Cryptography /Computer Security - 123seminarsonly.com · Cryptography /Computer Security Classical Cryptography . ... • Computer Security - generic name for the collection of tools

Cryptography /Computer Security

Classical Cryptography

Background

• Information Security requirements have changed in recent times

• traditionally provided by physical and administrative mechanisms

• computer use requires automated tools to protect files and other stored information

• use of networks and communications links requires measures to protect data during transmission

2 Cryptography -Lect-01

Definitions • Computer Security - generic name for the collection of tools

designed to protect data and to thwart hackers.

• Network Security - measures to protect data during their transmission

• Internet Security - measures to protect data during their transmission over a collection of interconnected networks.


Security

• Definition (Cambridge Dictionary of English) – Ability to avoid being harmed by any risk, danger

or threat

• …therefore, in practice, an impossible goal .

• What can we do then? – Be as secure as needed

– Ability to avoid being harmed too much by reasonably predictable risks, dangers or threats .


Security Goals Security Goal :

Confidentiality: Confidentiality is the term used to prevent the discloser the information to unauthorized access.

Integrity : Integrity means that changes need to be done only by an unauthorized entity.

Availability : Available the information resources.

Overall distribution of cyber security incidents and events for fiscal year 2009 first quarter (FY09 Q1)


Source : www.us-cert.gov

Which country has the most infected computers (October 2009)

Cryptography -Lect-01 7

Source http://www.net-security.org/

Aspect of Information Security

Every business has confidential information. Business would demand confidence, privacy, reliability and protection at all time. There are three aspect which are related to the information security:

1. Security threat & attack

2. Security Services.

3. Security mechanism

Security threats &Attacks Any action which leads to compromise the security of information is called security attack. Such attacks must be planned efforts.

Data / Information thread

Interruption

Modification

Fabrication Waste

Data tapping

Computer Virus

Unauthorized access

Fraud

Disclosure

Theft

Damage due to breakage

Abuse

Malicious leakage

Environmental Attack

Classification of threat There are four type of threats :

> Physical threat

> Accidental Error

> Unauthorized access

> Malicious Misuse

Cont….

Security Attack may be classified as:

1. Active Security attacks.

2. Passive security attacks.

Active Attack : An active attack may change the data or harm the system. Attack that threaten the integrity and availability are active attack.

Active Threats

Replay attack Modification DoS

Network Security

Masquerade

Cont…. Passive Attack: The attacker’s goal is just obtain the information. This attack threaten the confidentiality of data or information.

1. Release of message contents

2. Traffic analysis

- Location and Identity of host

- Frequency of messages

-length of messages generally transmitted

- Guessing of nature of information exchanged between the hosts.

Passive threats

Interception of Information

Release of Message contents

Data/Information Security

Traffic Analysis

Passive Vs Active attack

Passive attacks are more dangerous because they are not known. The only remedy to struggle this attacks is prevention rather then detection.

Opposite to the passive attack, active attacks require physical protection, detection, recovery from their effects such as interruption, loss, modification or delay etc.

Security Services International Telecommunication Union-Telecommunication Standardization Sector (ITU-T) divides the security services in to five categories :

1. Data confidentiality

- Connection confidentiality

- Connectionless Confidentiality

- Selective field confidentiality

- Traffic flow confidentiality.

2. Data Integrity

3. Authentication

- Entity Authentication (Used in association with a logical connection to provide confidence in the identity of the entities connected)

- Data origin Authentication(In e connection less transfer that the source of received data is as claimed)

4. Non-repudiation

5. Access Control

Security Mechanism The security mechanism is designed to implement the security services. ITU-T defines the security mechanism in to two part:

1. Specific Security Mechanism

- Encipherment

- Digital Signature

- Access Control

- Data Integrity

- Authentication Exchange

- Traffic Padding

- Routing Control

- Notarization

2. invasive Security Mechanism

- Trusted Functionality

- Security Level

- Event Detection

- Security Audit trial

Relationship between the security services and mechanism

Service Enciphe-rment

Digital Signature

Access Control

Data Integrity

Auth. Exchange

Traffic Padding

Routing Control

Notarizati-on

Peer Entity Auth.

