Novel Hybrid Public/Private Key Cryptography Based on Perfect Gaussian Integer Sequences

Abstract

This paper proposes a novel hybrid public/private key cryptography scheme based on perfect Gaussian integer sequences (PGISs) of period N = pq. First, a review study of construction degree-4 PGIS is addressed. We show that circular convolution over PGISs is a trapdoor one-way permutation function that enables simultaneous cipher encryption and digital signatures. To implement the proposed cipher encryption scheme, a private PGIS is assigned as the encryption key sequence for circular convolution with the plaintext to generate the ciphertext. The reverse decryption key sequence involves the time reflection and complex conjugation of the encryption sequence, which can be regenerated using a pair of public and private keys. The security level of the proposed scheme is the same as that of the Rivest-Shamir-Adleman (RSA) system; however, the capacity of a cryptosystem based on PGISs may outperform that of based on RSA, because the abundant PGISs are available. Simulation results show that the approximation error when finite digits are used to represent the irrational coefficients of a normalized PGIS can be relatively small compared with the noise. This contributes to the simplicity of this scheme's implementation. With the fast development of IoT (internet of things), the adaptation and applicability of the proposed scheme to IoT platforms are also addressed, where lightweight cryptographic functions are preferable due to the limited resources of IoT devices.

A Review Study of Prime Period Perfect Gaussian Integer Sequences

“…With the above mentioned significant results of theoretical PGIS study and matured construction techniques, exploring the application of PGIS has gradually become a new research topic [14,15,[31][32][33]. In [14], a PGIS was applied to orthogonal-frequency division multiplexing (OFDM) systems for peak-to-average power ratio (PAPR) reduction.…”

“…A code division multiple access (CDMA) scheme based on PGIS, called the PGIS-CDMA system, was developed by Chang [31], where a set of PGISs could substitute and outperform the PN codes (e.g., m-sequences, Gold sequences, Kasami sequences, and bent sequences) in a direct sequence (DS) CDMA system. A new application of the PGIS to cryptography referred to [32], in which a hybrid public/private key cryptography scheme based on the PGIS of period N = pq was proposed. This hybrid cryptosystem can take advantage of public and private-key systems, and it is with implementation simplicity for easy adaptation to an IoT platform.…”

Novel Zero Circular Convolution Sequences for Detection and Channel Estimations

“…The next step should be exploring the PGIS applications. Currently there are four PGIS applications can be traced in the literature [13], [14], [18], [36]. In [13], a PGIS was applied to OFDM systems for PAPR reduction.…”

Novel location permutation encryption based on exponential numbers

“…National institute of standards and technology (NIST) initiated a project to solicit, evaluate, and standardize lightweight cryptographic algorithms in Lightweight Cryptography Workshop 2015, and 10 finalists were announced in March 2021 1 . A novel trapdoor one-way permutation function based on operating circular convolution over perfect Gaussian integer sequences (PGISs) was proposed in Reference 2 . With this property, a hybrid public/private key cryptography scheme based on PGIS can serve as the candidate of lightweight cryptographic function 2 .…”

“…A novel trapdoor one-way permutation function based on operating circular convolution over perfect Gaussian integer sequences (PGISs) was proposed in Reference 2 . With this property, a hybrid public/private key cryptography scheme based on PGIS can serve as the candidate of lightweight cryptographic function 2 . More properties, construction and applications of PGISs can refer to References [3][4][5][6][7][8] .…”