1. Classical Encryption Techniques.ppt

Cryptography ppt

1. Cryptography and Cryptography and
Network SecurityNetwork Security
Chapter 2Chapter 2
Fifth EditionFifth Edition
by William Stallingsby William Stallings
Lecture slides by Lawrie BrownLecture slides by Lawrie Brown
Edited by Sharada ValivetiEdited by Sharada Valiveti

2. Chapter 2 – Chapter 2 – Classical EncryptionClassical Encryption
TechniquesTechniques

"I am fairly familiar with all the forms of secret "I am fairly familiar with all the forms of secret
writings, and am myself the author of a trifling writings, and am myself the author of a trifling
monograph upon the subject, in which I analyze monograph upon the subject, in which I analyze
one hundred and sixty separate ciphers," said one hundred and sixty separate ciphers," said
Holmes.Holmes.. .
——The Adventure of the Dancing MenThe Adventure of the Dancing Men, Sir Arthur , Sir Arthur
Conan DoyleConan Doyle

3. Symmetric EncryptionSymmetric Encryption
Or conventional / Or conventional / private-keyprivate-key / single-key / single-key
Sender and recipient share a common keySender and recipient share a common key
All classical encryption algorithms are All classical encryption algorithms are
private-keyprivate-key
Was only type prior to invention of public-Was only type prior to invention of public-
key in 1970’skey in 1970’s
And by far most widely used (still)And by far most widely used (still)
Is significantly faster than public-key Is significantly faster than public-key
cryptographycryptography

4. Some Basic TerminologySome Basic Terminology

plaintextplaintext - original message - original message

ciphertextciphertext - coded message - coded message

ciphercipher - algorithm for transforming plaintext to ciphertext - algorithm for transforming plaintext to ciphertext

keykey - info used in cipher known only to sender/receiver - info used in cipher known only to sender/receiver

encipher (encrypt)encipher (encrypt) - converting plaintext to ciphertext - converting plaintext to ciphertext

decipher (decrypt)decipher (decrypt) - recovering plaintext from ciphertext - recovering plaintext from ciphertext

cryptographycryptography - study of encryption principles/methods - study of encryption principles/methods

cryptanalysis (codebreaking)cryptanalysis (codebreaking) - study of principles/ - study of principles/
methods of deciphering ciphertext methods of deciphering ciphertext withoutwithout knowing key knowing key

cryptologycryptology - field of both cryptography and cryptanalysis - field of both cryptography and cryptanalysis

5. Symmetric Cipher ModelSymmetric Cipher Model

6. RequirementsRequirements

Two requirements for secure use of symmetric Two requirements for secure use of symmetric
encryption:encryption:

A strong encryption algorithmA strong encryption algorithm

A secret key known only to sender / receiverA secret key known only to sender / receiver

Mathematically have:Mathematically have:
Y Y = e(k, = e(k, xx) = e) = e
kk(x) = {x}(x) = {x}
kk
X X = d(k, = d(k, yy) = d) = d
kk(y)(y)

Assume encryption algorithm is knownAssume encryption algorithm is known

Kerckhoff’s principleKerckhoff’s principle: security in secrecy of key alone, : security in secrecy of key alone,
not in obscurity of the encryption algorithmnot in obscurity of the encryption algorithm

Implies a secure channel to Implies a secure channel to distribute keydistribute key

Central problem in symmetric cryptographyCentral problem in symmetric cryptography

7. CryptographyCryptography

Can characterize cryptographic system by:Can characterize cryptographic system by:

Type of encryption operations usedType of encryption operations used
•SubstitutionSubstitution
•TranspositionTransposition
•ProductProduct

Number of keys usedNumber of keys used
•Single-key or privateSingle-key or private
•Two-key or publicTwo-key or public

Way in which plaintext is processedWay in which plaintext is processed
•BlockBlock
•StreamStream

8. CryptanalysisCryptanalysis

Objective to recover key not just messageObjective to recover key not just message

General approaches:General approaches:

Cryptanalytic attackCryptanalytic attack

Brute-force attackBrute-force attack

If either succeed all key use compromisedIf either succeed all key use compromised

9. Cryptanalytic AttacksCryptanalytic Attacks
Ciphertext onlyCiphertext only

Only know algorithm & ciphertext, is Only know algorithm & ciphertext, is
statistical, can identify plaintext statistical, can identify plaintext
Known plaintextKnown plaintext

Know/suspect plaintext & ciphertextKnow/suspect plaintext & ciphertext
Chosen plaintextChosen plaintext