Y Y Y

Data Origin Auth.

Y Y

Access Control

Y

Confidentiality

Y Y

Traffic Flow con

Y Y Y

Data Integrity

Y Y Y

Non-repudia-tion

Y Y Y

Availability

Y Y

Cryptography

• Cryptography is the study of secret (crypto-)

writing (-graphy)

• Concerned with developing algorithms which may be used to:

– cover up the context of some message from all except the sender and recipient (privacy or secrecy), and/or

– Verify the correctness of a message to the recipient (authentication or integrity)

• It is referred to the science and art of transforming messages to make them secure and resistant to attack.

It basically divided in to two types:

> Symmetric Key Encipherment

> Asymmetric Key Encipherment


Purpose of Cryptography

• Secure stored information

• Secure transmitted information


Services Provided by Cryptography

• Confidentiality – provides privacy for messages and stored data by hiding

• Message Integrity – provides assurance to all parties that a message remains unchanged

• Non-repudiation – Can prove a document came from X even if X’ denies it

• Authentication – identifies the origin of a message

– verifies the identity of person using a computer system


Basic Terminology • Cryptography

– The art or science encompassing the principles and methods of transforming message an intelligible into one that is unintelligible, and then retransforming that message back to its original form

• Plaintext

– The original intelligible message

• Ciphertext – The transformed message

• Cipher

– An algorithm for transforming an intelligible message into one that is meaningless by transposition and/or substitution methods

• Key – Some critical information used by the cipher, known only to the sender &

receiver


• Encipher (encode) – Process of converting plaintext to ciphertext using a cipher and a key

• Decipher (decode) – The process of converting ciphertext back into plaintext using a cipher

and a key

• Cryptanalysis (codebreaking) – The study of principles and methods of transforming an unintelligible

message back into an intelligible message without knowledge of the key.

• Cryptology – The field encompassing both cryptography and cryptanalysis

Basic Terminology – contd..


• Encryption – The mathematical function mapping plaintext to ciphertext using the

specified key: Y = EK(X) or E(K, X)

• Decryption – The mathematical function mapping ciphertext to plaintext using the

specified key: X = DK(Y) or D(K, X) = EK

-1(Y)

Basic Terminology – contd.


• Cryptographic system (Cryptosystem)

A cryptosystem is a five-tuple (P, C, K, E, D), where following

conditions are satisfied :

1. P is a finite set of possible plaintexts

2. C is a finite set of possible ciphertexts

3. K, the keyspace, is a finite set of possible keys

4. For each K K, there is an encryption algorithm EK E

and a corresponding decryption algorithm DK D.

Basic Terminology –contd.


Simplified Conventional Encryption Model

• Requirements 1. Strong encryption algorithm 2. Share of the secret key in a secure fashion

• Conventional – Secret-Key ( Public-Key) – Single-Key ( Two-Key) – Symmetric ( Asymmetric)

Kerchhoff’s Principle

“Encryption algorithms being used should be assumed to be publicly known and the security of the algorithm should reside only in the key chosen”


Conventional Cryptosystem Model


Cryptanalysis Cryptanalysis (from the Greek kryptós, "hidden", and analýein, "to loosen" or "to untie") is the study

of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required to do so. Cryptanalysis refers to the study of ciphers, ciphertext, or cryptosystems (that is, to secret code systems) with a view to finding weaknesses in them that will permit retrieval of the plaintext from the ciphertext, without necessarily knowing the key or the algorithm. This is known as breaking the cipher or cryptosystem.

http://en.wikipedia.org/wiki/Greek_language

Exhaustive Key Search

• Brute-force attack

• Always theoretically possible to simply try every key

• Most basic attack, directly proportional to key size

• Assume either know or can recognize when plaintext is found

– Average Time Required for Exhaustive Key Search

Classical Encryption Techniques • Substitution Techniques

– Monoalphabetic Substitution

– Polyalphabetic Substitution

– Homophonic Substitution

– Polygraphic Substitution

• Transposition (Permutation) Techniques – Keyless Transposition Cipher

– Keyed Transposition Cipher

• Product Techniques – Substitution and transposition ciphers are concatenated


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Substitution cipher—formal definition

• A substitution technique is one in which the letters of plaintext are replaced by other letters or by the number or symbols. If the plaintext is viewed as a sequence of bit, then substitution

involves replacing bit pattern with cipher bit pattern.

