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NTRU-Like Random Congruential Public-Key Cryptosystem for Wireless Sensor Networks^{†}

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Department of Computer Systems Engineering, Palestine Technical University—Kadoorie, Tulkarm 7, Palestine

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Department of Computer Engineering, Eastern Mediterranean University, Famagusta 99628, North Cyprus via Mersin 10, Turkey

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Department of Information Technology, Palestine Technical University—Kadoorie, Tulkarm 7, Palestine

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Irbid National University, P.O. Box 2600, Irbid 21110, Jordan

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Department of Computer Information System, Hashemite University, P.O. Box 150459, Zarqa 13115, Jordan

^{6}

Federal University of Piauí, Teresina 64049-550, PI, Brazil

^{7}

Instituto de Telecomunicações, 6201-001 Covilhã, Portugal

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Author to whom correspondence should be addressed.

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This paper is an extended version of our paper published in Ibrahim, A.; Chefranov, A.; Hamad, N. NTRU-Like Secure and Effective Congruential Public-Key Cryptosystem Using Big Numbers. In Proceedings of the 2019 2nd International Conference on new Trends in Computing Sciences (ICTCS), Amman, Jordan, 9–11 October 2019; pp. 20–26.

Received: 17 April 2020 / Revised: 2 July 2020 / Accepted: 10 August 2020 / Published: 17 August 2020

(This article belongs to the Section Sensor Networks)

Wireless sensor networks (WSNs) are the core of the Internet of Things and require cryptographic protection. Cryptographic methods for WSN should be fast and consume low power as these networks rely on battery-powered devices and microcontrollers. NTRU, the fastest and secure public key cryptosystem, uses high degree, N, polynomials and is susceptible to the lattice basis reduction attack (LBRA). Congruential public key cryptosystem (CPKC), proposed by the NTRU authors, works on integers modulo q and is easily attackable by LBRA since it uses small numbers for the sake of the correct decryption. Herein, RCPKC, a random congruential public key cryptosystem working on degree $N=0$ polynomials modulo q, is proposed, such that the norm of a two-dimensional vector formed by its private key is greater than $\sqrt{q}$ . RCPKC works as NTRU, and it is a secure version of insecure CPKC. RCPKC specifies a range from which the random numbers shall be selected, and it provides correct decryption for valid users and incorrect decryption for an attacker using LBRA by Gaussian lattice reduction. RCPKC asymmetric encryption padding (RAEP), similar to its NTRU analog, NAEP, is IND-CCA2 secure. Due to the use of big numbers instead of high degree polynomials, RCPKC is about 27 times faster in encryption and decryption than NTRU. Furthermore, RCPKC is more than three times faster than the most effective known NTRU variant, BQTRU. Compared to NTRU, RCPKC reduces energy consumption at least thirty times, which allows increasing the life-time of unattended WSNs more than thirty times.