Select plaintext and obtain ciphertextSelect plaintext and obtain ciphertext
Chosen ciphertextChosen ciphertext

Select ciphertext and obtain plaintextSelect ciphertext and obtain plaintext
Chosen textChosen text

Select plaintext or ciphertext to en/decryptSelect plaintext or ciphertext to en/decrypt

10. Cipher StrengthCipher Strength

Unconditional securityUnconditional security

No matter how much computer power or time No matter how much computer power or time
is available, the cipher cannot be broken is available, the cipher cannot be broken
since the ciphertext provides insufficient since the ciphertext provides insufficient
information to uniquely determine the information to uniquely determine the
corresponding plaintext corresponding plaintext

Computational securityComputational security

Given limited computing resources (e.g. Time Given limited computing resources (e.g. Time
needed for calculations is greater than age of needed for calculations is greater than age of
universe), the cipher cannot be broken universe), the cipher cannot be broken

11. Encryption MappingsEncryption Mappings
A given key (k)A given key (k)

Maps any message Mi to Maps any message Mi to
some ciphertext E(k,Mi)some ciphertext E(k,Mi)

Ciphertext image of Mi is Ciphertext image of Mi is
unique to Mi under kunique to Mi under k

Plaintext pre-image of Ci is Plaintext pre-image of Ci is
unique to Ci under k unique to Ci under k
NotationNotation

key k and Mi in M, key k and Mi in M, ƎƎ! Cj ! Cj
in C such that E(k,Mi) = Cjin C such that E(k,Mi) = Cj

key k and ciphertext Ci key k and ciphertext Ci
in C, in C, !
Ǝ
!
Ǝ
Mj in M such that Mj in M such that
E(k,Mj) = Ci E(k,Mj) = Ci

EE
kk(.) is “one-to-one” (injective)(.) is “one-to-one” (injective)

If |M|=|C| it is also “onto” If |M|=|C| it is also “onto”
(surjective), and hence (surjective), and hence
bijective. bijective.
M1
M2
M3
Mi
Mn
C1
C2
C3
Ci
Cn
K
1
K
1
K
1
K1
K
1 K
1
A A
A A
M=set of all M=set of all
plaintexts plaintexts
C=set of all C=set of all
ciphertexts ciphertexts

12. Encryption Mappings (2)Encryption Mappings (2)

A given plaintext (Mi)A given plaintext (Mi)

Mi is mapped to Mi is mapped to somesome ciphertext ciphertext
E(K,Mi) by every key kE(K,Mi) by every key k

Different keys may map Mi to the Different keys may map Mi to the
same ciphertextsame ciphertext

There may be some ciphertexts to There may be some ciphertexts to
which Mi is never mapped by any which Mi is never mapped by any
keykey

NotationNotation

key k and Mi in M, key k and Mi in M, ƎƎ! !
ciphertext Cj in C such that ciphertext Cj in C such that
E(k,Mi) = CjE(k,Mi) = Cj

It is possible that there are keys k It is possible that there are keys k
and k’ such that E(k,Mi) = E(k’,Mi) and k’ such that E(k,Mi) = E(k’,Mi)

There may be some ciphertext Cj There may be some ciphertext Cj
for which for which ƎƎ key k such that key k such that
E(k,Mi) = Cj E(k,Mi) = Cj
M1
M2
M3
Mi
Mn
C1
C2
C3
Ci
Cn
K2,K89,...
Kj
K
1
,
K
7
5
7
,
.
.
.
K
3
,K
j’,...
K
m A A

13. Encryption Mappings (3)Encryption Mappings (3)

A ciphertext (Ci)A ciphertext (Ci)

Has a unique plaintext pre-Has a unique plaintext pre-
image under each k image under each k

May have two keys that map May have two keys that map
the same plaintext to itthe same plaintext to it

There may be some plaintext There may be some plaintext
Mj such that no key maps Mj Mj such that no key maps Mj
to Cito Ci

NotationNotation

key k and ciphertext Ci key k and ciphertext Ci
in C, in C, !
Ǝ
!
Ǝ
Mj in M such that Mj in M such that
E(k,Mj) = Ci E(k,Mj) = Ci

There may exist keys k, k’ There may exist keys k, k’
and plaintext Mj such that and plaintext Mj such that
E(k,Mj) = E(k’,Mj) = CiE(k,Mj) = E(k’,Mj) = Ci

There may exist plaintext Mj There may exist plaintext Mj
such that such that ƎƎ key k such that key k such that
E(k,Mj) = CiE(k,Mj) = Ci
M1
M2
M3
Mi
Mn
C1
C2
C3
Ci
Cn
K
1
,
K
1
7
,
.
.
.
K2,K89,...
Kj
K
3,K
94,...
Km
.
.
.
.
.
.
.
.
.
.
.
.
...
... A A

14. Encryption Mappings (4)Encryption Mappings (4)
Under what conditions will there always be Under what conditions will there always be
some key that maps some plaintext to a some key that maps some plaintext to a
given ciphertext? given ciphertext?