• Let P and C Z26 , K, consists of all possible permutations of the 26 symbols 0,1, …, 25 ( or a,b,…,z). For each permutation K, , define

e(x) = (x)

and d(y) = -1(y)

(-1 is the inverse permutation of )

Cryptography -Lect-01

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Substitution cipher—example • Given following “random” permutation , 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

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

• Thus e(a) = X, e(b) = N, etc. Correspondingly, d(X) = a, d(N) = b, d(A) = d, d(B) = l, etc.

• Given plaintext: cryptography – The ciphertext: YCDLMFOCXLGD


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Substitution cipher -- security

Question: what is the key space?

A key is a permutation of 26 letters, so 26! permutations, i.e., more than 4.0 1026 . Thus exhaustive key search is infeasible.

However, using frequency analysis, substitution cipher is easily broken.

Question: what is the relationship between shift and substitution cipher?

Shift cipher is a special case of substitution cipher which includes only 26 of 26! possible permutations.


Monoalphabetic Substitution Ciphers

In monoalphabetic cipher, a character or symbol in the plaintext always changed to same character or symbol in the cipher text regardless of its position in the text.

Plain: abcdefghijklmnopqrstuvwxyz

Cipher: DEFGHIJKLMNOPQRSTUVWXYZABC

• Key size = 26

• Unique mapping of plaintext alphabet to ciphertext alphabet

• For a long time thought secure, but easily breakable by frequency analysis attack.

There are four types of monoalphabetic Substitution cipher:

- Additive Cipher

- Shift Cipher

- caesar Cipher

- Affien Cipher


Relative Frequency of Letters in English Text


Additive Cipher The simplest monoalphabetic cipher is additive cipher. This cipher some times called a shift cipher or Caesar cipher. In this cipher plain text consist of lower case letters and the cipher text consist of upper case letters. Each character assigned an integer from 0 to 25. The secret key K is also an integer between 0 to 25.

Encryption: C= (P+K) mod 26

Decryption: P= (C-K) mod 26

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Shift cipher—formal definition

• Let P = C = K, = Z26 , for 0 K 25, define

eK(x) = x + K mod 26

and dK(y) = y - K mod 26

(x, y Z26 )


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Shift cipher -- security

Two basic properties for a cryptosystem:

1. Each encryption function eK and each decryption dK should be efficiently computable. 2. An opponent upon seeing a ciphertext string y, should be unable to determine the key K that was used, or the plaintext string x.

Question: is shift cipher secure?

Of course NOT, since there are only 26 possible keys, it is easy to be broken by exhaustive key search or by frequency analysis.

Example: JBCRCLQRWCRVNBJENBWRWN

On average, a plaintext will be computed after trying 26/2=13 times.

Plaintext: astitchintimesavesnine (K=9)


Caesar Cipher • The Caesar cipher involves replacing each letter of the alphabet

with the three places fuether down the alphabet.

• No key, just one mapping (translation)

0123456...

Plain: abcdefghijklmnopqrstuvwxyz

Cipher: DEFGHIJKLMNOPQRSTUVWXYZABC

3456789...

• ci=E(3,pi)=(pi+3) mod 26;

pi=D(3,ci)=(ci-3) mod 26


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Basic Math—number theory

• Integers: Z ={…,-3,-2,-1,0,1,2,3,…}

• Natural number: Zn={0,1,…,n-1}

• Greatest common divisor: d=gcd(a,b) – e.g., gcd(21,26)=1, gcd(6,26)=2.

• If gcd(a,b) =1, then a and b are co-prime, or a is relatively prime to b.


39

Affine cipher--introduction • Also a special case of substitution cipher

• Encryption function: e(x) = y = (ax+b) mod 26

• Decription function : d(y) = x = a-1 (y-b) mod 26

where a, b are keys Z26 and gcd(a, 26) =1. a-1 is the multiplicative inverse of key a and –b is the additative inverse of key b

• Why gcd(a, 26) =1?

when gcd (a, 26) =1, ax = (y – b) mod 26 has a unique solution x, i.e., x = a-1(y - b) mod 26. That is to say:

given ciphertext y, decrypt y to get plaintext x by computing a-1(y - b) mod 26.


