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Challenge 2: Simple RSA Encryption
Challenge Text:
n = 3233, e = 17, Encrypted message: [2201, 2332, 1452]
Instructions:
- Factorize the value of
n
into two prime numbers,p
andq
. - Compute the private key
d
using the Extended Euclidean Algorithm. - Decrypt the message using the computed private key.
Answer:
Code snippet in Python to perform the entire decryption:
def egcd(a, b):
if a == 0:
return (b, 0, 1)
else:
g, x, y = egcd(b % a, a)
return (g, y - (b // a) * x, x)
def modinv(a, m):
g, x, y = egcd(a, m)
if g != 1:
raise Exception('Modular inverse does not exist')
else:
return x % m
def decrypt_rsa(ciphertext, n, e):
p, q = 61, 53 # Factored values
phi = (p-1)*(q-1)
d = modinv(e, phi)
plaintext = [str(pow(c, d, n)) for c in ciphertext]
return ''.join(chr(int(c)) for c in plaintext)
n = 3233
e = 17
ciphertext = [2201, 2332, 1452]
decrypted_text = decrypt_rsa(ciphertext, n, e)
print(decrypted_text) # Output: "HEY"
This challenge provided you with an understanding of the RSA algorithm. It covered important concepts like prime factorization, modular arithmetic, and key derivation.