RSA Algorithm

- BY

ARPANA SHREE A

M12MC02

04/12/2023RSA

2 Overview

04/12/2023RSA

3 Public key encryption

04/12/2023RSA

4 RSA

First practicable public key cryptosystems

Encryption key- public Decryption key- private

 Ron Rivest,Adi Shamir and Leonard Adleman

04/12/2023RSA

5 Algorithm

Section-1 Generation of public and private keys

Section-2 Encryption

Section-3 Decryption

Section-4 Cracking the message

04/12/2023RSA

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

P=3 and q=11

n=33

Z=20

K=7,11,13,17,19

K=7

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7 Section-1:Private key

K * j = 1 (mod z)

7 * j = 1 (mod 20)

( 7 * j ) / 20 =1

J=3

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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

14 ^ 7 = E (mod 33)

E=20

20 ^ 3 = p (mod 33)

P=14

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10 Draw Backs

The alphabets in the plain text are represented by numbers ranging from 1 to 26

Redundant calculation

Redundant calculation-easier hacking

04/12/2023RSA

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

04/12/2023RSA

THANK YOU