Des

IFETCE/M.E CSE/NE7202-NIS/Unit 2 2
Learning Outcomes
• Recognise the different components of the cryptographic
process
• Identify some of the factors involved in selecting a cryptographic
algorithm
• Describe the model of a stream cipher
• Appreciate the types of application where a stream cipher is
most appropriate
• Describe the model of a block cipher
• Recall the basic design features and history of DES
• Comment on the security issues surrounding modern use of
DES

Overview
• Block Cipher Principles
– Stream and Block Ciphers
– Ideal Block Cipher
– The Feistel Cipher
• The Data Encryption Standard
– DES Details
– DES Design Issues
– The Strength of DES
– Differential and Linear Cryptanalysis

4
A symmetric classification
1 …… 1 …… 0 ……0 ……0
E
1……...1……..1…….0…….1
100110110100010111010010
1100100111010100100010011
E E E E
100110110100010111010010
110010011101010010001001
100110 110100 010111 010010
E E E E
110010 011101 010010 001001
… … … …
Stream cipher Block cipher

Stream Ciphers
Call the plaintext stream P, the ciphertext stream
C,
and the key stream K.
5

IFETCE/M.E CSE/NE7202-NIS/Unit 2
Model of a block cipher
• Encrypt a block of plaintext as a whole to
produce same sized ciphertext
• Typical block sizes are 64 or 128 bits
• Modes of operation used to apply block
ciphers to larger plaintexts
7
block of ciphertext

Reversible and Irreversible
Mappings
• n-bit block cipher takes n bit plaintext and produces n
bit ciphertext
• 2n
possible different plaintext blocks
• Encryption must be reversible (decryption possible)
• Each plaintext block must produce unique ciphertext
block
• Total transformations is 2n
!
8

General Block Substitution
9

Encryption/Decryption Tables
10

Ideal Block Cipher
• n-bit input maps to 2n
possible input states
• Substitution used to produce 2n
output states
• Output states map to n-bit output
• Ideal block cipher allows maximum number of
possible encryption mappings from plaintext
block
• Problems with ideal block cipher:
– Small block size: equivalent to classical substitution cipher;
cryptanalysis based on statistical characteristics feasible
– Large block size: key must be very large;
performance/implementation problems
11

Practical Block Ciphers
• Modern block ciphers use a key of K bits to specify a
random subset of 2K
mappings.
• If K ≈ N,
– 2K
is much smaller than 2N
!
– But is still very large.
• If the selection of the 2K
mappings is random, the
resulting cipher will be a good approximation of the
ideal block cipher.
• Horst Feistel, in1970s, proposed a method to achieve
this.
12

Feistel Structure for Block
Ciphers
• Feistel proposed applying two or more simple
ciphers in sequence so final result is
cryptographically stronger than component
ciphers
• n-bit block length; k-bit key length; 2k
transformations
• Feistel cipher alternates: substitutions,
transpositions(permutations)
• Applies concepts of diffusion and confusion
• Applied in many ciphers today
13

Diffusion and Confusion
• Diffusion
– Statistical nature of plaintext is reduced in ciphertext
– E.g. A plaintext letter affects the value of many ciphertext
letters
– How: repeatedly apply permutation (transposition) to data,
and then apply function
• Confusion
– Make relationship between ciphertext and key as complex as
possible
– Even if attacker can find some statistical characteristics of
ciphertext, still hard to find key
– How: apply complex (non-linear) substitution algorithm
14

Feistel Structure for Block
Ciphers
• Approach:
– Plaintext split into halves
– Subkeys (or round keys) generated from
key
– Round function, F, applied to right half
– Apply substitution on left half using XOR
– Apply permutation: interchange to halves
15

The Feistel
Cipher
Structure
iφ
µ
16

Round i
+
f
Li-1 Ri-1
ki
Li Ri
17

Using the Feistel Structure
• Exact implementation depends on various design
features
– Block size, e.g. 64, 128 bits: larger values leads to more
diffusion
– Key size, e.g. 128 bits: larger values leads to more
confusion, resistance against brute force
– Number of rounds, e.g. 16 rounds
– Subkey generation algorithm: should be complex
– Round function F: should be complex
• Other factors include fast encryption in software and
ease of analysis
• Tradeoff: security vs performance
18

