About RSA encryption and decryption principle

Preface ：

With the deepening of our study , Information security is becoming more and more important , The code we publish may contain our private information , For example, connect with Alipay sandbox api, When downloading some professional software, we need to input the public key and private key to verify our identity information , It is equivalent to unlocking with a key , The public key represents the lock , The private key represents the key to unlock , The public key and private key are interchangeable , Understand this , Let's talk about their principle in detail .

RSA Key distribution ：

First take two prime numbers （p,q）,N=pq

Then find their Euler function T = (p-1)(q-1)

Take out the public key E The rule is 1. It's a prime number .

2.1< Public key <T ;

3. No T Factor of

Public key selected E Then calculate the private key D （D*E）%T=1

This completes the distribution of public and private keys

for example p=3,q=11 N=pq=33

T=(3-1)(11-1)=20

Select a public key at random E=3 Then the key can be D=7

Public key E（3,33） Private key D（7,33）

According to the following encryption formula 1 2 3 Encrypted into

1,29,9

According to the decryption formula below, the original number is

1,2,3

Key encryption ：( Plaintext ^E)%N= Ciphertext

Key decryption ：( Ciphertext ^E)%N= Plaintext

RSA The principle of public key cryptography is ： According to number theory , It's easier to find two large primes , But factoring their products is extremely difficult , Therefore, the product can be disclosed as the encryption key

result ：