Novel Encryption Scheme Based on Continued Fraction and Permutation

An arbitrary positive rational number has a unique continued fraction expression. In this study, we propose a novel cryptosystem based on continued fraction and permutation, which is a two-step encryption operation. First, we can encode message or data stream into a set of quotient numbers, and then determine uniquely two large integers as the first step ciphertext accordingly. The operation of a continued fraction is equivalent to the execution of Euclid’s algorithm. Euclid’s algorithm belongs to the polynomial complexity; thus, both encryption and decryption of the proposed scheme are quick and efficient. The first step ciphertext is subject to permutation encryption to derive the final ciphertext. Any factorial function resulting from the execution time of solving a factorial function with input size n > 30 is still infeasible for the current computing system. The proposed two-step encryption scheme can possess two merits: efficiency and confidentiality, and the scheme is considered a lightweight cryptosystem, which applies to the limited resources of internet of things devices.