RSA (Rivest–Shamir–Adleman) is an algorithm used by modern computers to encrypt and decrypt messages. It is an asymmetric cryptographic algorithm.

1. RSAAlgorithminCryptography
Presented By
M.Srinadh

2. OUTLINES :
Introduction to Cryptography
Types of Cryptography
RSAAlgorithm
Advantages & Disadvantages
Applications

3. Introduction to Cryptography :
Cryptography is an Ancient Greek word which means ‘ ‘
‘hidden secret in writing’.
Cryptography is the practice and study of techniques
for secure communications in the presence of third
parties called adversaries.

4. Private key Cryptography :
Private key Cryptography is also known as
symmetric – key algorithms.
In this the same Cryptography key is used for both
encryption and decryption.

5. Public key Cryptography :
Public key Cryptography is also known as Asymmetric
key Cryptography.
Here we uses two keys for performing encryption and
decryption.

6. RSAAlgorithm :
 RSA is invented by Rivest, Shamir and Adleman of MIT.
 It is most widely used for secure data transmission.
 RSAAlgorithm is known as Public key Cryptography.

7. RSAAlgorithm :
RSAAlgorithm consists of following steps
 Key Generation
 Encryption
 Decryption

8. Key Generation :
1. Select two prime numbers p & q
2. Calculate n = p * q
3. Calculate m = Φ ( n) = ( p - 1 ) * ( q - 1)
4. Choose a small number e , co prime to m , with
GCD (Φ ( n), e ) = 1 , 1 < e < Φ ( n)
5. Calculate de mod Φ ( n) = 1

9. Encryption :
Plaintext, M < n
C = Me mod n
Decryption :
Ciphertext, C
M = Cd mod n

10. RSAAlgorithm Example :
1. Let p = 3, q = 11
2. n = p * q = 3 * 11 = 33
3. Φ ( n) = (p-1)*(q-1) = 20
4. Let e =7 such that 1 < 7 < 20 , GCD ( 7, 20 ) = 1
5. ed = 1 mod Φ ( n)
7 * d = 1 mod 20
So 7 * d mod 20 = 1
 7 * 3 mod 20 = 1
 Here d = 3

11. Encryption :
Plaintext, M < e
C = Me mod n
Let M = 31
Then , C = 317 mod 33
We get C = 4
Decryption :
Ciphertext, C
M = Cd mod n
M = 43 mod 33
M = 31

12. Advantages :
 Very fast, very simple encryption and verification.
 Easy to implement than Elliptical Curve Cryptography.
Easier to Understand
Widely deployed, better industry support.
Disadvantages :
Very slow key Generation.
Slow decryption, which is slightly tricky to implement
securely.

14. Thank You