Rsa explaied with code in python

rsa (rivest-shamir-adleman) is a public-key cryptographic algorithm that is widely used for secure data transmission. it involves generating a public key and a private key, where the public key can be shared with others for encryption and the private key is kept secret for decryption.

here's an overview of how rsa works:
1. choose two large prime numbers, p and q.
2. calculate the product n = p * q. n is used as the modulus for both the public and private keys.
3. calculate euler's totient function φ(n) = (p-1)(q-1).
4. choose an integer e such that 1 e φ(n) and gcd(e, φ(n)) = 1. e is the public key exponent.
5. calculate the modular multiplicative inverse d of e modulo φ(n). d is the private key exponent.

the public key is (e, n) and the private key is (d, n).

encryption: to encrypt a message m, compute c = m^e mod n.

decryption: to decrypt the ciphertext c, compute m = c^d mod n.

here's an example python code implementing rsa encryption and decryption:

this code demonstrates how to generate rsa key pairs, encrypt a message, and decrypt the ciphertext using the rsa algorithm in python.

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