Block Ciphers and Data Encryption Standard-Network Security-Lecture Slides, Slides of Cryptography and System Security

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Network^ Security(Lec 6)(Block Ciphers^ &^ Data

Encryption Standard)

Modern^ (Digital)

Cryptography

^ With^ the^ advent^ of^ digital

computers,^ research^ and development^ into^ methods

of^ digital^ cryptography

started^ (in the^ 70’s)  Modern^ digital^ ciphers

operate^ on^ binary^ (plaintext)

data using^ a^ binary^ key^ to^ generate

binary^ ciphertext ^ There^ are^ two^ general

types^ of^ modern^ digital

ciphers: ^ Block^ ciphers^ (e.g.,^ DES,

KASUMI^ and^ Rijndael) ^ Stream^ ciphers^ (e.g.,

RC4,^ A5^ and^ E0)

Block^ Ciphers  Let P denote the set of^ all^ possible^ plaintext^ symbols,

C denote^ the^ set^ of all^ possible^ ciphertext^ symbols,

and^ K denote^ the^ set^ of^ all

possible^ keys (the^ keyspace )  A^ symmetric‐key^ block^ cipher

E^ is^ a^ function: ^ E^ :^ P x^ K^ ‐>^ C ^ Moreover,^ for^ every^ key^

k^ in^ K^ ,^ we^ have^ invertible^ functions ^ E^ :^ P^ ‐>^ CK^ ^ D^ :^ C‐>^ PK^ ‐^1 ^ and^ D^ =^ E^ .K^ K  In^ other^ words,^ the^ key^ determines

the^ bijective^ mapping^ of^ plaintext

to ciphertext^ and^ also^ determines

the^ inverse^ mapping^ of^ ciphertext

to plaintext

Block^ Cipher

Principles

A^ block^ cipher^ operated

on^ a^ plaintext^ block

of^ n

bits^ to^ produce^ a^ ciphertext block

of^ n^ bits.

n^ There are 2 possible

different^ plaintext

blocks^ and

for^ the^ encryption

to^ be^ reversible^ ,^ each

must

produce^ a^ unique^

ciphertext block,^ called

reversible

or^ non‐singular.

Block^ Ciphers

Principles

Block^ and^ Key

Size/Length

^ If^ the^ key^ is^ fixed,^ and^ hence

determines^ a^ specific^ mapping,

the^ block cipher^ can^ be^ considered^ simply

as^ a^ large^ lookup‐table^ (substitution cipher)  In^ particular,^ identical^ plaintext

blocks^ encrypt^ to^ identical

ciphertext blocks  Since^ modern^ ciphers^ are^ implemented

on^ digital^ systems,^ it^ is^ common

to measure^ block^ sizes^ in^ bits  We^ say^ that^ a^ block^ cipher^

has^ a^ block^ size^ (or^ block^ length

) of^ m^ bits, which^ means^ that^ |P|^ =^ |C|

m = 2 ^ Similarly^ We^ say^ that^ a^ block

cipher^ has^ a^ key^ size^ (or^ key

length ) of^ k^ bits, k which means that |K| = 2

Block^ Ciphers:

Problems

Another^ problem

is^ that^ if^ an^ attacker

correctly^ guesses

the^ plaintext^ that

corresponds^ to^ some

ciphertext^ then^ he

can

build^ a^ lookup‐table

of^ plaintext‐ciphertext

pairs^ corresponding

to^ a^ particular^ key,

known

as^ a^ codebook Codebooks^ can^ be

used^ to^ decrypt^

ciphertext

blocks^ without^ knowledge

of^ the^ key

Block^ Ciphers:

The^ solution

^ Both^ problems^ are^ solved

by^ increasing^ the^ block

length,^ and thus^ increasing^ the^ number

of^ possible^ messages.^

If^ n^ is sufficiently^ large,^ and^ an

arbitrary^ reversible^ substitiution between^ plaintext^ and

ciphertext is^ allowed^ ,

then^ statistical analysis^ is^ infeasible.  It^ also^ becomes^ impractical

for^ an^ attacker^ to^ build

plaintext‐ ciphertext codebooks  Typically^ the^ message^ block

length^ m^ would^ be^ at^ least^64 bits (^64) (2 =^ 18446744073709551616)

