Cryptography and Cryptography and Network SecurityNetwork Security

Chapter 2Chapter 2Fourth EditionFourth Edition

by William Stallingsby William Stallings

Chapter 2 – Chapter 2 – Classical EncryptionClassical EncryptionTechniquesTechniques

CRYPTOLOGY

Definition:Cryptology : from the Greek

Crypto meaning secret or hidden, and

ology meaning theory, or science

Two major divisions: Cryptography & Cryptanalysis

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 usedand by far most widely used

Some Basic TerminologySome Basic Terminology plaintextplaintext - original message - original message ciphertextciphertext or cryptogramor cryptogram - coded message ( - coded message (The

transformed message). ciphercipher - algorithm for transforming plaintext to ciphertext - algorithm for transforming plaintext to ciphertext keykey or cryptovariableor cryptovariable – The information – The information used in used in

conjunction with the algorithm to create ciphertext from conjunction with the algorithm to create ciphertext from plaintextplaintext

encipher (encrypt)encipher (encrypt) - converting plaintext to ciphertext - converting plaintext to ciphertext decipher (decrypt)decipher (decrypt) - recovering ciphertext from plaintext - recovering ciphertext from plaintext 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

Symmetric Cipher ModelSymmetric Cipher Model

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

(conventional) symmetric encryption:(conventional) 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:C C = E= EKK(P)(P)P P = D= DKK(C)(C)

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 by:characterize cryptographic system by:1- The type of operations used for transforming plaintext to ciphertext:- there 1- The type of operations used for transforming plaintext to ciphertext:- there

are two general principles ..are two general principles .. - Substitution, in which each element in the plaintext is mapped into - Substitution, in which each element in the plaintext is mapped into

another element.another element. - Transposition, in which elements in the plaintext are rearranged.- Transposition, in which elements in the plaintext are rearranged. - Product: - Product: involve multiple stages of substitutions and transpositionsinvolve multiple stages of substitutions and transpositions 2- The number of keys used:-2- The number of keys used:- - Secret -key (symmetric-key or single-key), where both sender and receiver - Secret -key (symmetric-key or single-key), where both sender and receiver

use the same key.use the same key. - Public-key (asymmetric or two-key), where both sender and receiver each - Public-key (asymmetric or two-key), where both sender and receiver each

uses different key.uses different key.3- The way in which the plaintext is processed:-3- The way in which the plaintext is processed:- - Block Cipher.- Block Cipher. - Stream Cipher- Stream Cipher

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

Cryptanalytic AttacksCryptanalytic Attacks ciphertext onlyciphertext only

only know algorithm & ciphertext, is statistical, only know algorithm & ciphertext, is statistical, know or can identify plaintext 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 en/decryptselect plaintext or ciphertext to en/decrypt

More DefinitionsMore Definitions unconditional securityunconditional securityif the ciphertext generated by the scheme does not contain enough if the ciphertext generated by the scheme does not contain enough

information to determine uniquely the corresponding plaintextinformation to determine uniquely the corresponding plaintext no matter how much computer power or time is no matter how much computer power or time is

available, the cipher cannot be broken since the available, the cipher cannot be broken since the ciphertext provides insufficient information to uniquely ciphertext provides insufficient information to uniquely determine the corresponding plaintext determine the corresponding plaintext

computational securitycomputational security given limited computing resources (eg time needed given limited computing resources (eg time needed

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

BruteBrute Force SearchForce 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 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

Types of CiphersTypes of Ciphers A A Simple Substitution Simple Substitution cipher, or cipher, or MonoalphabeticMonoalphabetic cipher, is one in which each cipher, is one in which each

character in the plain text is replaced with a corresponding character of cipher-text.character in the plain text is replaced with a corresponding character of cipher-text.

A A HomophonicHomophonic substitutionsubstitution cipher is like a simple substitution crypto-system, cipher is like a simple substitution crypto-system, except that a single character of plaintext can map to one of several characters of except that a single character of plaintext can map to one of several characters of ciphertext. For Example, A could correspond to 5, 14 and 147.ciphertext. For Example, A could correspond to 5, 14 and 147.

A A Polygram substitutionPolygram substitution cipher is one which blocks of characters are encrypted in cipher is one which blocks of characters are encrypted in groups. For Example, ABA could correspond to RTQ.groups. For Example, ABA could correspond to RTQ.

The Playfair cipher is an example of this type of cipher and was used by the British in World The Playfair cipher is an example of this type of cipher and was used by the British in World War One. War One.