If for an intercepted ciphertext cIf for an intercepted ciphertext c
jj, there is , there is
some plaintext msome plaintext m
ii for which there does not for which there does not
exist any key k that maps mexist any key k that maps m
ii to c to c
jj, then the , then the
attacker has learned somethingattacker has learned something

If the attacker has ciphertext cIf the attacker has ciphertext c
jj and known and known
plaintext mplaintext m
ii, then many keys may be , then many keys may be
eliminatedeliminated

15. Brute Force SearchBrute Force Search
Always possible to simply try every key Always possible to simply try every key
Most basic attack, exponential in key length Most basic attack, exponential in key length
Assume either know / recognise plaintextAssume either know / recognise plaintext
Key Size (bits)Number of Alternative
Keys
Time required at 1
decryption/µs
Time required at 10
6

decryptions/µs
32 2
32
= 4.3  10
9
2
31
µs = 35.8 minutes2.15 milliseconds
56 2
56
= 7.2  10
16
2
55
µs = 1142 years 10.01 hours
128 2
128
= 3.4  10
38
2
127
µs = 5.4  10
24
years5.4  10
18
years
168 2
168
= 3.7  10
50
2
167
µs = 5.9  10
36
years5.9  10
30
years
26 characters
(permutation)
26! = 4  10
26
2  10
26
µs= 6.4  10
12
years6.4  10
6
years

16. Classical Substitution Classical Substitution
CiphersCiphers

Where Where letters of plaintext are replaced by letters of plaintext are replaced by
other letters or by numbers or symbolsother letters or by numbers or symbols

Or if plaintext is Or if plaintext is viewed as a sequence of viewed as a sequence of
bits, then substitution involves replacing bits, then substitution involves replacing
plaintext bit patterns with ciphertext bit plaintext bit patterns with ciphertext bit
patternspatterns

17. Caesar CipherCaesar Cipher
Earliest known substitution cipherEarliest known substitution cipher
By Julius Caesar By Julius Caesar
First attested use in military affairsFirst attested use in military affairs
Replaces each letter by 3rd letter onReplaces each letter by 3rd letter on
Example:Example:
Meet me after the toga partyMeet me after the toga party
Phhw ph diwhu wkh wrjd sduwbPhhw ph diwhu wkh wrjd sduwb

18. Caesar CipherCaesar Cipher

Can define transformation as:Can 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 = 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 =
ININ
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 = 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 =
OUTOUT

Mathematically give each letter a numberMathematically give each letter a number
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 za 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
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 250 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Then have Caesar (rotation) cipher as:Then have Caesar (rotation) cipher as:
c c = E(k, = E(k, pp) = () = (p p + + kk) mod (26)) mod (26)
p p = D(k, c) = (c – = D(k, c) = (c – kk) mod (26)) mod (26)

19. Cryptanalysis of Caesar Cryptanalysis of Caesar
Cipher Cipher

Only have 26 possible ciphers Only have 26 possible ciphers

A maps to A,B,..Z A maps to A,B,..Z

Could simply try each in turn Could simply try each in turn

A A brute force searchbrute force search

Given ciphertext, just try all shifts of lettersGiven ciphertext, just try all shifts of letters

Do need to recognize when have plaintextDo need to recognize when have plaintext

Eg. Break ciphertext "GCUA VQ DTGCM"Eg. Break ciphertext "GCUA VQ DTGCM"

20. Affine CipherAffine Cipher

Broaden to include multiplicationBroaden to include multiplication

Can define affine transformation as:Can define affine transformation as:
C C = e(k, = e(k, pp) = (a) = (ap p + + bb) mod (26)) mod (26)
P P = d(k, c) = (a= d(k, c) = (a
-1-1
(c – (c – b)b)) mod (26)) mod (26)

Key k=(a,b)Key k=(a,b)

A must be relatively prime to 26A must be relatively prime to 26

So there exists unique inverse So there exists unique inverse aa
-1-1

21. Affine Cipher - ExampleAffine Cipher - Example
Example k=(17,3):Example k=(17,3):
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 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 = INz = IN
D U L C T K B S J A R I Z Q H Y P G X O F W N E V D U L C T K B S J A R I Z Q H Y P G X O F W N E V
M = OUTM = OUT
Example:Example:
meet me after the toga partymeet me after the toga party
ZTTO ZT DKOTG OST OHBD YDGOVZTTO ZT DKOTG OST OHBD YDGOV
Now how many keys are there?Now how many keys are there?

