It’s also possible to generate the keys (or directly encrypt the message) using python, just by using the awesome pycrypto package. To decrypt messages you can use the follwoing command: $> openssl rsautl -in encrypted_message.bin -inkey private.key -decrypt -hexdump Finally pipe your output to some file - Viola! $> gcc private-from-pq.c -o gen -lssl -lcrypto After compilation, call the generated binary and provide your $q$ and $p$ as arguments. You will need openssl-dev and provide -lssl -lcrypto as compiler flags. I used this c program to calculate the private key. These can be calculated, but this is not easy so I will look them up ). Now we have to find the factors $(p,q)$ of the modulus $n$.
To get the corresponding decimal values we have to convert the hex-values. The second Integer is the modulo and the last int is the exponent.
These values can be extracted out of the public key file. First we need to gather some information like modulo $n$ and the exponent $e$. If you want to know how RSA works, take a look at one of the million blog posts out there. So RSA is not bad, but please use a suitable key size.įor this blog post it’s not important, why RSA is secure and works, it’s just a tutorial how to calculate a private key if it get’s lost (will just work for unsecure keys indeed) or to demonstrate that small key sizes are unsecure. Why weak? Because a (only) 268-bit key was used for encryption. I had to decrypt a weak RSA encrypted message.
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