A A Polyalphabetic substitutionPolyalphabetic substitution cipher is made up of multiple Monoalphabetic cipher is made up of multiple Monoalphabetic ciphers. The particular cipher used changes with the position of each character in the ciphers. The particular cipher used changes with the position of each character in the plain text. For Example Vigenere cipher.plain text. For Example Vigenere cipher.

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 onexample: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 zD 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 numbermathematically give each letter a numbera 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 z0 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 a could simply try each in turn a brute force brute force searchsearch

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"

Brute-force cryptanalysis is easily Brute-force cryptanalysis is easily performed withperformed with Caesar Cipher :Caesar Cipher :

The encryption and decryption algorithms The encryption and decryption algorithms are knownare known

There are only 25 keys to try (25 different There are only 25 keys to try (25 different k values)k values)

The language of plaintext is known and The language of plaintext is known and easily recognizableeasily recognizable

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 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: abcdefghijklmnopqrstuvwxyzCipher: DKVQFIBJWPESCXHTMYAUOLRGZNCipher: DKVQFIBJWPESCXHTMYAUOLRGZN

Plaintext: ifwewishtoreplacelettersPlaintext: ifwewishtoreplacelettersCiphertext: WIRFRWAJUHYFTSDVFSFUUFYA Ciphertext: WIRFRWAJUHYFTSDVFSFUUFYA

Monoalphabetic Cipher Monoalphabetic Cipher SecuritySecurity

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

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 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

English Letter FrequenciesEnglish Letter Frequencies

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 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 peaks/troughs if caesar cipher look for common 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 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

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

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 righteach with letter to right (wrapping back to start (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 (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 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

Playfair Example

Use the following table:C H A R LE S B D FG I/J K M NO P Q T UV W X Y Z

Encrypting the message:THE SCHEME REALLY WORKS

Playfair Example Break the plaintext in a two character Break the plaintext in a two character

diagram:diagram: Plaintext is divided into 2-letter diagramPlaintext is divided into 2-letter diagram Use X to separate double letterUse X to separate double letter Use X to pad the last single letterUse X to pad the last single letter

TH ES CH EM ER EA LTH ES CH EM ER EA LXX LY WO RK S LY WO RK SXX

Cont. Playfair Example

C H A R LE S B D FG I/J K M NO P Q T UV W X Y Z

TH -> PR ES -> SB CH -> HA EM -> DG ER -> DC EA -> BC LX -> AZ LY -> RZ WO -> VP RK -> AM SX -> BW

Cont. Playfair Example

Thus the message:" THE SCHEME REALLY WORKSTHE SCHEME REALLY WORKS“Becomes"PR SB HA DG DC BC AX RZ VP AM BW “

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 (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 letters be broken, given a few hundred letters since still has much of plaintext structure since still has much of plaintext structure

Hill CipherHill Cipher The Hill Cipher uses matrix The Hill Cipher uses matrix

multiplication to encrypt a message. multiplication to encrypt a message. First, you need to assign two numbers First, you need to assign two numbers to each letter in the alphabet and also to each letter in the alphabet and also assign numbers to space, . , and ? or !. assign numbers to space, . , and ? or !. The key space is the set of all invertible The key space is the set of all invertible matrices over Zmatrices over Z2626. 26 was chosen . 26 was chosen because there are 26 characters, which because there are 26 characters, which solves some problems later on. solves some problems later on.

Hill Cipher Hill Cipher exampleexample

Encryption:Use the table and 00 for spaces:

A B C D E F G H I J K L M N O P Q R S 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19T U V W X Y Z20 21 22 23 24 25 26

Consider the following message:

Herbert Yardley wrote The American Black Chamber

Hill Cipher Hill Cipher exampleexample

Break the message into: he rb er ty ar dl ey wr ot et he am er ic an bl ac kc

ha mb er

Now convert letters into number-pair:8 5 18 2 5 18 20 25 1 18 4 12 5 25 23 18 15 20

5 20 8 5 1 13 5 18 9 3 1 14 2 12 1 3 11 3 8 1 13 2 5 18

Now using the matrix (key)

12050703

K

Hill Cipher Hill Cipher exampleexample

3 7 8 595 12 5 100

Make the first pair a column vector (h (8) e (5)), and multiply that matrix by the key.

Of course, we need our result to be mod 26 59 7

mod26100 22

The ciphertext is G (7) V (22).

Hill Cipher Hill Cipher exampleexample

For the next pair r (18) b (2), 3 7 18 16

mod 265 12 2 10

and 16 corresponds to P and 10 corresponds to J.

