RSA Algorithm

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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