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# Cryptography

Nov 22, 2014

## Documents

vagi-gowda

#### decryption method

KUVEMPU

UNIVERSITY

Seminar On

CRYPTOGRAPHYSeminar Guide: Murugendrappa. N Lecturer, Department Of Electronics Jnana Sahyadri Shankaraghatta.

Seminar By: Deepti.S M.Sc. semester semester Department Of Electronics Electronics Jnana Sahyadri Shankaraghatta. 1

Contents :

Introduction to Cryptography. Why Cryptography. Encryption and Decryption. The Encryption model. Cryptography in Mathematical Representation. Algorithm Secrecy. Some methods of Encryption. 1.Substitution cipher. 2.Transposition cipher. 3. One Time Pad. Fundamental Cryptographic principle. Uses of Encryption. Reference.2

Introduction to cryptographyCryptography comes from Greek word crypto-secret graphy cryptowriting. Definition : Cryptography deals with all aspects of secure messaging, authentication, digital signatures, electronic money, and other applications Historically, four groups of people have used and contributed to the art of cryptography: the military, the diplomatic corps, diarists, and lovers. Of these, the military has had the most important role and has shaped the field over the centuries. Within military organizations, the messages to be encrypted have traditionally been given to poorly-paid, low-level poorlylowcode clerks for encryption and transmission.3

Why Cryptography?Concerned with developing algorithms which may be used to:

Conceal the context of some message from all except the sender and recipient (privacy or secrecy). Verify the correctness of a message to the recipient (authentication). Forms the basis of many technological solutions to computer and communications security problems.4

Encryption and DecryptionEncryption and Decryption normally works in the following way:A message in its original form (plaintext) is encrypted into an unintelligible form (ciphertext) by a set of procedures known as an Encryption. Encryption. Algorithm and a variable, called a key; and key; The ciphertext is transformed (decrypted) back into plaintext using the encryption algorithm and a key known as an Decryption. Decryption.

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The Encryption model

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Definitions:Plain text : In cryptographic terminology, the message is called plaintext or cleartext. cleartext. Encryption method : Encoding the contents of the message in such a way that hides its contents from outsiders is called encryption method . text. Cipher text : The encrypted message is called the cipher text. The Decryption method : The process of retrieving the plaintext from the ciphertext is called decryption method . Encryption and decryption key : Encryption and decryption usually make use of a key, and the coding method is such key, that decryption can be performed only by knowing the proper key.7

Intruder : The enemy or crooks, hears and accurately copies down the complete cipher text called intruder. intruder. Passive Intruder : The intruder does not know what the decryption key is and so cannot decrypt the cipher text easily and he can just listen to the communication channel. Active Intruder : The intruder can also record messages and play them back later, inject his own messages, or modify messages before they get to the receiver. Cryptanalysis : The art of breaking ciphers. Cryptographers: Cryptographers: People who do cryptography are cryptographers. Cryptanalysts : practitioners of cryptanalysis are cryptanalysts. Cryptology : Is the actual study of codes and cipher. It is both 8 cryptography & cryptanalysis.

Cryptography in Mathematical Representation

Encryption C = EK(P). Decryption P = EK-1(C). EK is chosen as a cryptographic system.

The parameter that selects the individual transformation is called the key K, selected from a keyspace K. A cryptographic system is a single parameter family of invertible transformations. EK ; K in K : P p C -1 ; K in K : C p P with the inverse algorithm EK such that the inverse is unique. Usually we assume the cryptographic system is public, and 9 only the key is secret information.

Algorithm Secrecy

The idea that the cryptanalyst knows the algorithms and that the secrecy lies exclusively in the keys is called Kerchoff's principle

Kerchoffs Principle: All algorithms must be public; Principle: only the keys are secret

All modern algorithms use a key to control encryption and decryption; a message can be decrypted only if the key matches the encryption key. The key used for decryption can be of different from the encryption key, but for most algorithms

they are the same.

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Some Methods Of Encryption

Substitution Cipher. Transposition Cipher. One Time Pad.

Substitution cipher : In substitution ciphers letters are replaced by other letters. There are two types. 1. Monoalphabetic - only one substitution. 2. Polyalphabetic - where several substitutions.11

Caesar Cipher - A Monoalphabetic Substitution CipherReplace each letter of message by a letter a fixed distance away e.g. use the 3rd letter on Reputedly used by Julius Caesar, e.g.

