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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