12 x 26 = 31212 x 26 = 312
Still can be brute force attacked!Still can be brute force attacked!

22. Monoalphabetic CipherMonoalphabetic Cipher
Rather than just shifting the alphabet Rather than just shifting the alphabet
Could shuffle (permute) the letters arbitrarily Could shuffle (permute) the letters arbitrarily
Each plaintext letter maps to a different random Each plaintext letter maps to a different random
ciphertext letter ciphertext letter
Hence key is 26 letters long Hence key is 26 letters long
Plain: abcdefghijklmnopqrstuvwxyzPlain: abcdefghijklmnopqrstuvwxyz
Cipher: DKVQFIBJWPESCXHTMYAUOLRGZNCipher: DKVQFIBJWPESCXHTMYAUOLRGZN
Plaintext: ifwewishtoreplacelettersPlaintext: ifwewishtoreplaceletters
Ciphertext: WIRFRWAJUHYFTSDVFSFUUFYACiphertext: WIRFRWAJUHYFTSDVFSFUUFYA

23. Monoalphabetic Cipher Monoalphabetic Cipher
SecuritySecurity

Key size is now 25 characters…Key size is now 25 characters…

Now have a total of 26! = 4 x 10Now have a total of 26! = 4 x 10
2626
keys keys

With so many keys, might think is secure With so many keys, might think is secure

But would be But would be !!!WRONG!!!!!!WRONG!!!

Problem is language characteristicsProblem is language characteristics

24. Language Redundancy and Language Redundancy and
CryptanalysisCryptanalysis

Human languages are Human languages are redundantredundant

E.G., "Th lrd s m shphrd shll nt wnt" E.G., "Th lrd s m shphrd shll nt wnt"

Letters are not equally commonly used Letters are not equally commonly used

In english E is by far the most common letter In english E is by far the most common letter

Followed by T,R,N,I,O,A,S Followed by T,R,N,I,O,A,S

Other letters like Z,J,K,Q,X are fairly rare Other letters like Z,J,K,Q,X are fairly rare

Have tables of single, double & triple letter Have tables of single, double & triple letter
frequencies for various languagesfrequencies for various languages

25. English Letter FrequenciesEnglish Letter Frequencies

26. English Letter FrequenciesEnglish Letter Frequencies
Sorted Relative Frequencies
0.000
2.000
4.000
6.000
8.000
10.000
12.000
14.000
ETAOINSHRDLCUMWFGYPBVKJXQZ

27. English Letter Frequencies
0.000
2.000
4.000
6.000
8.000
10.000
12.000
14.000
ABCDEFGHIJKLMNOPQRSTUVWXYZ
Frequences for Cipher-0
0.000
2.000
4.000
6.000
8.000
10.000
12.000
14.000
ABCDEFGHIJKLMNOPQRSTUVWXYZ
What kind of cipher is this?What kind of cipher is this?

28. English Letter Frequencies
0.000
2.000
4.000
6.000
8.000
10.000
12.000
14.000
ABCDEFGHIJKLMNOPQRSTUVWXYZ
Frequencies for Cipher-1
0.000
2.000
4.000
6.000
8.000
10.000
12.000
14.000
ABCDEFGHIJKLMNOPQRSTUVWXYZ
What kind of cipher is this?What kind of cipher is this?

29. Use in CryptanalysisUse in Cryptanalysis

Key concept - monoalphabetic substitution Key concept - monoalphabetic substitution
ciphers do not change relative letter frequencies ciphers do not change relative letter frequencies

Discovered by Arabian scientists in 9Discovered by Arabian scientists in 9
thth
century century

Calculate letter frequencies for CiphertextCalculate letter frequencies for Ciphertext

Compare counts/plots against known values Compare counts/plots against known values

If caesar cipher look for common peaks/troughs If caesar cipher look for common peaks/troughs

Peaks at: A-E-I triple, N-O pair, R-S-T triplePeaks at: A-E-I triple, N-O pair, R-S-T triple

Troughs at: J-K, U-V-W-X-Y-ZTroughs at: J-K, U-V-W-X-Y-Z

For For monoalphabetic must identify each lettermonoalphabetic must identify each letter

Tables of common double/triple letters helpTables of common double/triple letters help
(Digrams and trigrams)(Digrams and trigrams)

Amount of ciphertext is important – statistics!Amount of ciphertext is important – statistics!

