encrypt basics

7/31/2019 Encrypt Basics

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Basics of Cr ypt ogr aphy


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Ter minology

Plaint ext - t he or iginal message

Cipher t ext - t he coded message

Cipher - algor it hm f or t r ansf or ming plaint ext t ocipher t ext

key - inf o used in cipher known only t osender / r eceiver

Cr ypt analysis (codebreaking) - t he st udy of

pr inciples/ met hods of decipher ing cipher t extwit hout knowing key

Cr ypt ology - t he f ield of bot h cr ypt ography andcrypt analysis


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Mor e Ter minology

Symmet r ic Encr ypt ion

Bot h Sender / Receiver use t he same

algor it hms/ keys f orencr ypt ion/ decr ypt ion

Asymmet r ic Encr ypt ion

Sender / r eceiver can employ dif f er entkeys


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Symmet r ic Encrypt ion Model


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Encr ypt ion Basics

Gen() algor it hm f or gener at ing keys

Encr ypt ion algor it hm t o conver t

plaint ext int o cipher t ext E(M, keys) = C

Decr ypt ion algor it hm t o conver t

cipher t ext t o plaint ext D(C, keys) = M


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Some ear ly cipher s

Subst it ut ion (eg., Caesar cipher )

Secur it y is har d: t f dvsj uz j t ibse

C = (M+k) mod 26

M = (C-k) mod 26

Only 26 possibilit ies wit h EnglishAlphabet

Br ut e For ce sear ch can decr ypt


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Monoalphabet ic cipher

I nst ead of plain r ot at ion, use r andom

let t er subst it ut ion

Key is 26 let t er s longPlain: abcdefghijklmnopqrstuvwxyz

Cipher: DKVQFIBJWPESCXHTMYAUOLRGZN

Plaintext: security is hard

Ciphertext: AFVOYWUZ WA JDYQ


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Monoalphabet ic cipher

26! Combinat ions

Dif f icult t o decr ypt ?

Not r eally!

Language gives lot s of hint s

Single let t er s are I or A

Most common let t er E

Use Lang. char act er ist ics t o break


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English let t er Fr equencies


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Br eaking subst it ut ion cipher s

Use Let t er f r equencies of cipher t ext

Compar e t o plaint ext f r equencies

These dont change enable analysis

Use common t wo-let t er wor ds et c.


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Measur es of cipher s

Shannon Secrecy

Pr (M = m| E(K,m) = c) = Pr (M = m)

Pr obabilit y of guessing t he plaint ext

knowing t he cipher t ext = pr obabili t y of

guessing plaint ext wit hout knowing

cipher t ext


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Per f ect Secr ecy

Pr ( E(K, m) = c) = Pr (E(K, m) = c)

Pr obabilit y of any message giving a

cipher t ext is t he same


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Block vs. St r eam cipher s

Block cipher s encr ypt block at a t ime

Message is br oken int o blocks and

encrypt ed

St r eam cipher s pr ocess a bit or byt eat a t ime dur ing

encr ypt ion/ decr ypt ion


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Shannon and ciphers

Claude Shannon int r oduced idea ofsubst it ut ion-per mut at ion (S-P) net wor ks(1949) t he basis of moder n block ciphers

S-P net wor ks ar e based on t he t wopr imit ive crypt ogr aphic oper at ions: subst it ut ion(S-box)

per mut at ion(P-box)

Pr ovide conf usionand dif f usionof message


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Conf usion and Dif f usion

Cipher needs t o complet ely obscur e

st at ist ical pr oper t ies of or iginal message

Shannon suggest ed conf usion & dif f usion Dif f usion dissipat es st at ist ical st r uct ure

of plaint ext over bulk of cipher t ext

Conf usion makes r elat ionship bet ween

cipher t ext and key as complex as possible


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Shannons one-t ime pad

Choose a key as long as t he message

E (M, k) = k XOR M = C

D (C, k) = k XOR C = M Choose k r andomly (unif or mly

dist r ibut ed in {0,1}l ), l = message

lengt h One-t ime pad has per f ect secr ecy

Pr ( m xor k = c) = Pr (m xor k = c) = 2-l


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One t ime pad

Each key wor ks only once

Wor ks wit h f ixed lengt h messages

Key lengt h = message lengt h

Not ver y pr act ical


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Fiest el Cipher


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Fiest el Cipher (I BM, 70s)

Par t it ions input block int o t wo halves

Employs mult iple r ounds of processing

Per f orms a subst it ut ion on lef t dat a halfbased on a f n. of r ight half & subkey

Employs permut at ion swapping halves

I mplement s Shannons subst it ut ion-per mut at ion net wor k concept


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Cipher par amet er s

Block size incr easing size improves secur it y, but slows cipher

key size

incr easing size improves secur it y, makes exhaust ive keysear ching har der , but may slow cipher

Number of r ounds incr easing number improves secur it y, but slows cipher

Subkey generat ion

great er complexit y can make analysis harder , but slowscipher

Round f unct ion great er complexit y can make analysis harder , but slows

cipher


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Decr ypt ion


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DES cipher

Dat a Encr ypt ion St andar d

Most widely used block cipher in

world Adopt ed in 1977 by NI ST as a

st andar d

Encr ypt s 64-bit dat a using 56-bit key Based on I BMs Lucif er cipher (128-

bit key)


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DES Encrypt ion


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I nit ial per mut at ion

Fir st st ep of t he dat a comput at ion

I P r eor der s t he input dat a bit s

Even bit s t o LH half , odd bit s t o RHhalf

Quit e r egular in st r uct ur e

easy t o build h/ w


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DES Rounds

Uses t wo 32-bit L & R halves

Similat t o Feist el cipher can descr ibe as:

Li = Ri1Ri = Li1 xor F(Ri1, Ki)

Takes 32-bit R half and 48-bit subkey and: expands R t o 48-bit s using perm E

adds t o subkey passes t hr ough 8 S-boxes t o get 32-bit r esult

f inally per mut es t his using 32-bit perm P


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DES Round


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St r engt h of DES

56-bit keys have 256 = 7.2 x 1016 values

Br ut e f or ce sear ch r equir es lot of wor k

But , possible in 1997 on I nt ernet in a f ew mont hs

in 1998 on dedicat ed h/ w in a f ew days

in 1999 above combined in 22hr s!

Must be able t o r ecognize plaint ext

Alt er nat ives t o DES being consider ed


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Ref er ences

[1] Net wor k Secur it y Essent ials,Applicat ions and St andar ds, 2nd

edit ion by William St allings Chapt er 2

encrypt basics

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