40

Basic Math-number theory

• Theorem: the congruence ax b mod m has a unique solution x Zm for each b Zm if and only if gcd(a, m) = 1.

• Theorem: suppose a Zm and gcd(a, m) = 1. Then there exists a unique element Zm , denoted by a-1, such that aa-1 a-1a 1 mod m. a-1 is called the multiplicative inverse of a.


Affine Cipher • ci=E(k,pi)=(k1pi+k2) mod 26;

gcd(k1,26)=1

pi=D(k,ci)=(k1-1(ci-k2)) mod 26

• Key k = (k1,k2)

• Number of keys = (26) x 26 = 12 x 26 = 312

(m):= the number of integers in Zm that are relatively prime to m

k1{1,3,5,7,9,11,15,17,19,21,23,25}

• Caesar/Shift ciphers are special cases of affine ciphers


42

Affine cipher—security

• In Z26 , 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23 and 25 are

relatively prime to 26. – 1-1 = 1, 3-1 = 9, 5-1 = 21, 7-1 = 15, …., 25-1 = 25

• Therefore Affine cipher has 12 26 = 312 possible keys. (Of course this is much too small to be secure)


43

Basic Math-number theory

• Theorem: suppose m = i=1n pi

ei , where the pi’s are distinct primes and ei > 0, then the number of integers in Zm that are relatively prime to m, denoted by (m), is (m)= i=1

n (pi

ei - piei-1

). (m) is called Euler phi-function or Euler totient function .

• 26=213= 21131, – (26)=(21 -20)(131- 130)=112=12

• 100= 2252 , (100)=(22 -21)(52- 51)=2 20=40

• |Zn*|= (n)


44

Affine cipher—example

• Suppose K=(7,3) then – eK(x)= (7x+3) mod 26

– dK(y)= 15y-19 mod 26 (i.e., 7-1(y-3) mod 26)

• Check dK(eK(x))=x

• Given plaintext: hot

• Get ciphertext: AXG


45

Example (S. Singh, The Code Book, 1999)

• Ciphertext • PCQ VMJYPD LBYK LYSO KBXBJXWXV BXV ZCJPO EYPD KBXBJYUXJ

LBJOO KCPK. CP LBO LBCMKXPV XPV IYJKL PYDBL, QBOP KBO BXV OPVOV LBO LXRO CI SX'XJMI, KBO JCKO XPV EYKKOV LBO DJCMPV ZOICJO BYS, KXUYPD: 'DJOXL EYPD, ICJ X LBCMKXPV XPV CPO PYDBLK Y BXNO ZOOP JOACMPLYPD LC UCM LBO IXZROK CI FXKL XDOK XPV LBO RODOPVK CI XPAYOPL EYPDK. SXU Y SXEO KC ZCRV XK LC AJXNO X IXNCMJ CI UCMJ SXGOKLU?'

OFYRCDMO, LXROK IJCS LBO LBCMKXPV XPV CPO PYDBLK

Any Guesses???

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Frequency Analysis

• Identyfying comon letters, digrams and trigrams... • PCQ VMJYPD LBYK LYSO KBXBJXWXV BXV ZCJPO EYPD KBXBJYUXJ LBJOO KCPK. CP

LBO LBCMKXPV XPV IYJKL PYDBL, QBOP KBO BXV OPVOV LBO LXRO CI SX'XJMI, KBO JCKO XPV EYKKOV LBO DJCMPV ZOICJO BYS, KXUYPD: 'DJOXL EYPD, X LBCMKXPV XPV CPO PYDBLK Y BXNO ZOOP JOACMPLYPD LC UCM LBO IXZROK CI FXKL XDOK XPV LBO RODOPVK CI XPAYOPL EYPDK. SXU Y SXEO KC ZCRV XK LC AJXNO X IXNCMJ CI UCMJ SXGOKLU?'