30. Example CryptanalysisExample Cryptanalysis

Given ciphertext:Given ciphertext:
UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZUZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ
VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSXVUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX
EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQEPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ

Count relative letter frequencies (see text)Count relative letter frequencies (see text)

31. Example CryptanalysisExample Cryptanalysis
given ciphertext:given ciphertext:
UUZZQSOVUOHXMOQSOVUOHXMOPPVGVGPPOOZPZPEVSGEVSGZZWSWSZZOOPPFFPPESXUDBMETSXAIESXUDBMETSXAIZZ
VUEVUEPPHHZZHMDHMDZZSHSHZZOWSFOWSFPPAAPPPPDTSVDTSVPPQUZWYMXUQUZWYMXUZZUHSXUHSX
EEPPYEYEPPOOPPDDZZSSZZUFUFPPOMBOMBZZWWPPFUFUPZPZHMDJUDTMOHMQHMDJUDTMOHMQ
guess P & Z are e and tguess P & Z are e and t
guess ZW is th and hence ZWP is “the”guess ZW is th and hence ZWP is “the”
proceeding with trial and error finally get:proceeding with trial and error finally get:
it was disclosed yesterday that several informal butit was disclosed yesterday that several informal but
direct contacts have been made with politicaldirect contacts have been made with political
representatives of the viet cong in moscowrepresentatives of the viet cong in moscow

32. Playfair CipherPlayfair Cipher

Not even the large number of keys in a Not even the large number of keys in a
monoalphabetic cipher provides security monoalphabetic cipher provides security

One approach to improving security was to One approach to improving security was to
encrypt multiple letters encrypt multiple letters

TheThe playfair cipher playfair cipher is an example is an example

Invented by Charles Wheatstone in 1854, Invented by Charles Wheatstone in 1854,
but named after his friend Baron Playfair but named after his friend Baron Playfair

33. Playfair Key MatrixPlayfair Key Matrix

a 5X5 matrix of letters based on a keyword a 5X5 matrix of letters based on a keyword

fill in letters of keyword (sans duplicates) fill in letters of keyword (sans duplicates)

fill rest of matrix with other lettersfill rest of matrix with other letters

eg. using the keyword MONARCHYeg. using the keyword MONARCHY
MM OO NN AA RR
CC HH YY BB DD
EE FF GG I/JI/J KK
LL PP QQ SS TT
UU VV WW XX ZZ

34. Encrypting and DecryptingEncrypting and Decrypting

Plaintext is encrypted two letters at a time Plaintext is encrypted two letters at a time
1.1.If a pair is a repeated letter, insert filler like 'X’If a pair is a repeated letter, insert filler like 'X’
2.2.If both letters fall in the same row, replace If both letters fall in the same row, replace
each with letter to right (wrapping back to start each with letter to right (wrapping back to start
from end) from end)
3.3.If both letters fall in the same column, replace If both letters fall in the same column, replace
each with the letter below it (wrapping to top each with the letter below it (wrapping to top
from bottom)from bottom)
4.4.Otherwise each letter is replaced by the letter Otherwise each letter is replaced by the letter
in the same row and in the column of the other in the same row and in the column of the other
letter of the pairletter of the pair

35. Playfair ExamplePlayfair Example
Message = Move forwardMessage = Move forward
Plaintext = mo ve fo rw ar dx Plaintext = mo ve fo rw ar dx
Here x is just a filler, message is padded and segmentedHere x is just a filler, message is padded and segmented
Ciphertext = ON UF PH NZ RM BZCiphertext = ON UF PH NZ RM BZ
MM OO NN AA RR
CC HH YY BB DD
EE FF GG I/JI/J KK
LL PP QQ SS TT
UU VV WW XX ZZ
mo -> ON; mo -> ON; ve -> UF; ve -> UF; fo -> PH, etc.fo -> PH, etc.

