
• Modern Symmetric Ciphers (DES)
 Basic Terminology
• plaintext - the original message
• ciphertext - the 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) - the study of principles/
methods of deciphering ciphertext without knowing key
• cryptology - the field of both cryptography and
cryptanalysis
 Classification of Cryptography
• Number of keys used
– Hash functions: no key
– Secret key cryptography: one key
– Public key cryptography: two keys - public, private
• Type of encryption operations used
– substitution / transposition / product
• Way in which plaintext is processed
– block / stream
 Secret Key vs. Secret Algorithm

• Secret algorithm: additional hurdle

• Hard to keep secret if used widely:
– Reverse engineering, social engineering
• Commercial: published
– Wide review, trust
• Military: avoid giving enemy good ideas
 Cryptanalysis Scheme
• Ciphertext only:
– Exhaustive search until “recognizable plaintext”
– Need enough ciphertext
• Known plaintext:
– Secret may be revealed (by spy, time), thus <ciphertext,
plaintext> pair is obtained
– Great for monoalphabetic ciphers
• Chosen plaintext:
– Choose text, get encrypted
– Useful if limited set of messages
Unconditional vs. Computational Security
• Unconditional security
– No matter how much computer power is available, the
cipher cannot be broken
– The ciphertext provides insufficient information to
uniquely determine the corresponding plaintext
– Only one-time pad scheme qualifies
• Computational security
– The cost of breaking the cipher exceeds the value of
the encrypted info
– The time required to break the cipher exceeds the
useful lifetime of the info
 Brute Force Search
• Always possible to simply try every key
• Most basic attack, proportional to key size
• Assume either know / recognise plaintext
 Outline
• Overview of Cryptography
• Classical Symmetric Cipher
– Substitution Cipher
– Transposition Cipher
• Modern Symmetric Ciphers (DES)
Symmetric Cipher Model
 Requirements
• Two requirements for secure use of symmetric
encryption:
– a strong encryption algorithm
– a secret key known only to sender / receiver
Y = EK(X)
X = DK(Y)
• Assume encryption algorithm is known
• Implies a secure channel to distribute key
 Classical Substitution Ciphers
• Letters of plaintext are replaced by other
letters or by numbers or symbols
• Plaintext is viewed as a sequence of bits, then
substitution replaces plaintext bit patterns
with ciphertext bit patterns
 Caesar Cipher
• Earliest known substitution cipher
• Replaces each letter by 3rd letter on
• Example:
meet me after the toga party
PHHW PH DIWHU WKH WRJD SDUWB
 Caesar Cipher
• 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

0 1 2 3 4 5 6 7 8 9 10 11 12

n o p q r s t u v w x y Z

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 25 possible ciphers
– A maps to B,..Z
• Given ciphertext, just try all shifts of letters
• Do need to recognize when have plaintext
• E.g., 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
• 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
• Is that secure?
• Problem is language characteristics
– Human languages are redundant
– Letters are not equally commonly used
English Letter Frequencies
 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

