chapter 2 cryptography

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Basic Encryption Concepts

Chapter 1


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Some terminologies

Sender, S usually is referred as Alice. Is aperson who sends a message

Recipient, R usually is referred as Bob. Isa person who receives a message sent byAlice

Attacker or also called as anintruder/interceptor


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Some terminologies

Encryption: or also called as encoding,encipherment

Definition: process of scrambling a message so thatits meaning is not obvious/unreadable/cannot be

understood

Decryption: also called as decoding,decipherment.

A reverse process of encryption

A system for encryption and decryption iscalled a cryptosystem


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Some terminologies

Plaintext,p: original form of a message

Ciphertext, c: the encrypted form of amessage

Key: a device to encrypt and decrypt themessage

In mathematical form,C = E k(M)

Encryption

Plaintext

Key Ciphe

rtext

Decryption

Originalplaintext

Key


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Some terminologies

Cryptanalysis: by an attacker, trying to findout the original message by studying theencryption and encrypted messages.

A person who does the cryptanalysis iscalled a cryptanalyst

Tries to break the algorithm


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The intruder

Block message: prevent it from reaching R,affecting availability

Intercept message: read or listen it,affecting the confidentiality

Modify message: seize or change it in someway, affecting the integrity

Fabricate an authentic-looking message:

arrange for it to be delivered as is it camefrom S, affecting the authenticity


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Therefore the securityobjectivesConfidentiality

Integrity

Authenticity

Availability

(CIAA)


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Two types of cryptosystem:

Symmetric encryption: Encryption anddecryption are using the same key. It is amirror-image process.

Eg: Data Encryption Standard (DES),Advanced Encryption Standard (AES)

Asymmetric encryption: encryption anddecryption are using different keys and

process.Alice encrypts a message using Bobs public

key and Bob decrypt the message using hisprivate key


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Two ways of doing encryptionalgorithmSubstitution: a process of exchanging a

series of bits to another series of bits

Provide diffusion

Permutation: or also called as transposition,a process of rearranging the order of bits

Provide confusion

Both diffusion and confusion arecryptographic concepts introduced byShannon.


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Confusion

The cipher must show an avalanche effect.

The desired effect is called Strict AvalancheCriterion (SAC)

Definition: if a single bit is complemented in inputbits, it will cause each of the output bit to changewith a probability of half (0.5)

Avalanche effect can be achieved using

permutation.


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Example of encryption usingsubstitution technique

1) Caesar CipherEach letter is translated to the letter a fixed

number of places after it in the alphabet.

Caesar used a shift of 3

Encryption using caesar cipher:

c i= E(pi) =pi + 3

Decryption using caesar cipher:p i= D(ci) = ci - 3


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Caesar Cipher

Full translation chart of caesar cipher:

Eg: using this encryption, the message

TREATY IMPOSSIBLE

Would be encoded as

P:T R E A T Y I M P O S S I B L E

c: w u h d w b l p s r v v l e o h

Plaintext 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

Ciphertext d e f g h i j k l m n o p q r s t u v w x y z a b c


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weaknesses of Ceasar cipher

The same letters always translated to thesame another letters

The ciphertexts retain the space as in theplaintext

Therefore a cryptanalyst can easily derive apattern from ciphertext if the plaintext is inenglish words


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Example of encryption usingsubstitution technique

1) Vernam CipherA type of one-time pad (OTP) encryption

OTP is considered as a perfect cipher.

OTP involves an arbitrary longnonrepeating sequence of numbers thatare combined with the plaintext.

Different message will be using different

nonrepeating key, and this key is notreused. In other words, the key is only usedonce.


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Vernam cipher

Eg:

Plaintext V E R N A M C I P H E R

Numeric equivalent 21 4 17 13 0 12 2 8 15 7 4 17

+ random number 76 48 16 82 44 3 58 11 60 5 48 88

= sum 97 52 33 95 44 15 60 19 75 12 52 105

= mod 26 19 0 7 17 18 15 8 19 23 12 0 1

Ciphertext t a h r s p i t x m a b


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Example of encryption usingpermutation technique

1) columnar transpositionsRearrange the characters of the plaintext

into columns


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Example of columnartranspositionPlaintext: THIS IS TO SHOW HOW ACOLUMNAR TRANSPOSITION WORKS.

We arrange the letters in five columns as:

T H I S IS T O S H

O W H O W

A C O L U

M N A R TR A N S P

O S I T I

O N W O R

K S x x x

The resulting ciphertext wouldthen be read down the columnsas:

tsoamrook htwcnasnsiohoaniwx xsolrstoxihwutpirx


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Good Encryption algorithm

Shannon proposed several characteristicson a good cipher:

1.The amount of secrecy needed shoulddetermine the amount of labor appropriate

for the encryption and decryption

2.The set of eys and the enciphering algorithmshould be free from complexity

3.The implementation of the process should beas simple as possible

4. Errors in ciphering should not propagate andcause corruption of further information in the

message


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Stream cipher

Caesar and vernam cipher are streamciphers

The cipher operates bit by bit

More suitable for communication

Find out what are the

disadvantages andadvanta es of


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Block cipher

The cipher operates on a block of bits

Harder for a cryptanalyst to break the code.

A block cipher encrypts a group of plaintext

symbols as one block. Columnartransposition are examples of blockciphers.


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Example of block ciphers

Data Encryption Standard (DES)

Two fundamental building blocks ofencryption: substitution and transposition

The strength: repeated application of thesetwo techniques, one of top of the other, fora total of 16 cycles.

Encrypt the plaintext as blocks of 64 bits.

The key is 64 bits long

Suitable for implementation on a single-purpose chip.


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DES

Figure 2-8 Cycles of Substitution andPermutation.


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Example of block cipher

Advanced Encryption Standard (AES)

Invented by two Belgian cryptographers,Vincent Rijmen and Joan Daemen

Fast algorithm, has strong mathematicalfoundation; uses substitution, transposition,and the shift, exclosive OR, and additionoperations.

It also repeats cycles, or also called rounds.

There are 10,12 or 14 cycles for keys of128, 192 and 256 bits respectively.


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AES

Consists of four steps:

Byte substitution; uses substitution boxstructure similar to the DES, substituting eachbyte of a 128 bit block according to a

substitution table

Shift row: a transposition step.

Mix column: this step involves shifting left and

exclusive-Oring bits with themselves.Add subkey: Here, a portion of the key unique

to this cycle is exclusive-Ored with the cycleresult.


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AES

Figure: AES Algorithm.You may go here http://www.cs.bc.edu/~

straubin/cs381-05/blockciphers/rijndael_ingles2004.swf

to experience the simulation of AES
http://www.cs.bc.edu/~straubin/cs381-05/blockciphers/rijndael_ingles2004.swfhttp://www.cs.bc.edu/~straubin/cs381-05/blockciphers/rijndael_ingles2004.swfhttp://www.cs.bc.edu/~straubin/cs381-05/blockciphers/rijndael_ingles2004.swfhttp://www.cs.bc.edu/~straubin/cs381-05/blockciphers/rijndael_ingles2004.swf


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Comparison of DES and AES

DES AESDate 1976 1999

Block size 64 bits 128 bits

Key length 56 bits

(effectivelength)

128, 192, 256

(and possiblymore) bits

Encryptionprimitives

Substitutionand

permutation

Substitution,shift, bit mixing

Cryptographicprimitives

Confusion anddiffusion

Confusion anddiffusion

Design Open Open

Design Closed Open

chapter 2 cryptography

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