36. Security of Playfair CipherSecurity of Playfair Cipher
Security much improved over monoalphabeticSecurity much improved over monoalphabetic
Since have 26 x 26 = 676 digrams Since have 26 x 26 = 676 digrams
Would need a 676 entry frequency table to Would need a 676 entry frequency table to
analyse (versus 26 for a monoalphabetic) analyse (versus 26 for a monoalphabetic)
And correspondingly more ciphertext And correspondingly more ciphertext
Was widely used for many yearsWas widely used for many years

Eg. By US & British military in WW1Eg. By US & British military in WW1
It It cancan be broken, given a few hundred letters be broken, given a few hundred letters
Since still has much of plaintext structure Since still has much of plaintext structure

37. Polyalphabetic CiphersPolyalphabetic Ciphers

Polyalphabetic substitution ciphersPolyalphabetic substitution ciphers

Improve security using multiple cipher alphabets Improve security using multiple cipher alphabets

Make cryptanalysis harder with more alphabets to Make cryptanalysis harder with more alphabets to
guess and flatter frequency distribution guess and flatter frequency distribution

Use a key to select which alphabet is used for each Use a key to select which alphabet is used for each
letter of the message letter of the message

Use each alphabet in turn Use each alphabet in turn

Repeat from start after end of key is reached Repeat from start after end of key is reached

38. Vigenère CipherVigenère Cipher

Simplest polyalphabetic substitution cipherSimplest polyalphabetic substitution cipher

Effectively multiple caesar ciphers Effectively multiple caesar ciphers
Key is multiple letters long K = kKey is multiple letters long K = k
11 k k
22 ... k ... k
dd

II
thth
letter specifies i letter specifies i
thth
alphabet to use alphabet to use

Use each alphabet in turn Use each alphabet in turn

Repeat from start after d letters in Repeat from start after d letters in
messagemessage

Decryption simply works in reverse Decryption simply works in reverse

39. Example of Example of Vigenère CipherVigenère Cipher

Write the plaintext out Write the plaintext out

Write the keyword repeated above itWrite the keyword repeated above it

Use each key letter as a Caesar cipher key Use each key letter as a Caesar cipher key

Encrypt the corresponding plaintext letterEncrypt the corresponding plaintext letter

Eg using keyword Eg using keyword deceptivedeceptive
Key: deceptivedeceptivedeceptiveKey: deceptivedeceptivedeceptive
Plaintext: wearediscoveredsaveyourselfPlaintext: wearediscoveredsaveyourself
Ciphertext:zicvtwqngrzgvtwavzhcqyglmgjCiphertext:zicvtwqngrzgvtwavzhcqyglmgj

40. AidsAids

Simple aids can assist with en/decryption Simple aids can assist with en/decryption

A A saint-cyr slidesaint-cyr slide is a simple manual aid is a simple manual aid

A slide with repeated alphabet A slide with repeated alphabet

Line up plaintext 'A' with key letter, eg 'C' Line up plaintext 'A' with key letter, eg 'C'

Then read off any mapping for key letter Then read off any mapping for key letter

Can bend round into a Can bend round into a cipher diskcipher disk

Or expand into a Or expand into a vigenère tableauvigenère tableau

41. Security of Security of Vigenère CiphersVigenère Ciphers

Have multiple ciphertext letters for each Have multiple ciphertext letters for each
plaintext letterplaintext letter

Hence letter frequencies are obscuredHence letter frequencies are obscured

But not totally lostBut not totally lost

Start with letter frequenciesStart with letter frequencies

See if it looks monoalphabetic or notSee if it looks monoalphabetic or not

If not, then need to determine number of If not, then need to determine number of
alphabets, since then can attack eachalphabets, since then can attack each

42. Frequencies After Polyalphabetic Frequencies After Polyalphabetic
EncryptionEncryption
Letter Relative Frequency
0.000
2.000
4.000
6.000
8.000
10.000
12.000
14.000
equiprobable
unencrypted
two keys
four keys
eight keys

43. Frequencies After Polyalphabetic Frequencies After Polyalphabetic
EncryptionEncryption
Sorted relative frequencies
0
2
4
6
8
10
12
14
147101316192225
Equiprobible
Unencrypted/1 key
two keys
four keys
eight keys

44. Kasiski MethodKasiski Method

Method developed by babbage / kasiski Method developed by babbage / kasiski

Repetitions in ciphertext give clues to period Repetitions in ciphertext give clues to period

So find same plaintext a multiple of key length So find same plaintext a multiple of key length
apart apart

Which results in the same ciphertext Which results in the same ciphertext

Of course, could also be random flukeOf course, could also be random fluke

E.G. Repeated “VTW” in previous exampleE.G. Repeated “VTW” in previous example

Distance of 9 suggests key size of 3 or 9Distance of 9 suggests key size of 3 or 9

Then attack each monoalphabetic cipher Then attack each monoalphabetic cipher
individually using same techniques as beforeindividually using same techniques as before

