RSA is a public-key cryptosystem that uses both public and private keys for encryption and decryption. It was the first practical implementation of such a cryptosystem. The algorithm involves four main steps: 1) generation of the public and private keys, 2) encryption of messages using the public key, 3) decryption of encrypted messages using the private key, and 4) potential cracking of the encrypted message. It works by using two large prime numbers to generate the keys and performs exponentiation and modulo operations on messages to encrypt and decrypt them. There were some drawbacks to the original RSA algorithm related to redundant calculations and representing letters numerically that opened it up to easier hacking. Enhancements to RSA improved it by choosing

1. - BY
ARPANA SHREE A
M12MC02

2. Overview
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3. Public key encryption
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4. RSA
First practicable public key cryptosystems
Encryption key- public
Decryption key- private
 Ron Rivest,Adi Shamir and Leonard Adleman
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5. Algorithm
Section-1
Generation of public and private keys
Section-2
Encryption
Section-3
Decryption
Section-4
Cracking the message
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6. Section-1-Public key
 Pick two prime numbers p&q
 Calculate n=p*q
 Calculate z=(p-1)*(q-1)
 Choose the prime number ‘k’ such
that k is co-prime of z and k
should not be divisible by z
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P=3 and q=11
n=33
Z=20
K=7,11,13,17,19
K=7

7. Section-1:Private key
 K * j = 1 (mod z)
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7 * j = 1 (mod 20)
( 7 * j ) / 20 =1
J=3

8. Algorithm
Section-1
Generation of public and private keys
Section-2
Encryption
Section-3
Decryption
Section-4
Cracking the message
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9. Section-2:Encryption and Decryption
 P ^ K = E (mod n)
 P: Plain text
 N and k are public keys
 E:Encrypted message
 E ^ J = P (mod n)
 E:Encrypted message
 J: Server’s secret key
 P:Plain text that we want
to recover
 N:Server public key
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14 ^ 7 = E (mod 33)
E=20
20 ^ 3 = p (mod 33)
P=14

10. Draw Backs
The alphabets in the plain text are represented
by numbers ranging from 1 to 26
Redundant calculation
Redundant calculation-easier hacking
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11. Enhancement of RSA:Section-1
Select two distinct prime numbers
Compute n=p*q
Compute φ(n)=(p-1) * (q-1)
Choose integer e such that 1 < e < φ(n) and
GCD(e,φ(n))=1
Public key: (e,n)
Private Key: (d,n)
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12. Enhancement of RSA:Section-2
 Encryption
 C=M ^ e (mod n)
 C:Cipher Text
 M:Plain text
 e:integer
 Decryption
 M=C ^ d (mod n)
 C:Cipher Text
 M:Plain Text
 D:Private key
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13. THANK YOU
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