Do this for every pair and obtainGVPJKGAJYMRHHMMSCCYEGVPEKGVCWQLXXOBMEZAKKG

Hill Cipher Hill Cipher Decryption:Decryption:

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 make cryptanalysis harder with more alphabets

to guess and flatter frequency distribution to guess and flatter frequency distribution use a key to select which alphabet is used for use a key to select which alphabet is used for

each letter of the message 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 ciphersimplest polyalphabetic substitution cipher 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 messagerepeat from start after d letters in message decryption simply works in reverse decryption simply works in reverse

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

Plaintext THISPROCESSCANALSOBEEXPRESSEDKeyword CIPHERCIPHERCIPHERCIPHERCIPHECiphertext VPXZTIQKTZWTCVPSWFDMTETIGAHLH

based on a Vigenère Table shown next

Vigenère CipherVigenère Cipher ABCDEFGHIJKLMNOPQRSTUVWXYZA ABCDEFGHIJKLMNOPQRSTUVWXYZB BCDEFGHIJKLMNOPQRSTUVWXYZAC CDEFGHIJKLMNOPQRSTUVWXYZABD DEFGHIJKLMNOPQRSTUVWXYZABCE EFGHIJKLMNOPQRSTUVWXYZABCDF FGHIJKLMNOPQRSTUVWXYZABCDEG GHIJKLMNOPQRSTUVWXYZABCDEFH HIJKLMNOPQRSTUVWXYZABCDEFGI IJKLMNOPQRSTUVWXYZABCDEFGHJ JKLMNOPQRSTUVWXYZABCDEFGHIK KLMNOPQRSTUVWXYZABCDEFGHIJL LMNOPQRSTUVWXYZABCDEFGHIJKM MNOPQRSTUVWXYZABCDEFGHIJKLN NOPQRSTUVWXYZABCDEFGHIJKLMO OPQRSTUVWXYZABCDEFGHIJKLMNP PQRSTUVWXYZABCDEFGHIJKLMNOQ QRSTUVWXYZABCDEFGHIJKLMNOPR RSTUVWXYZABCDEFGHIJKLMNOPQS STUVWXYZABCDEFGHIJKLMNOPQRT TUVWXYZABCDEFGHIJKLMNOPQRSU UVWXYZABCDEFGHIJKLMNOPQRSTV VWXYZABCDEFGHIJKLMNOPQRSTUW WXYZABCDEFGHIJKLMNOPQRSTUVX XYZABCDEFGHIJKLMNOPQRSTUVWY YZABCDEFGHIJKLMNOPQRSTUVWXZ ZABCDEFGHIJKLMNOPQRSTUVWXY

Vigenère CipherVigenère Cipher By using math. Equation:By using math. Equation:

C= E(p) = (p+kC= E(p) = (p+kii) mod (26)) mod (26)

Plaintext THISPROCESSCANALSOBEEXPRESSEDKeyword CIPHERCIPHERCIPHERCIPHERCIPHECiphertext VPXZTIQKTZWTCVPSWFDMTETIGAHLH

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 look monoalphabetic or notsee if look monoalphabetic or not if not, then need to determine number of if not, then need to determine number of

alphabets, since then can attach eachalphabets, since then can attach each

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 letters knowing keyword can recover the first few 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: deceptivewearediscoveredsavplaintext: wearediscoveredsaveyourselfplaintext: wearediscoveredsaveyourselfciphertext:ZICVTWQNGKZEIIGASXSTSLVVWLAciphertext:ZICVTWQNGKZEIIGASXSTSLVVWLA

Another Classical Substitution CiphersAnother Classical Substitution Ciphers Keyword mixedKeyword mixed

Example:Example:

keyword= AHMAD keyword= AHMAD becomesbecomes AHMD AHMD K= 3K= 3A 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

X Y Z A H M D B C E F G I J K L N O P Q R S T U V W X Y Z A H M D B C E F G I J K L N O P Q R S T U V W

M= BE OR NOT TO BEM= BE OR NOT TO BEC=C= YH KO J KQ QKYHYH KO J KQ QKYH

Another Classical Substitution CiphersAnother Classical Substitution Ciphers

Transposed keyword mixedTransposed keyword mixed

Example:Example:

1- keyword= AHMAD 1- keyword= AHMAD becomes becomes AHMD AHMD2- A H M D 2- A H M D B C E FB C E F G I J KG I J K L N O PL N O P Q R S TQ R S T U V W XU V W X Y Z Y Z

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 Z3- 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 G L Q U Y H C I N R V Z M E J O S W D F K P T XA B G L Q U Y H C I N R V Z M E J O S W D F K P T X4- M= BE OR NOT TO BE4- M= BE OR NOT TO BE C= BQ JO ZMW WM BQ C= BQ JO ZMW WM BQ

One-Time PadOne-Time Pad This technique was introduced by army signal This technique was introduced by army signal

officer Joseph Mauborgne. Which is also called officer Joseph Mauborgne. Which is also called Vernam. Vernam.