OFYRCDMO, LXROK IJCS LBO LBCMKXPV XPV CPO PYDBLK

• First guess: LBO is THE

47

Frequency Analysis

• Assuming LBO represents THE we replace L with T, B with H, and O with E and get

• PCQ VMJYPD THYK TYSE KHXHJXWXV HXV ZCJPE EYPD KHXHJYUXJ THJEE KCPK. CP THE THCMKXPV XPV IYJKT PYDHT, QHEP KHO HXV EPVEV THE LXRE CI SX'XJMI, KHE JCKE XPV EYKKOV THE DJCMPV ZEICJE HYS, KXUYPD: 'DJEXT EYPD, ICJ X LHCMKXPV XPV CPE PYDHLK Y HXNE ZEEP JEACMPTYPD TC UCM THE

IXZREK CI FXKL XDEK XPV THE REDEPVK CI XPAYEPT EYPDK. SXU Y SXEE KC ZCRV XK TC AJXNE X IXNCMJ CI UCMJ SXGEKTU?'

EFYRCDME, TXREK IJCS THE LHCMKXPV XPV CPE PYDBTK

• More guesses…?

48

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

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

• Plaintext Now during this time Shahrazad had borne King Shahriyar three sons. On the thousand and first night, when she had ended the tale of Ma'aruf, she rose and kissed the ground before him, saying: 'Great King, for a thousand and one nights I have been recounting to you the fables of past ages and the legends of ancient kings. May I make so bold as to crave a favour of your majesty?’ Epilogue, Tales from the Thousand and One Nights

Frequency Statistics of Language • In addition to the frequency info of single letters, the

frequency info of two-letter (digram) or three-letter (trigram) combinations can be used for the cryptanalysis

• Most frequent digrams – TH, HE, IN, ER, AN, RE, ED, ON, ES, ST, EN, AT, TO, NT, HA,

ND, OU, EA, NG, AS, OR, TI, IS, ET, IT, AR, TE, SE, HI, OF

• Most frequent trigrams – THE, ING, AND, HER, ERE, ENT, THA, NTH, WAS, ETH, FOR,

DTH


Polyalphabetic Cipher • In polyalphabetic ciphers, each occurrence of a character may

have different substitute. The relationship between a character in the plaintext to a character in the plaintext to a character in the

ciphretext is one-to-many. • Typically a set of monoalphabetic substitution rules is used

• There are five type of polyalphebetic cipher:

– Auto key cipher

– Playfier cipher

– Hill cipher

– Vigenere cipher

– One time pad (vernam cipher)


Auto key cipher--example • In this cipher, the key is a stream of subkeys, in which each

subkey is used to encrypt the corresponding character in the plaintext. The first subkey is predetermined and secret. The second subkey is the value of first plain text character. The third subkey is the value of second plain text character.

• Encryption function : Ci = (Pi+ki) mod 26

• Decryption function : Pi = (Ci-ki) mod 26

Example : Consider the plaintext is “attack is today” and initial secret key is 12. What will be the ciphetext?

Attack on auto key cipher : The auto key cipher definitely hides the single letter frequency statistic of the plain text. The first subkey can be only one value of 25. So brute-force attack can easily break it.


Playfair Cipher

• Best-known multiple-letter substitution cipher

• Digram cipher (digram to digram, i.e., E(pipi+1) = cici+1 through keyword-based 5x5 transformation table)

•

• Great advance over simple monoalphabetic cipher (26 letters 26x26=676 digrams)

• Still leaves much of the structure of the plaintext language relatively easy to break

Keyword = monarchy Plaintext: H S E A A R M U Ciphertext: B P I M R M C M

M O N A R

C H Y B D

E F G I/J K

L P Q S T

U V W X Z


Encrypting and Decrypting

• plaintext is encrypted two letters at a time 1. if a pair is a repeated letter, insert filler like 'X’ 2. if both letters fall in the same row, replace each

with letter to right 3. if both letters fall in the same column, replace

each with the letter below it 4. otherwise each letter is replaced by the letter in

the same row and in the column of the other letter of the pair


Security of Playfair Cipher

• security much improved over monoalphabetic

• since have 26 x 26 = 676 digrams

• would need a 676 entry frequency table to analyse (verses 26 for a monoalphabetic) .

