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I need to decrypt c and I was given only n, e and c and computing p and q or phi(n) would be close to impossible so what other alternatives do I have? I tried calculating p and q but I made very little progress with the search in the last 24 hours of continuous running the program.
These are the values I was given:n: 58900433780152059829684181006276669633073820320761216330291745734792546625247e: 65537c: 56191946659070299323432594589209132754159316947267240359739328886944131258862
Also, in another challenge only c and n were given and the values were a lot bigger. Do you have any suggestions for that too?
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To decrypt a ciphertext C using an RSA public key we simply compute the plaintext M as: M = Cd mod N. Note that both RSA encryption and RSA decryption involve a modular exponentiation and so we would be well advised to use the Repeated Squares Algorithm if we want to make these processes reasonably efficient.
For RSA encryption, the numbers n and e are called public keys. The (numeric) message is decomposed into numbers (less than n ), for each number M the encrypted (numeric) message C is C≡Me(modn)
RSA algorithm uses the following procedure to generate public and private keys: Select two large prime numbers, p and q. Multiply these numbers to find n = p x q, where n is called the modulus for encryption and decryption. If n = p x q, then the public key is <e, n>.
Well, seems the questions are CTF related because the patterns of n, e, and c are weak numbers.
You can solved it with RsaCtfTool
python RsaCtfTool -n 58900433780152059829684181006276669633073820320761216330291745734792546625247 -e 65537 --uncipher 56191946659070299323432594589209132754159316947267240359739328886944131258862
timctf{CENSORED}
58
https://www.dcode.fr/rsa-cipher Try this one but it need p and q. So I use the hand calculator to find p and q. Using Fact(n), ex: Fact(91)= 7x13, so p=7, q=13
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