IFETCE/M.E CSE/NE7202-NIS/Unit 2 September, 2006
Feistel decryption
• same as encryption, except
• ciphertext is input
• use keys in reverse order
• at each round the output is equal to the
corresponding value of the encryption
process with the two halves of the value
swapped
• final permutation (swap) realigns 2 halves

Feistel Example
20

Data Encryption Standard
• Symmetric block cipher
– 56-bit key, 64-bit input block, 64-bit output block
• One of most used encryption systems in world
– Developed in 1977 by NBS/NIST
– Designed by IBM (Lucifer) with input from NSA
– Principles used in other ciphers, e.g. 3DES, IDEA
• Simplified DES (S-DES)
– Cipher using principles of DES
– Developed for education (not real world use)
21

Simplied DES
• Input (plaintext) block: 8-bits
• Output (ciphertext) block: 8-bits
• Key: 10-bits
• Rounds: 2
• Round keys generated using permutations and
left shifts
• Encryption: initial permutation, round function,
switch halves
• Decryption: Same as encryption, except round
keys used in opposite order
22

S-DES Algorithm
23

S-DES Operations
• EP (expand and permutate)
– Input : 1 2 3 4
– Output: 4 1 2 3 2 3 4 1
• IP (initial permutation)
– Input : 1 2 3 4 5 6 7 8
– Output: 2 6 3 1 4 8 5 7
• IP-1
(inverse of IP)
• LS-1 (left shift 1 position)
• LS-2 (left shift 2 positions)
24

S-DES Key Generation
25

S-DES Encryption
Details
26

S-DES S-Boxes
• S-DES (and DES) perform substitutions using
S-Boxes
• S-Box considered as a matrix: input used to
select row/column; selected element is output
• 4-bit input: bit1; bit2; bit3; bit4
• bit1bit4 species row (0, 1, 2 or 3 in decimal)
• Bit2bit4 species column
• 2-bit output
27

S-DES Example
• Plaintext: 01110010
• Key: 1010000010
• Ciphertext: 01110111
28

S-DES Summary
• Educational encryption algorithm
• S-DES expressed as functions:
ciphertext = IP-1
(fK2 (SW (fK1 (IP (plaintext)))))
plaintext = IP-1
(fK1 (SW (fK2 (IP (ciphertext)))))
• Security of S-DES:
–10-bit key, 1024 keys: brute force easy
–If know plaintext and corresponding ciphertext, can
we determine key? Very hard
29

Comparing DES and S-DES
S-DES
• 8-bit blocks
• 10-bit key: 2 x 8-bit round
keys
• IP: 8-bits
• F operates on 4 bits
• 2 S-Boxes
• 2 rounds
DES
• 64-bit blocks
• 56-bit key: 16 x 48-bit
round keys
• IP: 64 bits
• F operates on 32 bits
• 8 S-Boxes
• 16 rounds
30
S-DES encryption:
ciphertext = IP-1
(fK2 (SW (fK1 (IP (plaintext)))))
DES encryption:
ciphertext = IP-1
(fK16 (SW (fK15 (SW (: : : (fK1 (IP
(plaintext))))))))

Design Principles of DES
• To achieve high degree of diffusion and
confusion.
• Diffusion: making each plaintext bit
affect as many ciphertext bits as
possible.
• Confusion: making the relationship
between the encryption key and the
ciphertext as complex as possible.
1

General DES
Encryption
Algorithm
32

Round Keys Generation
• Main key: 64 bits.
• 56-bits are selected and permuted using Permuted
Choice One (PC1); and then divided into two 28-bit
halves.
• In each round:
– Left-rotate each half separately by either 1 or 2
bits according to a rotation schedule.
– Select 24-bits from each half, and permute the
combined 48 bits.
– This forms a round key.

