Ch02...1

Cryptography and Cryptography and Network SecurityNetwork Security

Chapter 2Chapter 2

Fourth EditionFourth Edition

by William Stallingsby William Stallings

Lecture slides by Vijay KattaLecture slides by Vijay Katta

04/12/23 Vijay Katta

Chapter 2 – Chapter 2 – Classical Classical EncryptionEncryptionTechniquesTechniques

Many savages at the present day regard Many savages at the present day regard their names as vital parts of themselves, their names as vital parts of themselves, and therefore take great pains to conceal and therefore take great pains to conceal their real names, lest these should give to their real names, lest these should give to evil-disposed persons a handle by which evil-disposed persons a handle by which to injure their owners. to injure their owners.

——The Golden Bough, The Golden Bough, Sir James George Sir James George FrazerFrazer


Symmetric EncryptionSymmetric Encryption

or conventional / or conventional / private-keyprivate-key / single- / single-keykey

sender and recipient share a common sender and recipient share a common keykey

all classical encryption algorithms are all classical encryption algorithms are private-keyprivate-key

was only type prior to invention of was only type prior to invention of public-key in 1970’spublic-key in 1970’s

and by far most widely usedand by far most widely used


Some Basic TerminologySome Basic Terminology

plaintextplaintext - original message - original message ciphertextciphertext - coded message - coded message ciphercipher - algorithm for transforming plaintext to - algorithm for transforming plaintext to

ciphertext 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 ciphertext from - recovering ciphertext from

plaintextplaintext 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 - field of both cryptography and

cryptanalysiscryptanalysis


Symmetric Cipher ModelSymmetric Cipher Model


Basic ConceptsBasic Concepts CipherCipher

An algorithm for transforming an intelligible An algorithm for transforming an intelligible message into unintelligible by transposition message into unintelligible by transposition and/or substitution, or some other techniquesand/or substitution, or some other techniques

KeysKeys Some critical information used by the cipher, Some critical information used by the cipher,

known only to the sender and/or receiverknown only to the sender and/or receiver EncipherEncipher (encode) (encode)

The process of converting plaintext to ciphertextThe process of converting plaintext to ciphertext DecipherDecipher (decode) (decode)

The process of converting ciphertext back into The process of converting ciphertext back into plaintextplaintext


Basic ConceptsBasic Concepts ciphercipher

an algorithm for encryption and decryption. The an algorithm for encryption and decryption. The exact operation of ciphers is normally controlled by exact operation of ciphers is normally controlled by a key — some secret piece of information that a key — some secret piece of information that customizes how the ciphertext is producedcustomizes how the ciphertext is produced

ProtocolsProtocols specify the details of how ciphers (and other specify the details of how ciphers (and other

cryptographic primitives) are to be used to achieve cryptographic primitives) are to be used to achieve specific tasks. specific tasks.

A suite of protocols, ciphers, key management, user-A suite of protocols, ciphers, key management, user-prescribed actions implemented together as a prescribed actions implemented together as a system constitute a system constitute a cryptosystemcryptosystem; ;

this is what an end-user interacts with, e.g. PGPthis is what an end-user interacts with, e.g. PGP


Encryption and Encryption and DecryptionDecryption

Plaintext ciphertext

Encipher C = E(K1)(P)

Decipher P = D(K2)(C)

K1, K2: from keyspace

These two keys could be different; could be difficult to get one from the other


What is Security?What is Security? Two fundamentally different securitiesTwo fundamentally different securities

Unconditional securityUnconditional security No matter how much computer power is available, the No matter how much computer power is available, the

cipher cannot be brokencipher cannot be broken Using Shannon’s information theoryUsing Shannon’s information theory

The entropy of the message I(M) is same as the entropy of The entropy of the message I(M) is same as the entropy of the message I(M|C) when known the ciphertext (and the message I(M|C) when known the ciphertext (and possible more) possible more)

Computational securityComputational security Given limited computing resources (e.g time needed for Given limited computing resources (e.g time needed for

calculations is greater than age of universe), the cipher calculations is greater than age of universe), the cipher cannot be brokencannot be broken

