RSA Encryption presentation for Education.pptx

This is for those student who will not be able to study in books and not for time to create a power point presentation for her semester project and her presentation.

1. RSA Encryption

2. RSA algorithm is a public-key encryption algorithm that is widely used in securing data transmission over the internet. It was invented by Ron Rivest, Adi Shamir, and Leonard Adleman in 1977. The RSA algorithm uses two keys, a public key, and a private key, to encrypt and decrypt messages. The public key is used to encrypt the message, while the private key is used to decrypt it. This makes it possible for anyone to send encrypted messages to a recipient without having to share a secret key. Introduction to RSA Algorithms

3. Secret Key (Symmetric) Public Key (Asymmetric) 1 Key = encrypt & decrypt Advantage: Fast Disadvantage: Not safe Two separate keys 1 public key to encrypt 1 private key to decrypt

4. How RSA Algorithm Works The RSA algorithm works by using large prime numbers to generate the public and private keys. The first step is to select two large prime numbers, p and q. These numbers are multiplied together to get n = p * q. The value of n is then used to generate the public and private keys. To generate the public key, e is selected such that e and (p-1)*(q-1) are coprime. The value of e is then paired with n to create the public key, ( n,e ). To generate the private key, d is calculated such that d*e mod (p-1)*(q-1) = 1. The value of d is then paired with n to create the private key, ( n,d ).

5. Prime Numbers Given two large prime numbers, p and q, we already know: Simple: Find product N, where N= p*q Difficult: Factor N, when p and q are unknown 203477 = ? * ? 439 * 541 = 237499 Easy Hard

6. Generating Keys Public Key Private Key Let n = p* q Find Φ(n)= (p-1)(q-1) Choose e such that gcd (e, Φ(n))=1 Choose two large prime integers p,q Find Φ(n)= (p-1)(q-1) Find d such that d is multiplicative inverse of e.d ( modΦ (n))=1 de ≣ 1(mod Φ(n))

7. Example Message: “Hi” = 89 p = 11 q = 13 n = 11 * 13 = 143 Φ(143) = (11 – 1)(13 – 1) = 120 Set e = 7 d = 103

8. Alice Bob Public Key n = 143 e = 7 Hi Secret Key p = 11 p = 13 Φ(n) = 120 d = 103 Hi = 89 67 89 = Hi 67 89 Hi

9. Digital Signature