A^ simple^ block

cipher

-^ Except^ for^ small^ message

block^ or^ key^ lengths,

it^ is

infeasible^ for^ the^ block

cipher^ designer^ to^ explicitly

specify^ a^ plaintext^ to

ciphertext^ mapping^

for^ every

possible^ key:^ this^ would

k^ be like specifying 2

codebooks

-^ It^ is^ far^ more^ practical

to^ specify^ the^ block^

cipher^ as^ an

equation^ or^ an^ algorithm • So^ for^ example,^ a^ simple

block^ cipher^ with^ parameters

( m , k )^ =^ (64,64)^ might

be^ specified^ by:C = P K P = C K

Another^ simple

block^ cipher

^ The^ problem^ with^ the

previous^ simple^ block^

cipher^ is^ that^ it^ is trivially^ broken^ with^ one

known^ plaintext^ by^ K^ =

P^ C

^ This^ block^ cipher^ is^ weak

because^ it^ is^ purely^ linear

and^ thus easily^ solvable  By^ using^ both^ linear^ and

nonlinear^ operations^ we

make^ the block^ cipher^ somewhat

more^ difficult^ to^ manipulate

by^ simple algebra  So^ for^ example,^ a^ slightly

better^ idea^ would^ be^ the

( m , k )^ = (64,128)^ block^ cipher:  C^ =^ (P^ K^0

)^ +^ K

^ P^ =^ (C^ – K

)^ K 10

^ where^ K0and^ K^

are^ key‐dependent^ variables 1

called subkeys  In^ this^ case,^ each^ subkey

is^ half^ of^ the^ key^ K,^ and

thus^ has length^64 bits

Confusion^ and

Diffusion

^ The^ mixture^ of^ linear^ and

non‐linear^ operations^ makes

it^ difficult^ to express^ the^ key^ in^ terms^ of

the^ plaintext^ and^ ciphertext

blocks,^ thus preventing^ a^ simple^ known

plaintext^ attack ^ The^ idea^ of^ mixing^ linear

and^ nonlinear^ operations^ in

order^ to^ obscure^ the relationship^ between^ the^ plaintext,

ciphertext^ and^ key,is^ called

confusion and^ is^ an^ important^ principle

of^ cipher^ design ^ An^ equally^ important^ principle

of^ block^ cipher^ design^ is^ that

of^ diffusion , i.e.,^ the^ idea^ that^ every^ bit^

of^ the^ ciphertext^ should^ depend

on^ every^ bit^ of the^ plaintext^ and^ also^ every

bit^ of^ the^ key ^ This^ ensures^ that^ the^ statistics

of^ the^ plaintext^ are^ dissipated

within^ the ciphertext^ so^ that^ an^ attacker

cannot^ predict^ the^ plaintext

that corresponds^ to^ a^ particular

ciphertext,^ even^ after^ observing

a^ number^ of “similar”^ plaintexts^ and^ their

corresponding^ ciphertexts

Iterated^ ciphers  A simple method^ of^ achieving^ confusion

and^ diffusion^ in^ a block^ cipher^ is^ by^ repeatedly

applying^ keyed^ substitutions

and permutations^ to^ the^ message  The^ substitutions^ are^ used

to^ introduce^ nonlinearity

into^ the message^ (confusion)^ and

the^ permutations^ are^ required^ to ensure^ that^ bits^ are^ affected

by^ different^ substitutions

on subsequent^ iterations^ (diffusion) ^ A^ block^ cipher^ based

on^ this^ principle^ is^ called

an^ iterated cipher

Iterated^ ciphers  By iterating the round^ function^ a^ fixed

number^ of^ times^ we automatically^ obtain^ some

security^ as^ a^ consequence

of^ the fact^ that,^ after^ each^ iteration

(or^ round ),^ the^ output

bits become^ increasingly^ dependent

on^ the^ input^ bits ^ We^ can^ use^ different

subkeys^ in^ each^ iteration

so^ that,^ for^ a^4 ‐ round^ block^ cipher,^ the

encryption^ function^ becomes: ^ C^ =^ E(P,K)

=^ ((((P,K),K),K^12

),K) 34

^ Similarly,^ decryption

would^ be^ achieved^ by: ^ P^ =^ D(C,K)

–1–1–1–1 = ((((C,K

),K),K),K) 4321

^ where,^ for^ a^ fixed

–1^ K, is^ the^ inverse^ function

of^  docsity.com

Example:^ Iterated

Ciphers

Data^ (Plaintext)RoundSubkey^1 FunctionRoundSubkey^2 Function… Data^ (Ciphertext)

IteratedBlock^ CipherKeyKeySchedule^