What do we mean “broken”?What do we mean “broken”? Proved by some complexity equivalence approachProved by some complexity equivalence approach


RequirementsRequirements two requirements for secure use of two requirements for secure use of

symmetric encryption:symmetric 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= EKK((XX))

X X = D= DKK((YY)) assume encryption algorithm is knownassume encryption algorithm is known implies a secure channel to distribute keyimplies a secure channel to distribute key


CryptographyCryptography

characterize cryptographic system characterize cryptographic system by:by: type of encryption operations usedtype of encryption operations used

substitution / transposition / productsubstitution / transposition / product number of keys usednumber of keys used

single-key or private / two-key or publicsingle-key or private / two-key or public way in which plaintext is processedway in which plaintext is processed

block / streamblock / stream


CryptanalysisCryptanalysis

objective to recover key not just objective to recover key not just messagemessage

general approaches:general approaches: cryptanalytic attackcryptanalytic attack brute-force attackbrute-force attack


Cryptanalytic AttacksCryptanalytic Attacks ciphertext onlyciphertext only

only know algorithm & ciphertext, is only know algorithm & ciphertext, is statistical, know or can identify plaintext statistical, know or 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 select plaintext or ciphertext to

en/decrypten/decrypt


Brute Force SearchBrute Force Search always possible to simply try every key always possible to simply try every key most basic attack, proportional to key size most basic attack, proportional to key size 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 106 decryptions/µs

32 232 = 4.3 109 231 µs = 35.8 minutes 2.15 milliseconds

56 256 = 7.2 1016 255 µs = 1142 years 10.01 hours

128 2128 = 3.4 1038 2127 µs = 5.4 1024 years 5.4 1018 years

168 2168 = 3.7 1050 2167 µs = 5.9 1036 years 5.9 1030 years

26 characters (permutation)

26! = 4 1026 2 1026 µs = 6.4 1012 years 6.4 106 years


Classical Substitution Classical Substitution CiphersCiphers

where where letters of plaintext are letters of plaintext are replaced by other letters or by replaced by other letters or by numbers or symbolsnumbers or symbols

or if plaintext is or if plaintext is viewed as a viewed as a sequence of bits, then substitution sequence of bits, then substitution involves replacing plaintext bit involves replacing plaintext bit patterns with ciphertext bit patternspatterns with ciphertext bit patterns


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 partyPHHW PH DIWHU WKH WRJD SDUWBPHHW PH DIWHU WKH WRJD SDUWB


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 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

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 CD 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

mathematically give each letter a mathematically give each letter a numbernumbera 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 cipher as:then have Caesar cipher as:c c = E(= E(pp) = () = (p p + + kk) mod (26)) mod (26)

p p = D(c) = (c – = D(c) = (c – kk) mod (26)) mod (26)


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 given ciphertext, just try all shifts of

lettersletters do need to recognize when have do need to recognize when have

plaintextplaintext eg. break ciphertext "GCUA VQ DTGCM"eg. break ciphertext "GCUA VQ DTGCM"


Monoalphabetic CipherMonoalphabetic Cipher rather than just shifting the alphabet rather than just shifting the alphabet could shuffle (jumble) the letters arbitrarily could shuffle (jumble) the letters arbitrarily each plaintext letter maps to a different each plaintext letter maps to a different

random ciphertext letter random ciphertext letter hence key is 26 letters long hence key is 26 letters long

Plain: abcdefghijklmnopqrstuvwxyzPlain: abcdefghijklmnopqrstuvwxyzCipher: DKVQFIBJWPESCXHTMYAUOLRGZNCipher: DKVQFIBJWPESCXHTMYAUOLRGZN

Plaintext: ifwewishtoreplacelettersPlaintext: ifwewishtoreplacelettersCiphertext: WIRFRWAJUHYFTSDVFSFUUFYA Ciphertext: WIRFRWAJUHYFTSDVFSFUUFYA