• was widely used for many years – eg. by US & British military in WW1

• it can be broken, given a few hundred letters

• since still has much of plaintext structure


55

Hill cipher -- introduction

• Another polyalphabetic cipher.

• Invented in 1929 by Lester S. Hill.

• Let m be an positive integer, and let P = C (Z26)

m

• First divide the characters in plaintext into blocks of m characters, take m linear combinations of the m characters, thus producing the m characters in ciphertext.


56

Hill cipher -- example Suppose m=2, a plaintext element is written as x=(x1,x2) and a ciphertext element as y=(y1,y2). Here y1 would be a linear combination of x1 and x2, as would y2.

Suppose we take: y1=(11x1 + 3x2) mod 26 y2=(8x1 + 7x2) mod 26 then y1 and y2 can be computed from x1 and x2

We can write the above computations in matrix notation:

(y1, y2) = (x1, x2) ( ) 11 8 3 7

or y = xK where y=(y1, y2) , x=(x1, x2), and K=( ) 11 8 3 7

Assume all operations are performed by modulo 26.


57

Hill cipher – example Example 1.5, suppose key is:

K=( ) K-1=( ) 11 8 3 7

then 7 18 23 11

Given plaintext: july , the ciphertext is: DELW

On the other hand, from DELW, we can get july.


58

Hill cipher – algebra foundation 1. Determinant of a matrix A, denoted by det A :

-- if A(aij) is 22, then det A =a11a22 – a12a21

-- if A(aij) is 33, then det A =a11a22a33 + a12a23a31 + a13a21a32

- a13a22a31 - a12a21a33 - a11a23a32

2. Theorem: suppose K=( ) k11 k12

k21 k22 with kij Z26

Then K has an inverse if and only if det K is invertible in Z26

if and only if gcd(det K, 26)=1

Moreover,

K-1=(det K)-1( ) k22 -k12

-k21 k11 Where det K = k11k22 – k12k21

compute the inverse matrix of example 1.5.


Hill Cipher

• Multi-letter cipher

• Takes m successive plaintext letters and substitutes for them m ciphertext letters

• 3x3 Hill cipher:

• K =

• C = EK(P) = KP ; P = DK(C) = K-1C = K-1KP = P

• m x m Hill cipher hides (m-1)-letter frequency info

• Strong against for the ciphertext-only attack, but easily broken with known plaintext attack

– with m plaintext-ciphertext pairs, each of length m; K = CP-1

c1 = (k11p1 + k12p2 + k13p3) mod 26 c2 = (k21p1 + k22p2 + k23p3) mod 26 c3 = (k31p1 + k32p2 + k33p3) mod 26

k11 k12 k13

k21 k22 k23

k31 k32 k33


60

Vigenere cipher--introduction

• In substitution ciphers, once a key is chosen, each character in the plaintext is constantly mapped into a unique character in ciphertext, called monoalphabetic cryptosystems.

• If the same character at different locations in plaintext is mapped into different characters in ciphertext, called polyalphabetic cryptosystems.

• Vigenere cipher is a kind of polyalphabetic cipher:

– Each key consists of m characters, called keyword.

– Encrypt m characters at a time, i.e., each plaintext element is equivalent to m characters.


61

Vigenere cipher—formal definition

• Let m be an positive integer. – Define P = C = K,= (Z26)

m.

– For each K= (k1,k2,…,km), define

eK(x1,x2,…,xm) = (x1+ k1, x2+ k2,…, xm+ km)

and

dK(y1,y2,…,ym) = (y1- k1, y2- k2,…, ym- km)

Where all operations are performed in Z26, i.e, mod 26..


62

Vigenere cipher—example

• Suppose m=6 and keyword = CIPHER

• Given plaintext: – thiscryptosystemisnotsecure

• The ciphertext will be – VPXZGIAXIVWPUBTTMJPWIZITWZT

• On the contrary, subtract the keyword from ciphertext to get the plaintext.


Security of Vigenère Ciphers

• have multiple ciphertext letters for each plaintext letter

• hence letter frequencies are masked

• but not totally lost

• start with letter frequencies

– see if look monoalphabetic or not

• if not, then need to determine number of alphabets, since then can attach each


64

Vigenere cipher—security Question: what is the key space? Suppose the keyword length is m.