 One-Time Pad
• If a truly random key as long as the message is
used, the cipher will be secure - One-Time pad
• E.g., a random sequence of 0’s and 1’s XORed to
plaintext, no repetition of keys
• Unbreakable since ciphertext bears no
statistical relationship to the plaintext
• For any plaintext, it needs a random key of the
same length
– Hard to generate large amount of keys
• Have problem of 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
• E.g., 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
 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
 Outline
• Overview of Cryptography
• Classical Symmetric Cipher
• Modern Symmetric Ciphers (DES)
 Block vs Stream Ciphers
• Block ciphers process messages in into blocks,
each of which is then en/decrypted
• Like a substitution on very big characters
– 64-bits or more
• Stream ciphers process messages a bit or byte
at a time when en/decrypting
• Many current ciphers are block ciphers, one of
the most widely used types of cryptographic
algorithms
 Block Cipher Principles
• Most symmetric block ciphers are based on a
Feistel Cipher Structure
• Block ciphers look like an extremely large
substitution
• Would need table of 264 entries for a 64-bit
block
• Instead create from smaller building blocks
• Using idea of a product cipher
 Substitution-Permutation Ciphers
• Substitution-permutation (S-P) networks
[Shannon, 1949]
– modern substitution-transposition product cipher
• These form the basis of modern block ciphers
• S-P networks are based on the two primitive
cryptographic operations
– substitution (S-box)
– permutation (P-box)
• provide confusion and diffusion of message
 Confusion and Diffusion
• Cipher needs to completely obscure statistical
properties of original message
• A one-time pad does this
• More practically Shannon suggested S-P networks
to obtain:
• Diffusion – dissipates statistical structure of
plaintext over bulk of ciphertext
• Confusion – makes relationship between
ciphertext and key as complex as possible
 Feistel Cipher Structure
• Feistel cipher implements Shannon’s S-P
network concept
– based on invertible product cipher
• Process through multiple rounds which
– partitions input block into two halves
– perform a substitution on left data half
– based on round function of right half & subkey
– then have permutation swapping halves
 Feistel
Cipher
Structure
DES (Data Encryption Standard)
• Published in 1977, standardized in 1979.
• Key: 64 bit quantity=8-bit parity+56-bit key
– Every 8th bit is a parity bit.
• 64 bit input, 64 bit output.

64 bit M 64 bit C
DES
Encryption

56 bits
 DES Top View
56-bit Key
64-bit
48-bitInput
K1
Generate keys
Permutation Initial Permutation
48-bit K1
Round 1
48-bit K2
Round 2
…... 48-bit K16
Round 16

Swap Swap 32-bit halves

Permutation Final Permutation

64-bit Output
 Bit Permutation (1-to-1)

1 2 3 4 32
0 0 1 0 ……. 1
Input:

1 bit

Output 1 0 1 1 …….. 1
22 6 13 32 3
 Per-Round Key Generation
Initial Permutation of DES key

C i-1 28 bits D i-1 28 bits

Circular Left Shift Circular Left Shift

One
round Permutation Round 1,2,9,16:
with Discard single shift
Others: two bits
48 bits
Ki
Ci 28 bits Di 28 bits
 A DES Round
32 bits Ln 32 bits Rn

E
One Round 48 bits
Mangler
Encryption Function 48 bits
S-Boxes Ki

32 bits

32 bits Ln+1 32 bits Rn+1

 Mangler Function
4 4 4 4 4 4 4 4

6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6

+ + + + + + + +

S1 S2 S3 S4 S5 S6 S7 S8 The permutation produces

“spread” among the
4 4 4 4 4 4 4 4 chunks/S-boxes!

Permutation
 Bits Expansion (1-to-m)
1 2 3 4 5 32
Input: 0 0 1 0 1……. 1

Output

1 0 0 1 0 1 0 1 …….. 1 0
1 2 3 4 5 6 7 8 48
 S-Box (Substitute and Shrink)
• 48 bits ==> 32 bits. (8*6 ==> 8*4)
• 2 bits used to select amongst 4 substitutions
for the rest of the 4-bit quantity

2 bits I1
row I2
O1
I3 Si O2
I4 O3
I5 O4

4 bits I6
column i = 1,…8.
 S-Box Examples
Each row and column contain different numbers.

0 1 2 3 4 5 6 7 8 9…. 15

0 14 4 13 1 2 15 11 8 3

1 0 15 7 4 14 2 13 1 10

2 4 1 14 8 13 6 2 11 15

3 15 12 8 2 4 9 1 7 5

Example: input: 100110 output: ???

 DES Standard
• Cipher Iterative Action • Key Generation Box :
: – Input: 56 bits
– Input: 64 bits
– Output: 48 bits
– Key: 48 bits
– Output: 64 bits

One round (Total 16 rounds)

 DES Box Summary
• Simple, easy to implement:
– Hardware/gigabits/second,
software/megabits/second
• 56-bit key DES may be acceptable for non-
critical applications but triple DES (DES3)
should be secure for most applications today
• Supports several operation modes (ECB CBC,
OFB, CFB) for different applications