Permutation Tables for DES
34

Permutation Tables for DES
35

Single Round of DES Algorithm
Introduction to Cryptography and Security Mechanisms 2005 36

Calculation of F(R,K)

The S-Boxes
• Eight S-boxes each map 6 to 4 bits
• Each S-box is specified as a 4 x 16
table
– each row is a permutation of 0-15
– outer bits 1 & 6 of input are used to select
one of the four rows
– inner 4 bits of input are used to select a
column
• All the eight boxes are different.

Definition of DES S-Boxes
39

Definition of DES S-Boxes
40

DES Key Schedule Calculation
41

Avalanche Effect
• Avalanche effect:
– A small change in the plaintext or in the key results in a
significant change in the ciphertext.
– an evidence of high degree of diffusion and confusion
– a desirable property of any encryption algorithm
• DES exhibits a strong avalanche effect
– Changing 1 bit in the plaintext affects 34 bits in the
ciphertext on average.
– 1-bit change in the key affects 35 bits in the ciphertext
on average.

The Avalanche Eect
• Following examples show the number of
bits that change in output when two
different inputs are used, differing by 1
bit
• Plaintext 1: 02468aceeca86420
• Plaintext 2: 12468aceeca86420
• Ciphertext difference: 32 bits
• Key 1: 0f1571c947d9e859
• Key 2: 1f1571c947d9e859
• Ciphertext difference: 30
43

Avalanche Eect in DES: Change
in Plaintext
44

Avalanche Eect in DES: Change
in Key
45

Key Size
• Although 64 bit initial key, only 56 bits used in
encryption (other 8 for parity check)
• 256
= 7.2 × 1016
– 1977: estimated cost $US20m to build machine to
break in 10 hours
– 1998: EFF built machine for $US250k to break in 3
days
– Today: 56 bits considered too short to withstand
brute force attack
• 3DES uses 128-bit keys
46

Attacks on DES
• Timing Attacks
– Information gained about key/plaintext by observing how long
implementation takes to decrypt
– No known useful attacks on DES
• Differential Cryptanalysis
– Observe how pairs of plaintext blocks evolve
– Break DES in 247 encryptions (compared to 255); but require
247 chosen plaintexts
• Linear Cryptanalysis
– Find linear approximations of the transformations
– Break DES using 243 known plaintexts
47

Multiple Encryption with DES
• DES is vulnerable to brute force attack
• Alternative block cipher that makes use of
DES software/equipment/knowledge: encrypt
multiple times with different keys
• Options:
1. Double DES: not much better than single DES
2. Triple DES (3DES) with 2 keys: brute force 2112
3. Triple DES with 3 keys: brute force 2168
48

Double Encryption
• For DES, 2 × 56-bit keys, meaning 112-bit key length
• Requires 2111
operations for brute force?
• Meet-in-the-middle attack makes it easier
49

Meet-in-the-Middle Attack
• Double DES Encryption: C = E(K2;E(K1; P))
• Say X = E(K1; P) = D(K2; C)
• Attacker knows two plaintext, ciphertext pairs (Pa; Ca) and (Pb;
Cb)
1. Encrypt Pa using all 256
values of K1 to get multiple values of X
2. Store results in table and sort by X
3. Decrypt Ca using al 256
values of K2
4. As each decryption result produced, check against table
5. If match, check current K1;K2 on Cb. If Pb obtained, then accept the keys
• With two known plaintext, ciphertext pairs, probability of
successful attack is almost 1
• Encrypt/decrypt operations required: 256
(twice as many as single
DES)
50

Triple Encryption
• 2 keys, 112 bits
• 3 keys, 168 bits
• Why E-D-E? To be compatible with single DES:
C = E(K1;D(K1;E(K1; P))) = E(K1; P)
51

Triple DES
ciphertext
Encrypt
Using DES
plaintext
Key K1
Decrypt
Using DES
Encrypt
Using DES
Key K2
Key K1
1
Key K = K1 and K2
3
2
4

53
DES
Parameter DES specification
Type of design Feistel Cipher
Number of rounds 16
Block size 64
Length of key 56
Public / proprietary Published as FIPS 46

54
Design criticisms
Criticism Comment
Secret design criteria
Design criteria of round function / key schedules secret.
(although actual design public)
Fear of trapdoors has proved unfounded.
Weak keys
Certain DES keys are weak.
(encryption and decryption has same effect)
Few such keys and their use easily avoided.
Inadequate key
length
56 bits an inadequate key length.
Criticised even in 1975
Unsubstantiated claims that NSA insisted on the
“small” key length.

