Below you will find pages that utilize the taxonomy term “RSA”

# Implement The RSA Algorithm

# Introduction

In our last post, we wrote some Python functions in preparation to implement the RSA algorithm. In this post, we will implement the RSA algorithm.

## Program On The Receiver’s Side

Create the public and private keys. Share the public key with the sender.

```
import random
from sympy import isprime
def gcd(a, b):
while b != 0:
a, b = b, a % b
return a
def modinv(a, m):
m0, x0, x1 = m, 0, 1
if m == 1:
return 0
while a > 1:
q = a // m
m, a = a % m, m
x0, x1 = x1 - q * x0, x0
if x1 < 0:
x1 += m0
return x1
def generate_prime_candidate(length):
p = random.getrandbits(length)
# Apply a mask to set MSB and LSB to 1 to ensure a proper length prime
p |= (1 << length - 1) | 1
return p
def generate_large_prime(length=1024):
p = 4
while not isprime(p):
p = generate_prime_candidate(length)
return p
def generate_keypair(keysize):
p = generate_large_prime(keysize)
q = generate_large_prime(keysize)
n = p * q
phi = (p - 1) * (q - 1)
# Choose e
e = random.randrange(2, phi)
g = gcd(e, phi)
while g != 1:
e = random.randrange(2, phi)
g = gcd(e, phi)
# Generate d
d = modinv(e, phi)
return ((n, e), (n, d))
def decrypt(private_key, ciphertext):
n, d = private_key
# Decrypt each character
plain = [chr((char ** d) % n) for char in ciphertext]
return ''.join(plain)
# RSA Key Generation
keysize = 8 # Small size for demonstration; use 1024 or 2048 for real applications
public_key, private_key = generate_keypair(keysize)
print(f"Public Key: {public_key}")
print(f"Private Key: {private_key}")
```

Execute the program on the receiver’s computer. Take note of the public and private key. Share the public key with the sender.

# Prepare To Implement The RSA Algorithm

# Prerequisites

- Familiarity with binary arithmetic. Know what are MSB and LSB.
- Bitwise operations. Logical shift.
- Primality Testing

# Introduction

Continuing with the series of posts on number theory and cryptograpy, let us take a look at the RSA algorithm.

Before writing the RSA program, let’s prepare some useful functions.

## GCD

Here’s a simple recurisve function to computed the GCD of two integers.

```
def gcd(a, b):
while b != 0:
a, b = b, a % b
return a
```

We have discussed the non-recursive implementation of the Euclidean algorithm at length in this series.

# The RSA Algorithm

# Introduction

Continuing with the series of posts on number theory and cryptograpy, let us take a look at the RSA algorithm.

RSA is an algorithm to perform encryption and decryption of data.

## The Basic Idea

RSA uses two keys to encrypt and decrypt messages:

**Public Key**: Anyone can see this key. It’s used to encrypt the message.**Private Key**: Only you should know this key. It’s used to decrypt the message.

When someone wants to send you a secret message, they use your public key to encrypt the message. Once it’s encrypted, only your private key can decrypt it.