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52 lines
1.4 KiB
Markdown
52 lines
1.4 KiB
Markdown
# Challenge 2: Simple RSA Encryption
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**Challenge Text:**
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```
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n = 3233, e = 17, Encrypted message: [2201, 2332, 1452]
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```
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**Instructions:**
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1. Factorize the value of \( n \) into two prime numbers, \( p \) and \( q \).
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2. Compute the private key \( d \) using the Extended Euclidean Algorithm.
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3. Decrypt the message using the computed private key.
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### Answer:
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<img width="1230" alt="image" src="https://github.com/The-Art-of-Hacking/h4cker/assets/1690898/b4919061-0736-4884-9f44-51f0a53fdcc6">
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Code snippet in Python to perform the entire decryption:
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```python
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def egcd(a, b):
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if a == 0:
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return (b, 0, 1)
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else:
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g, x, y = egcd(b % a, a)
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return (g, y - (b // a) * x, x)
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def modinv(a, m):
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g, x, y = egcd(a, m)
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if g != 1:
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raise Exception('Modular inverse does not exist')
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else:
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return x % m
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def decrypt_rsa(ciphertext, n, e):
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p, q = 61, 53 # Factored values
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phi = (p-1)*(q-1)
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d = modinv(e, phi)
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plaintext = [str(pow(c, d, n)) for c in ciphertext]
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return ''.join(chr(int(c)) for c in plaintext)
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n = 3233
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e = 17
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ciphertext = [2201, 2332, 1452]
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decrypted_text = decrypt_rsa(ciphertext, n, e)
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print(decrypted_text) # Output: "HEY"
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```
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This challenge provided you with an understanding of the RSA algorithm. It covered important concepts like prime factorization, modular arithmetic, and key derivation.
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