Searching for a DES key
Suppose that we have a machine consisting
of one million processors, each of which can
test one million keys per second.
How long is it likely to take before we find a
DES key during an exhaustive key search?

56
Searching for a DES key
Year Source Implemented? (Estimated)
Cost in US$
(Estimated)
Search time
1977 Diffie
Hellman
No 20 million 20 hours
1993 Wiener No 10.5 million
1.5 million
600 000
21 minutes
3.5 hours
35 hours
1997 Internet Yes Unknown 140 days
1998 Electronic
Frontier
Foundation
[www.eff.org]
Yes 210 000 56 hours

DES today
• Well accepted that a DES key can be found
by anyone determined enough.
• Differential and linear cryptanalysis provide
academic attacks on DES.
• DES is still in use in many applications.
• Triple DES or AES are commonly
recommended instead of DES .

Advanced Encryption Standard
• NIST called for proposals for new standard in 1997
– Aims: security, efficient software/hardware implementations, low
memory requirements, parallel processing
– Candidate algorithms from around the world
– Rijndael chosen, standard called AES created in 2001
• AES:
– Block size: 128 bits (others possible)
– Key size: 128, 192, 256 bits
– Rounds: 10, 12, 14 (depending on key)
– Operations: XOR with round key, substitutions using S-Boxes,
mixing using Galois Field arithmetic
• Widely used in file encryption, network communications
• Generally considered secure
58

Design requirements of AES
• The selection would be a public process and the
chosen algorithm and design details would be made
freely available for public use.
• The block size should be 128 bits.
• The block cipher would be designed to offer variable
key lengths of 128, 192 and 256 bits, to allow for
future developments in exhaustive key search efforts.
• The block cipher had to operate at a faster speed
than Triple DES across a number of different
platforms.
In 1998 NIST issued a call for proposals for a new block
cipher standard, to be referred to as the Advanced
Encryption Standard or AES.

Development of AES
• 15 candidate proposals, quickly reduced to 11 in August
1998.
• In April 1999, after a public consultation process, this
was reduced to five candidates: MARS, RC6, Rijndael,
SERPENT and TWOFISH.
• In October 2000 the winning algorithm Rijndael was
selected.
• Federal Information Processing Standard FIPS 197, the
Advanced Encryption Standard, published early 2001.
This standard specifies AES (Rijndael) as a FIPS-
approved symmetric encryption algorithm that may be
used by U.S. Government organizations (and others) to
protect sensitive information.
• AES now widely adopted and supported.

61
AES encryption round
Byte
substitution
Shift rows
Mix
columns
AES
S-box
Key
schedule
round key
++
key
current state
new state

Other Block Ciphers
• Blowsh (Schneier, open)
• Twosh (Schneier et al., open)
• IDEA (patented)
• Skipjack (NSA, Clipper)
• . . .
62

Summary
• Stream ciphers and block ciphers are different types of
symmetric encryption algorithm. They offer slightly
different properties and are therefore suitable for
different applications.
– Simple stream ciphers are fast and do not propagate errors,
making them suitable for poor quality channels and for
applications where errors are intolerable.
– Block ciphers do propagate errors (to a limited extent), but are
quite flexible and can be used in different ways in order to
provide different security properties (in some cases to achieve
some of the benefits of stream ciphers).
• The properties of cryptographic algorithms are not only
affected by algorithm design, but also by the ways in
which the algorithms are used. Different modes of
operation can significantly change the properties of a
block cipher.

Des

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