Des1

Block Ciphers

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

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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.

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1. Block ciphers

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

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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!

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General Block Substitution

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Encryption/Decryption Tables

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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

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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.

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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

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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

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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

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The Feistel Cipher Structure

i

16

Round i

+

f

Li-1 Ri-1

ki

Li Ri

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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

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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

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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)

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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 order22


S-DES Algorithm

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S-DES Operations

• P10 (permutate)Input : 1 2 3 4 5 6 7 8 9 10

Output: 3 5 2 7 4 10 1 9 8 6

• P8 (select and permutate)Input : 1 2 3 4 5 6 7 8 9 10

Output: 6 3 7 4 8 5 10 9

• P4 (permutate)Input : 1 2 3 4

Output: 2 4 3 124


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)

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S-DES Key Generation

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S-DES Encryption Details

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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

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S-DES Example

• Plaintext: 01110010

• Key: 1010000010

• Ciphertext?

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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

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Comparing DES and S-DESS-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

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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.

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General DES Encryption Algorithm

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Permutation Tables for DES

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Permutation Tables for DES

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Single Round of DES Algorithm

Introduction to Cryptography and Security Mechanisms 2005

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Calculation of F(R,K)


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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

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Definition of DES S-Boxes

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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.


DES Key Schedule Calculation

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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 Effect

• 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

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Avalanche Eect in DES: Change in Plaintext

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Avalanche Eect in DES: Change in Key

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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

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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

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DES Algorithm Design

• S-Boxes provide non-linearity: important part of DES, generally considered to be secure

• S-Boxes provide increased confusion

• Permutation P chosen to increase diffusion

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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

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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

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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)

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Triple DES

ciphertext

EncryptUsing DES

plaintext

Key K1

DecryptUsing DES

EncryptUsing DES

Key K2

Key K1

1

Key K = K1 and K2

3

2

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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)

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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 .

AES

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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

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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.

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AES encryption round

Byte substitution

Shift rows

Mix columns

AES S-box

Key schedule

round key++

key

current state

new state


Other Block Ciphers

• Blowfish (Schneier, open)

• Twosh (Schneier et al., open)

• IDEA (patented)

• Skipjack (NSA, Clipper)

• . . .

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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.

Des1

Internet

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block of ciphertext

block of plaintext

stream cipher block

output block

input block

block ciphers feistel

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