He suggested using a random key that is as long He suggested using a random key that is as long as the message. as the message.

A message encrypted using a one-time pad A message encrypted using a one-time pad cannot be broken because the encryption key is cannot be broken because the encryption key is a random number and because the key is used a random number and because the key is used only once only once

problems in generation & safe distribution of keyproblems in generation & safe distribution of key

One-Time Pad (OTP)One-Time Pad (OTP) Step 1:  Create the key...Step 1:  Create the key... You need to create a random key. You need to create a random key.

HLMSEZRBHPSJOTDWHLMSEZRBHPSJOTDW You need a method for converting alphabet You need a method for converting alphabet

characters into numbers.characters into numbers.

A B C D E F G H I J K L M N O P Q R S A B C D E F G H I J K L M N O P Q R S 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 191 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19T U V W X Y ZT U V W X Y Z20 21 22 23 24 25 2620 21 22 23 24 25 26

One-Time Pad (OTP)One-Time Pad (OTP) Step 1:  Step 1:   HLMSEZRBHPSJOTDWHLMSEZRBHPSJOTDW·    To make the key easier to work with, break it into blocks of two ·    To make the key easier to work with, break it into blocks of two

characters each, thuscharacters each, thus HL MS EZ RB HP SJ OT DWHL MS EZ RB HP SJ OT DW

Now use the conversion table shown above to convert the Now use the conversion table shown above to convert the alphabet characters into numbers. For example H=08 and L=12, alphabet characters into numbers. For example H=08 and L=12, so the first block HL becomes 0812.so the first block HL becomes 0812.     The result is      The result is 0812 1319 0526 1802 0816 1910 1520 04230812 1319 0526 1802 0816 1910 1520 0423. . (The key)(The key)

One-Time Pad (OTP)One-Time Pad (OTP) Step 2:  Format your message... Step 2:  Format your message...

·   Message ·   Message MY SECRET. MY SECRET. 1325 1905 1325 1905 0318 05200318 0520

Key Key HL MS EZ RB HP SJ OT DW HL MS EZ RB HP SJ OT DW 0812 0812 1319 0526 1802 0816 1910 1520 0423 1319 0526 1802 0816 1910 1520 0423

One-Time Pad (OTP)One-Time Pad (OTP) Guidelines... Guidelines... Rule 1 – Numbers.Rule 1 – Numbers.  Spell out all numbers in full in your  Spell out all numbers in full in your

plaintext. For example, 365 becomes THREE SIX FIVE.plaintext. For example, 365 becomes THREE SIX FIVE.          Rule 2 – Negatives.Rule 2 – Negatives.  Always add emphasis to the word NOT  Always add emphasis to the word NOT in your plaintext. For example, you would write AGENT ALPHA in your plaintext. For example, you would write AGENT ALPHA NOT RPT NOT AVAILABLE FOR MEETING TUESDAY, where NOT RPT NOT AVAILABLE FOR MEETING TUESDAY, where RPT stands for REPEAT.RPT stands for REPEAT.          Rule 3 – Punctuation.Rule 3 – Punctuation.  Use an X for each period in your  Use an X for each period in your plaintext. For example, MESSAGE RECEIVEDX SEND MORE plaintext. For example, MESSAGE RECEIVEDX SEND MORE INFOX. All other punctuation must be written out in full. For INFOX. All other punctuation must be written out in full. For example, COMMA.example, COMMA.          Rule 4 – Termination.Rule 4 – Termination.  End your plaintext with XX. If  End your plaintext with XX. If necessary, add dummy characters after XX in order to necessary, add dummy characters after XX in order to pad outpad out the message to frustrate cryptanalysis and to conclude on a the message to frustrate cryptanalysis and to conclude on a doublet (ensuring the numeric string ends with four digits).doublet (ensuring the numeric string ends with four digits).

One-Time Pad (OTP)One-Time Pad (OTP) Step 3:  Encrypt your message... Step 3:  Encrypt your message...

·   We need some way to indicate to our recipient where the key ·   We need some way to indicate to our recipient where the key begins, otherwise he/she won't be able to decrypt. Remember in begins, otherwise he/she won't be able to decrypt. Remember in our earlier example, we created a key and stroked off (in gray) our earlier example, we created a key and stroked off (in gray) the blocks we'd already used. Here's what our key looked like.the blocks we'd already used. Here's what our key looked like.