L FDPH L VDZ L FRQTXHUHG i came i saw i conquered

the mapping is

ABCDEFGHIJKLMNOPQRSTUVWXYZ DEFGHIJKLMNOPQRSTUVWXYZABC12

A Simple Substitution CipherPlaintext: abcdefghijklmnopqrstuvwxyz

QIAYMWFUBKPDGJZSOCVLXNETRH Ciphertext:13

Polyalphabetic Substitution ExampleSuppose that a polyalphabetic cipher of period 3 is being used, with the three monoalphabetic ciphers M1, M2, M3 as defined below. To encrypt a message, the first 3 letters of the plaintext are enciphered according to ciphers M1, M2, M3 respectively, with the process being repeated for each subsequent block of 3 plaintext letters.M1: M2: M3: a K P J b D A M c N G F d H U Z e P K R f A H N g W J L h X B D i C Y O j Z D W k I S G l M O I m Q E A n J M K o B Q E p Y N S q E W U r T F C s U Z Q t G I V u V T H v R C Y w F V X x O L T y S X P z L R B

Plaintext now is the time for every good man Ciphertext JQx CZ VXK VCER AQC PCRTX LBQZ QPK .

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Transposition CiphersTransposition or permutation ciphers hide the message contents by rearranging the order of the letters. The cipher is keyed by a word or phase not containing any repeated letters. Here MEGABUCK is the key.The purpose of the key is to number the column. Column1 being under the key letter closest to the start of the alphabet and so on. The plaintext is written horizontally in rows padded to fill the matrix if need be. The ciphertext readout by column, starting with the column whose key letter is the lowest.15

Transposition Cipher Example (1)M E G A B U C K 7 4 5 1 2 8 3 6 p l e a s e t r a n s f e r o n e m i l l i o n d o l l a r s t o m y s w i s s b a n k a c c o u n t s i x t w o t w o a b c dKey Weights to be used for double transposition

Plaintext pleasetransferonemilliondollarstomyswis sbankaccountsixtwotwo Ciphertext AFLLSKSOSELAWAIATOOSSCTCLNM OMANTESILYNTWRNNTSOWDPAEDO BUOERIRICXB16

Transposition Cipher Example(2)Key Weights to be used for double transposition

S H O E S 1 4 5 3 2 p a y m e

Plaintext paymebysundayorsufferthecons equences Ciphertext PBDSROUSENRECQEZMUOF EECZAYAUTNEZYSYFHSNZ

b y s u n d a y o r s u f f e r t h e c o n s e q u e n c e s z z z z17

One Time Pad - OTPIn this method we have to choose a random bit string as the key. Then convert the plain text into a bit string. For example using its ASCII representation finally, compute the XOR (exclusive OR) of these two strings bit by bit. The resulting ciphertext cannot be broken because it should be a large sample called one time pad with a one time pad there are many bits in the key as in the plaintext. This is the primary drawback of onetime pad, but it is also the source of its perfect security. It is essential that no portion of the key ever be reused for another encryption otherwise cryptanalysis can break the cipher 18

The cipher itself is exceedingly simple. To encrypt plaintext, P, with a key, K, producing ciphertext, C, simply compute the bitwise exclusive-or of the key and exclusivethe plaintext: P

+K

C

C = K XOR P

To decrypt ciphertext, C, the recipient computes C P = K XOR C It's that simple, and its perfectly secure, as long as the key is random and is not compromised.

+K

P

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Two Fundamental Cryptographic Principle

Redundancy :Cryptographic principle 1 : Messages must contain some redundancy.

Freshness :Cryptographic principle 2 : Some method is needed to foil replay attacks. i.e. some measures must be taken to ensure that each message received can be verified as being fresh20

Uses of Encryption

Protecting data from prying eyes is not the only security issue in networking Protecting data from being read by unauthorized persons Verifying the sender of each message Preventing unauthorized persons from inserting or deleting messages Making it possible for users to send signed documents electronically21

References

Computer Networks Tanenbaum third edition. Information Theory ,Coding and Cryptography Ranjan Bose. Internet

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