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Update 02_Diffie_Hellman_Key_Exchange.md

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Omar Santos 2023-08-15 09:51:13 -04:00 committed by GitHub
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crypto/challenges/02_Diffie_Hellman_Key_Exchange.md
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@ -12,24 +12,11 @@ n = 3233, e = 17, Encrypted message: [2201, 2332, 1452]
### Answer:
Here are the detailed solutions for each step:
**Step 1:** Factorize \( n = 3233 \) into two prime numbers:
\( p = 61 \), \( q = 53 \)
<img width="1230" alt="image" src="https://github.com/The-Art-of-Hacking/h4cker/assets/1690898/b4919061-0736-4884-9f44-51f0a53fdcc6">
**Step 2:** Compute the Euler's Totient function \( \phi(n) \):
\( \phi(n) = (p-1)(q-1) = 3120 \)
Compute the private key \( d \) such that:
\( de \equiv 1 \mod \phi(n) \)
Using Extended Euclidean Algorithm, we can find:
\( d = 2753 \)
**Step 3:** Decrypt the message using the private key:
Decrypted message: "HEY"
Here's a code snippet in Python to perform the entire decryption:
Code snippet in Python to perform the entire decryption:
```python
def egcd(a, b):
@ -61,4 +48,4 @@ decrypted_text = decrypt_rsa(ciphertext, n, e)
print(decrypted_text) # Output: "HEY"
```
This challenge provides an understanding of the RSA algorithm, which is foundational in modern cryptography. It covers important concepts like prime factorization, modular arithmetic, and key derivation.
This challenge provided you with an understanding of the RSA algorithm. It covered important concepts like prime factorization, modular arithmetic, and key derivation.