Is there a known 'non-brute force' method of determining a private key in an RSA system when all other parameters are know?
I found the values of a ciphertext ($C$), its corresponding plaintext ($P$) and the values of the public key ($e$,$N$) are known.
We know that: $$P = C^d \mod N$$
Here, the value of $P$ is known (the cipher text has been decrypted) and the values of $C$ and $N$. Given these parameters, is it possible to find $d$?
Also, how do I find an integer $k$ such that $(k\cdot N - P) = C^d$ ?
Any suggestions/discussions are welcome.