Finding Cases of Ciphertext equal to Plaintext in the RSA Algorithm

Abstract

The RSA Algorithm is the most widely used public key encryption method that has survived the past 34 years of scrutiny and criticism. Studying and understanding RSA is important for a student of cryptography or information security. Finding a good example that is small enough for easy standard calculation and large enough to be non-trivial was the main and initial goal of this study. In the course of studying the RSA algorithm, there were cases where the ciphertext would equal the plaintext. In other words, at these values, the encryption would not change the value of the original message as if the plaintext is falling through a hole and not get encrypted. These cases were called holes. Characterization of the holes become the second objective of this study.