Monoalphabetic Cipher Monoalphabetic Cipher SecuritySecurity

now have a total of 26! = 4 x 1026 now have a total of 26! = 4 x 1026 keys keys

with so many keys, might think is with so many keys, might think is secure secure

but would be but would be !!!WRONG!!!!!!WRONG!!! problem is language characteristicsproblem is language characteristics


Language Redundancy and Language Redundancy and CryptanalysisCryptanalysis

human languages are human languages are redundantredundant eg "th lrd s m shphrd shll nt wnt" eg "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 in English E is by far the most common

letter 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 have tables of single, double & triple

letter frequencies for various languagesletter frequencies for various languages


English Letter English Letter FrequenciesFrequencies


Use in CryptanalysisUse in Cryptanalysis key concept - monoalphabetic substitution key concept - monoalphabetic substitution

ciphers do not change relative letter ciphers do not change relative letter frequencies frequencies

discovered by Arabian scientists in 9discovered by Arabian scientists in 9thth 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 if caesar cipher look for common

peaks/troughs peaks/troughs peaks at: A-E-I triple, NO pair, RST triplepeaks at: A-E-I triple, NO pair, RST triple troughs at: JK, X-Ztroughs at: JK, X-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


Example CryptanalysisExample Cryptanalysis given ciphertext:given ciphertext:

UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZUZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZVUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSXVUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSXEPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQEPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ

count relative letter frequencies (see text)count relative letter frequencies (see text) guess P & Z are e and tguess P & Z are e and t guess ZW is th and hence ZWP is theguess 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 butdirect contacts have been made with politicaldirect contacts have been made with politicalrepresentatives of the viet cong in moscowrepresentatives of the viet cong in moscow


Playfair CipherPlayfair Cipher

not even the large number of keys in not even the large number of keys in a monoalphabetic cipher provides a monoalphabetic cipher provides security security

one approach to improving security one approach to improving security was to encrypt multiple letters was to encrypt multiple letters

thethe Playfair Cipher Playfair Cipher is an example is an example invented by Charles Wheatstone in invented by Charles Wheatstone in

1854, but named after his friend 1854, but named after his friend Baron Playfair Baron Playfair


Playfair Key MatrixPlayfair Key Matrix

a 5X5 matrix of letters based on a a 5X5 matrix of letters based on a keyword 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


Encrypting and Encrypting and DecryptingDecrypting

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 each if both letters fall in the same row, replace each

with letter to rightwith letter to right (wrapping back to start from (wrapping back to start from end) 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 (again wrapping to each with the letter below it (again wrapping to top from bottom)top from bottom)

4.4. otherwise each letter is replaced by the letter in otherwise each letter is replaced by the letter in the same row and in the column of the other the same row and in the column of the other letter of the pairletter of the pair


Security of Playfair Security of Playfair CipherCipher

security much improved over security much improved over monoalphabeticmonoalphabetic

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 (verses 26 for a monoalphabetic) analyse (verses 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 be broken, given a few hundred

letters letters since still has much of plaintext structure since still has much of plaintext structure


Polyalphabetic CiphersPolyalphabetic Ciphers

polyalphabetic substitution cipherspolyalphabetic substitution ciphers improve security using multiple cipher improve security using multiple cipher

alphabets alphabets make cryptanalysis harder with more make cryptanalysis harder with more

alphabets to guess and flatter frequency alphabets to guess and flatter frequency distribution distribution

use a key to select which alphabet is used use a key to select which alphabet is used for each letter of the message for each 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


Vigenère CipherVigenère Cipher

simplest polyalphabetic substitution simplest polyalphabetic substitution ciphercipher

effectively multiple caesar ciphers effectively multiple caesar ciphers key is multiple letters long K = kkey is multiple letters long K = k11 k k22 ... k ... kdd iithth letter specifies i letter specifies ithth 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


Example of Example of Vigenère Vigenère CipherCipher

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


AidsAids

simple aids can assist with simple aids can assist with en/decryption en/decryption

a a Saint-Cyr SlideSaint-Cyr Slide is a simple manual is a simple manual aid 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