45. Example of Example of Kasiski AttackKasiski Attack
Find repeated ciphertext trigrams (e.g., VTW)Find repeated ciphertext trigrams (e.g., VTW)
May be result of same key sequence and same May be result of same key sequence and same
plaintext sequence (or not)plaintext sequence (or not)
Find distance(s)Find distance(s)
Common factors are likely key lengthsCommon factors are likely key lengths
key: deckey: decepteptivedecivedecepteptivedeceptiveivedeceptive
plaintext: weaplaintext: wearedrediscoveiscoveredredsaveyourselfsaveyourself
ciphertext:ZICciphertext:ZICVTWVTWQNGRZGQNGRZGVTWVTWAVZHCQYGLMGJAVZHCQYGLMGJ

46. Autokey CipherAutokey Cipher

Ideally want a key as long as the messageIdeally want a key as long as the message

Vigenère proposed the Vigenère proposed the autokeyautokey cipher cipher

With keyword is prefixed to message as keyWith keyword is prefixed to message as key

Knowing keyword can recover the first few Knowing keyword can recover the first few
letters letters

Use these in turn on the rest of the messageUse these in turn on the rest of the message

But still have frequency characteristics to attack But still have frequency characteristics to attack

Eg. Given key Eg. Given key deceptivedeceptive
key: deceptivewearediscoveredsavkey: deceptivewearediscoveredsav
plaintext: wearediscoveredsaveyourselfplaintext: wearediscoveredsaveyourself
ciphertext:ZICVTWQNGKZEIIGASXSTSLVVWLAciphertext:ZICVTWQNGKZEIIGASXSTSLVVWLA

47. Homophone CipherHomophone Cipher

Rather than combine multiple monoalphabetic Rather than combine multiple monoalphabetic
ciphers, can assign multiple ciphertext ciphers, can assign multiple ciphertext
characters to same plaintext charactercharacters to same plaintext character

Assign number of homophones according to Assign number of homophones according to
frequency of plaintext character frequency of plaintext character

Gauss believed he made unbreakable cipher Gauss believed he made unbreakable cipher
using homophonesusing homophones

But still have digram/trigram frequency But still have digram/trigram frequency
characteristics to attack characteristics to attack

E.g., have 58 ciphertext characters, with each E.g., have 58 ciphertext characters, with each
plaintext character assigned to ceil(freq/2) plaintext character assigned to ceil(freq/2)
ciphertext characters – so e has 7 homophones, ciphertext characters – so e has 7 homophones,
t has 5, a has 4, j has 1, q has 1, etc.t has 5, a has 4, j has 1, q has 1, etc.

48. Vernam CipherVernam Cipher

Ultimate defense is to use a key as long as the Ultimate defense is to use a key as long as the
plaintextplaintext

With no statistical relationship to itWith no statistical relationship to it

Invented by AT&T engineer Gilbert Vernam in Invented by AT&T engineer Gilbert Vernam in
19181918

Specified in Specified in U.S. Patent 1,310,719, issued July , issued July
22, 191922, 1919

Originally proposed using a very long but Originally proposed using a very long but
eventually repeating keyeventually repeating key

Used electromechanical relaysUsed electromechanical relays

49. One-Time PadOne-Time Pad

If a truly random key as long as the message is If a truly random key as long as the message is
used, the cipher will be secure used, the cipher will be secure

Called a one-time pad (OTP)Called a one-time pad (OTP)

Is unbreakable since ciphertext bears no Is unbreakable since ciphertext bears no
statistical relationship to the plaintextstatistical relationship to the plaintext

Since for Since for any plaintextany plaintext & & any ciphertextany ciphertext there there
exists a key mapping one to otherexists a key mapping one to other

Can only use the key Can only use the key onceonce though though

Problems in generation & safe distribution of keyProblems in generation & safe distribution of key

50. Transposition CiphersTransposition Ciphers

Now consider classical Now consider classical transpositiontransposition or or
permutationpermutation ciphers ciphers

These hide the message by rearranging These hide the message by rearranging
the letter order the letter order

Without altering the actual letters usedWithout altering the actual letters used

Can recognise these since have the same Can recognise these since have the same
frequency distribution as the original text frequency distribution as the original text

51. Rail Fence cipherRail Fence cipher
Write message letters out diagonally over a Write message letters out diagonally over a
number of rows number of rows
Then read off cipher row by rowThen read off cipher row by row
Eg. Write message out as:Eg. Write message out as:
m e m a t r h t g p r ym e m a t r h t g p r y
e t e f e t e o a a te t e f e t e o a a t
Giving ciphertextGiving ciphertext
MEMATRHTGPRYETEFETEOAATMEMATRHTGPRYETEFETEOAAT