0812 1319 0526 1802 0816 1910 1520 04230812 1319 0526 1802 0816 1910 1520 0423

The starting position in the key is at block 1319. So we'll place The starting position in the key is at block 1319. So we'll place the string 1319 at the beginning of our message so the recipient the string 1319 at the beginning of our message so the recipient will know how to decrypt. The plaintext message of 1325 1905 will know how to decrypt. The plaintext message of 1325 1905 0318 0520 becomes 1319 1325 1905 0318 0520 because we 0318 0520 becomes 1319 1325 1905 0318 0520 because we place the pointer 1319 at the beginning of the string. place the pointer 1319 at the beginning of the string.

One-Time Pad (OTP)One-Time Pad (OTP) Step 3:  Encrypt your message... Step 3:  Encrypt your message...

·   First we write out the plaintext. Then directly below it we write ·   First we write out the plaintext. Then directly below it we write out the key. Then we add the key to the plaintext using out the key. Then we add the key to the plaintext using Fibonicci additionFibonicci addition. This means we do no carrying. For . This means we do no carrying. For example, 9 + 2 would yield 1 not 11. And 7 plus 6 would yield 3 example, 9 + 2 would yield 1 not 11. And 7 plus 6 would yield 3 not 13. Here's how the spy's working sheet would look.not 13. Here's how the spy's working sheet would look.

Plaintext 1319 1325 1905 0318 0520Plaintext 1319 1325 1905 0318 0520Key ----- 0526 1802 0816 1910Key ----- 0526 1802 0816 1910Ciphertext 1319 1841 2707 0124 1430Ciphertext 1319 1841 2707 0124 1430

          Encrypted message Encrypted message 1319 1841 2707 0124 1430 1319 1841 2707 0124 1430

One-Time Pad (OTP)One-Time Pad (OTP) Step 3:  Decrypting the message... Step 3:  Decrypting the message...

We subtract the key from the ciphertext using We subtract the key from the ciphertext using Fibonicci subtraction .Fibonicci subtraction .

We allow no negative numbers. We allow no negative numbers. For example, 2 - 9 would yield 3 (because we add For example, 2 - 9 would yield 3 (because we add

10 so that we're able to subtract 9 from 12). 10 so that we're able to subtract 9 from 12).

·  Ciphertext 1319 1841 2707 0124 1430·  Ciphertext 1319 1841 2707 0124 1430Key 1319 0526 1802 0816 1910Key 1319 0526 1802 0816 1910Plaintext ---- 1325 1905 0318 0520Plaintext ---- 1325 1905 0318 0520

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

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 ciphertextMEMATRHTGPRYETEFETEOAATMEMATRHTGPRYETEFETEOAAT

Columnar Transposition CiphersColumnar Transposition Ciphers

a more complex transpositiona more complex transpositioncolumnar transposition: columnar transposition: is rearrangement of characters of plain text is rearrangement of characters of plain text

into coulmns. into coulmns.

Write plaintext in a rectangle row by row.Write plaintext in a rectangle row by row. Permute the order of the columnsPermute the order of the columns Read the message off, column by columnRead the message off, column by column Key: 4 3 1 2 5 6 7Key: 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 zCiphertext: TTNAAPTMTSUOAODWCOIXKNLYPETZCiphertext: TTNAAPTMTSUOAODWCOIXKNLYPETZ

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

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 WW2(World War II)widely used in WW2(World War II)

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 2633=17576 alphabets=17576 alphabets

Hagelin Rotor MachineHagelin Rotor Machine

Confusion and DiffusionConfusion and Diffusion A substitution is said to add confusion to the A substitution is said to add confusion to the

encryption process whereas a transposition is encryption process whereas a transposition is said to add diffusion. said to add diffusion.

Confusion is intended to make the relationship Confusion is intended to make the relationship between the key and ciphertext as complex as between the key and ciphertext as complex as possible. Diffusion refers to rearranging or possible. Diffusion refers to rearranging or spreading out the characters in the message spreading out the characters in the message

Most modern block cipher systems apply a Most modern block cipher systems apply a number of rounds in succession to encrypt number of rounds in succession to encrypt plaintext. plaintext.

A round then can be said to add both confusion A round then can be said to add both confusion and diffusion to the encryptionand diffusion to the encryption

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 filehiding in LSB in graphic image or sound file

has drawbackshas drawbacks high overhead to hide relatively few info bitshigh overhead to hide relatively few info bits

Popular sites for Popular sites for Steganography information

http://www.ise.gmu.edu/~njohnson/Steganography

http://www.rhetoric.umn.edu/Rhetoric/misc/dfrank/stegsoft.html

http://www.topology.org/crypto.html

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 stenographystenography