Security of Security of Vigenère Vigenère CiphersCiphers

have multiple ciphertext letters for have multiple ciphertext letters for each plaintext lettereach plaintext 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 look monoalphabetic or notsee if look monoalphabetic or not if not, then need to determine number if not, then need to determine number

of alphabets, since then can attach of alphabets, since then can attach eacheach


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 an exact period apart so find same plaintext an exact period 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 eg repeated “VTW” in previous exampleeg repeated “VTW” in previous example suggests size of 3 or 9suggests 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


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 but still have frequency characteristics to

attack attack eg. given key eg. given key deceptivedeceptive

key: deceptivewearediscoveredsavkey: deceptivewearediscoveredsav

plaintext: wearediscoveredsaveyourselfplaintext: wearediscoveredsaveyourself

ciphertext:ZICVTWQNGKZEIIGASXSTSLVVWLAciphertext:ZICVTWQNGKZEIIGASXSTSLVVWLA


One-Time PadOne-Time Pad

if a truly random key as long as the if a truly random key as long as the message is used, the cipher will be secure message is used, the cipher will be secure

called a One-Time padcalled a One-Time pad 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 exists a key mapping one to otherthere exists a key mapping one to other can only use the key can only use the key onceonce though though problems in generation & safe distribution problems in generation & safe distribution

of keyof key


Transposition CiphersTransposition Ciphers

now consider classical now consider classical transpositiontransposition or or permutationpermutation ciphers ciphers

these hide the message by these hide the message by rearranging the letter order rearranging the letter order

without altering the actual letters without altering the actual letters usedused

can recognise these since have the can recognise these since have the same frequency distribution as the same frequency distribution as the original text original text


Rail Fence cipherRail Fence cipher write message letters out diagonally over write message letters out diagonally over

a number of rows a 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 ciphertextMEMATRHTGPRYETEFETEOAATMEMATRHTGPRYETEFETEOAAT


Row Transposition Row Transposition CiphersCiphers

a more complex transpositiona more complex transposition write letters of message out in rows write letters of message out in rows

over a specified number of columnsover a specified number of columns then reorder the columns according then reorder the columns according

to some key before reading off the to some key before reading off the rowsrowsKey: 3 4 2 1 5 6 7Key: 3 4 2 1 5 6 7Plaintext: 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 zCiphertext: TTNAAPTMTSUOAODWCOIXKNLYPETZCiphertext: TTNAAPTMTSUOAODWCOIXKNLYPETZ


Product CiphersProduct Ciphers ciphers using substitutions or transpositions ciphers using substitutions or transpositions

are not secure because of language are not secure because of language characteristicscharacteristics

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 two substitutions make a more complex

substitution substitution two transpositions make more complex two transpositions make more complex

transposition transposition but a substitution followed by a transposition but a substitution followed by a transposition

makes a new much harder cipher makes a new much harder cipher this is bridge from classical to modern ciphersthis is bridge from classical to modern ciphers


Rotor MachinesRotor Machines before modern ciphers, rotor machines before modern ciphers, rotor machines

were most common complex ciphers in usewere most common complex ciphers in use widely used in WW2widely used in WW2

German Enigma, Allied Hagelin, Japanese German Enigma, Allied Hagelin, Japanese PurplePurple

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 substitution, which rotated and changed after each letter was encryptedafter each letter was encrypted

with 3 cylinders have 26with 3 cylinders have 2633=17576 alphabets=17576 alphabets


Hagelin Rotor MachineHagelin Rotor Machine


SteganographySteganography

an alternative to encryptionan alternative to encryption hides existence of messagehides existence of message

using only a subset of letters/words in a using only a subset of letters/words in a longer message marked in some waylonger message marked in some way

using invisible inkusing invisible ink hiding in LSB in graphic image or sound hiding in LSB in graphic image or sound

filefile has drawbackshas drawbacks

high overhead to hide relatively few info high overhead to hide relatively few info bitsbits


SummarySummary

have considered:have considered: classical cipher techniques and classical cipher techniques and

terminologyterminology 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 stenographystenography

Ch02...1

Technology

Transcript of Ch02...1