52. Row Transposition CiphersRow Transposition Ciphers

Is a more complex transpositionIs a more complex transposition

Write letters of message out in rows over a Write letters of message out in rows over a
specified number of columnsspecified number of columns

Then reorder the columns according to Then reorder the columns according to
some key before reading off the rowssome key before reading off the rows
Key: Key: 43125674312567
Column Out 4 3 1 2 5 6 7Column Out 4 3 1 2 5 6 7
Plaintext: a t t a c k pPlaintext: a t t a c k p
o s t p o n eo s t p o n e
d u n t i l td u n t i l t
w o a m x y zw o a m x y z
Ciphertext: TTNAAPTMTSUOAODWCOIXKNLYPETZCiphertext: TTNAAPTMTSUOAODWCOIXKNLYPETZ

53. Block Transposition CiphersBlock Transposition Ciphers

Arbitrary block transposition may be usedArbitrary block transposition may be used

Specify permutation on blockSpecify permutation on block

Repeat for each block of plaintextRepeat for each block of plaintext
Key: Key: 49312856074931285607
Plaintext: attackpost poneduntil twoamxyzabPlaintext: attackpost poneduntil twoamxyzab
Ciphertext: CTATTSKPAO DLEONIDUPT MBAWOAXYTZCiphertext: CTATTSKPAO DLEONIDUPT MBAWOAXYTZ

54. Product CiphersProduct Ciphers
Ciphers using substitutions or transpositions are Ciphers using substitutions or transpositions are
not secure because of language characteristicsnot secure because of language characteristics
Hence consider using several ciphers in Hence consider using several ciphers in
succession to make harder, but: succession to make harder, but:

Two substitutions make a more complex substitution Two substitutions make a more complex substitution

Two transpositions make more complex transposition Two transpositions make more complex transposition

But a substitution followed by a transposition makes a But a substitution followed by a transposition makes a
new much harder cipher new much harder cipher
This is bridge from classical to modern ciphersThis is bridge from classical to modern ciphers

55. Rotor MachinesRotor Machines
Before modern ciphers, rotor machines were Before modern ciphers, rotor machines were
most common complex ciphers in usemost common complex ciphers in use
Widely used in WW2Widely used in WW2

German Enigma, Allied Hagelin, Japanese PurpleGerman Enigma, Allied Hagelin, Japanese Purple
Implemented a very complex, varying Implemented a very complex, varying
substitution ciphersubstitution cipher
Used a series of cylinders, each giving one Used a series of cylinders, each giving one
substitution, which rotated and changed after substitution, which rotated and changed after
each letter was encryptedeach letter was encrypted
With 3 cylinders have 26With 3 cylinders have 26
33
=17576 alphabets=17576 alphabets

56. Hagelin Rotor MachineHagelin Rotor Machine

57. Rotor Machine PrinciplesRotor Machine Principles

58. Rotor CiphersRotor Ciphers

Each rotor implements some permutation Each rotor implements some permutation
between its input and output contactsbetween its input and output contacts

Rotors turn like an odometer on each key Rotors turn like an odometer on each key
stroke (rotating input and output contacts)stroke (rotating input and output contacts)

Key is the sequence of rotors and their Key is the sequence of rotors and their
initial positionsinitial positions

59. SteganographySteganography

An alternative to encryptionAn alternative to encryption

Hides existence of messageHides existence of message

Using only a subset of letters/words in a longer Using only a subset of letters/words in a longer
message marked in some waymessage marked in some way

Using invisible inkUsing invisible ink

Hiding in LSB in graphic image or sound fileHiding in LSB in graphic image or sound file

Hide in “noise”Hide in “noise”

Has drawbacksHas drawbacks

High overhead to hide relatively few info bitsHigh overhead to hide relatively few info bits

Advantage is can obscure encryption useAdvantage is can obscure encryption use

60. SummarySummary

Have considered:Have considered:

Classical cipher techniques and terminologyClassical cipher techniques and terminology

Monoalphabetic substitution ciphersMonoalphabetic substitution ciphers

Cryptanalysis using letter frequenciesCryptanalysis using letter frequencies

Playfair cipherPlayfair cipher

Polyalphabetic ciphersPolyalphabetic ciphers

Transposition ciphersTransposition ciphers

Product ciphers and rotor machinesProduct ciphers and rotor machines

SteganographySteganography

61. Thank you!!!