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Public Key CryptographyAnd RSA

BY

Swasti sundar sahoo

(0501206091)

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Cryptography

The art of secret message writing.

Creating texts that can be only read

by authorized individuals .

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Terminology Plaintext: Original intelligible message

Encryption algorithm: It performs

various substitutions andtransformations on the plaintext

Key: Is a word that is used to encrypt the plaintext

Ciphertext: Is a scrambled message produced as output

Decryption algorithm: Opposite of encryption algorithm

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D

ecryptionThe quickThe quickbrown foxbrown fox

jumps overjumps over

the lazythe lazydogdog

AxCv;5bmEseTfid3)AxCv;5bmEseTfid3)fGsmWe#4^,sdgfMwifGsmWe#4^,sdgfMwi

r3:dkJeTsY8Rr3:dkJeTsY8R\\s@!q3s@!q3%%

DecryptionDecryptionAlgorithmAlgorithm

CipherCipher--texttext

keykey

PlainPlain--text outputtext output

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Mathematical Notation

P: plaintext

C: ciphertext

K : key

E: encryption function

D: decryption function

C = Ek(P)

P = Dk(C)

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Types of Cryptography

Using Keys

Secret key cryptography: one key

Public key cryptography: two keys -

public, private

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EncryptionEncryptionAlgorithmAlgorithm

The quickThe quickbrown foxbrown fox

jumps overjumps overthe lazythe lazy

dogdog

AxCv;5bmEseTfid3)AxCv;5bmEseTfid3)fGsmWe#4^,sdgfMwifGsmWe#4^,sdgfMwir3:dkJeTsY8Rr3:dkJeTsY8R\\s@!q3s@!q3

%%

The quickThe quickbrown foxbrown fox

jumps overjumps overthe lazythe lazy

dogdogDecryptionDecryptionAlgorithmAlgorithm

PlainPlain--text inputtext inputCipherCipher--texttext

Same keySame key(shared secret)(shared secret)

PlainPlain--text outputtext output

Secret Key Cryptography

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Public Key

Cryptography

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Public-Key Cryptography 1976: W. Diffie and M.E. Hellman

proposed the first public-key

public-key/asymmetric cryptography

involves the use oftwo keys:

aprivate-key, which is kept private

apublic-key, which may be known byanybody

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Essential Steps

Each user generates a pair of keys Each user places one key in public

register

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Public Key Cryptography

EncryptionEncryptionAlgorithmAlgorithm

Py75c%bn&*)9|fDe^Py75c%bn&*)9|fDe^bDFaq#xzjFr@g5=&nbDFaq#xzjFr@g5=&n

mdFg$5knvMdrkvegmdFg$5knvMdrkvegMsMs

The quickThe quickbrown foxbrown fox

jumps overjumps over

the lazythe lazydogdog

ClearClear--text Inputtext Input

The quickThe quickbrown foxbrown fox

jumps overjumps over

the lazythe lazydogdog

DecryptionDecryptionAlgorithmAlgorithm

CipherCipher--texttext ClearClear--text Outputtext Output

Different keysDifferent keys

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Public Key Cryptography

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Public Key Cryptography

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Public Key Cryptography

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Public Key Cryptography

Solves problem of

passing the key

Only the private key

must be kept secret

Extremely slow

Large key size

Advantage Disadvantages

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RSAAlgorithm

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RSA

By Rivest, Shamir &Adleman

Best known & widely used

It is based on number theory

The key size ranges between

512 and 2048

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The RSA Algorithm Key

Generation1. Selectp,q ; p and qboth prime

2. Calculate n = p x q

3. Calculate

4. Select integere

5. Calculate d

)1)(1()( !* qpn

)(1;1)),(gcd( neen *!*

)(mod1 ned *!

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Plaintext: p

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RSA Example1. Select primes: p=17 & q=11

2. Compute n =p*q=1711=187

3. Compute (n)=(p1)(q-1)=1610=160

4. Select e : gcd(e,160)=1; e=7

5 Compute d = e-1 mod J(n) =7 mod 160

=23

-1

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Conclusion Cryptography is used to keep secret the

message. The long message is kept secret

through symmetric key cryptography due to

its same encrypt and decrypt key. Public

key cryptography is efficient for short

messages and RSA algorithm is a popularalgorithm for public key cryptography.

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Biblography

Cryptography And Network Security-William Stallings

Applied Cryptography

- Bruce Schneier

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THANK YOU