Polynomial based RSA

Abstract: The RSA public-key cryptosystem has a major role in information security even today, after more than three decades since it was invented. The reason why is that the security provided by this algorithm relies on the fact that integer factorization is considered to be a hard problem. The day someone finds an efficient algorithm to factor integers, is the day when the RSA cryptosystem, used millions of times every day, will not be secure anymore. A good perspective is to look ahead of that day, and start thinking about alternatives. A polynomial version of the RSA cryptosystem is one such idea someone can think about. The idea will be analyzed from three main points of view, namely whether it is easy to encrypt messages, whether it is correct, that is whether the private key will always restore the plaintext, and the last point to be analyzed is the degree of difficulty of breaking the code, or in other words how secure  the algorithm is. The original RSA cryptosystem and the polynomial version will be discussed in parallel all the time.