There are total 26m possible keys.

Suppose m=5, then 265 = 1.1 107 , which is large enough to preclude exhaustive key search by hand.

We see that one character could be mapped into m different characters when the character is in m different positions.

However, we will see that there will be a systemic method to break Vigenere cipher. Finding the length of key. (Kasiski test) Finding the key itself.


One-Time Pad

• Perfect substitution cipher • Improved Vernam cipher • Use a random key (pad) which is as long as the

message, with no repetitions. – Key distribution is a problem – Or, random key stream generation is a problem

• With such key, plaintext and ciphertext are statistically independent

• Unconditionally secure (Unbreakable)


Transposition (Permutation) Techniques

A transposition cipher does not substitute one symbol for another, instead it changes the location of the symbol. A very different kind of mapping is achieved by performing some sort of permutation on the plaintext letters. A symbol in the 1st position of the plaintext may appear in the 10th position of the ciphertext.

This may be two types:

- Keyless transposition cipher

- Keyed transposition cipher

Cryptography -Lect-01 66

Keyless Transposition Techniques

• Hide the message by rearranging the letter order without altering the actual letters used

• Rail Fence Cipher(Column by Column -> Row by Row)

– Write message on alternate rows, and read off cipher row by row

– Example:

• Row by Row->Column by Column

– Message is written in rectangle, row by row, but read off column by column; The order of columns read off is the key

– Example:

• Read it column wise : MMTAEEHREAEKTTP

M e m a t r h t g p r y

e t e f e t e o a a t MEMATRHTGPRYETEFETEOAAT


m e e t

m e a t

t h e p

a r k

Keyed Transposition Cipher The keyless cipher permute the characters by using writing plaintext in one way and reading it in another way. In the keyed cipher, the plaintext is divide into groups of predetermined size, called blocks, then use a key to permute the character in each block separately.

Example: Suppose the key is,

And the plaintext is “Enemy attacks tonight ” . What will be the ciphertext ??

3 1 4 5 2

1 2 3 4 5 Encryption Decryption

Rotor Machines • Mechanical cipher machines, extensively used in WWII;

Germany (Enigma), Japan (Purple), Sweden (Hagelin) • Each rotor corresponds to a

substitution cipher

• A one-rotor machine produces a polyalphabetic cipher with period 26

• Output of each rotor is input to next rotor

• After each symbol, the “fast” rotor is rotated

• After a full rotation, the adjacent rotor is rotated (like odometer)

- An n rotor machine produces a polyalphabetic cipher with period 26n 69 Cryptography -Lect-01

Steganography • “The art of covered writing” • “Security by obscurity” • Hide messages in other messages • Conceal the existence of message • Conceal what you are communicating (Sending encrypted

messages would make you a spy)

– Character marking. Overwrite with a pencil – Invisible ink, - Pin punctures, - First letter of each word – Letter position on page, - Drawings, - Codes – Typewriter correction ribbon – Microdots

– Digital steganography – Spread spectrum

Digital Watermarking

Covert channel or Subliminal channel


Steganography - Example

News Eight Weather: Tonight increasing snow. Unexpected precipitation

Smothers Eastern towns. Be extremely cautious and use snowtires especially

heading east. The highways are knowingly slippery. Highway evacuation is

suspected. Police report emergency situations in downtown ending near

Tuesday

First letter of each word yields: Newt is upset because he thinks he is

President

This example was created by Neil F. Johnson, and was published in

Steganography,Technical Report TR_95_11_nfj, 1995.

URL: http://www.jjtc.com/pub/tr_95_11_nfj/

From WWII German spy (Kahn):

Apparently neutral’s protest is thoroughly discounted and ignored. Isman

hard hit. Blockade issue affects pretext for embargo on by products, ejecting

suets and vegetable Oils.

Second letter of each word yields: Pershing sails from NY June 1. 71 Cryptography -Lect-01

http://www.jjtc.com/pub/tr_95_11_nfj/

Thank you

Documents

Cryptography /Computer Security - 123seminarsonly.com · Cryptography /Computer Security Classical Cryptography . ... • Computer Security - generic name for the collection of tools