Rsa private public key encryption in python
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rsa (rivest-shamir-adleman) is one of the first public-key cryptosystems and is widely used for secure data transmission. the rsa algorithm involves a pair of keys: a public key (which can be shared with everyone) and a private key (which must be kept secret). here's a step-by-step tutorial on how rsa works and how to implement it using python.
step 1: understanding rsa key generation
1. **choose two prime numbers**: select two distinct prime numbers \( p \) and \( q \).
2. **calculate \( n \)**: compute \( n = p \times q \). this value will be used as the modulus for both the public and private keys.
3. **calculate the totient**: compute \( \phi(n) = (p - 1)(q - 1) \), which is used to determine the public and private keys.
4. **choose public exponent \( e \)**: choose an integer \( e \) such that \( 1 e \phi(n) \) and \( e \) is coprime to \( \phi(n) \). common choices for \( e \) include 3, 17, or 65537.
5. **calculate private exponent \( d \)**: compute \( d \) as the modular multiplicative inverse of \( e \) modulo \( \phi(n) \). this means \( d \times e \equiv 1 \mod \phi(n) \).
step 2: implementing rsa in python
let's implement rsa encryption and decryption using the `cryptography` library in python.
#### installation
first, ensure you have the `cryptography` library installed. you can install it using pip:
#### example code
here's a complete example demonstrating rsa key generation, encryption, and decryption:
explanation of the code
**key generation**: the `generate_keys` function creates a new rsa private and public key pair.
**saving keys**: the `save_private_key` and `save_public_key` functions save the keys to pem files.
**encryption**: the `encrypt_message` function takes a public key and a plaintext message and returns the encrypted message using oaep padding.
**decryption**: the `decrypt_message` function takes the private key and an encrypted message and returns the decrypted plaintext.
conclusion
you now ...
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