D-NTRU: More efficient and average-case IND-CPA secure NTRU variant

Wang, Baocang; Lei, Hao; Hu, Yupu

doi:10.1016/j.ins.2018.01.037

Cited by 14 publications

(36 citation statements)

References 4 publications

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“…In spite of the big numbers, f and r, meeting (36) used in RCPKC, it guarantees that the decryption correctness condition (15) holds (see (39)) due to the use of Conditions (33), (36), (38), (46) and (50) instead of Conditions 7, (11), and (12), used in the original insecure CPKC (see Sections 3.3-3.3.2) considered in [26]. It was found that the insecurity of the original CPKC stems from the use of Conditions (7), (11) and (12), defining smaller than √ q numbers f , g, m, r meeting Minkowski's boundary (27) and the decryption correctness condition (15).…”

Section: Discussionmentioning

confidence: 99%

“…Since qLen > mgLen by definition (38), Succ OW RCPKC (A 1 , P ) decreases exponentially in qLen, and Assumption 1 holds. Similarly, the attacker can try the following methods with an exponentially decreasing success probability: Furthermore, the adversary can apply the GLR attack to get ( f , g).…”

Section: Rcpkc Asymmetric Encryption Padding and Its Ind-cca2 Securitymentioning

confidence: 98%

“…The private key components, ( f , g), meet (8), (9), (33) and (34), where qLen, mgLen meet (38) and (43), where (F, G) is an SV obtained in the result of the GLR attack on the lattice E(V1, V2) defined by (24). The public key component, h, is defined by (10).…”

Section: Rcpkc1 Definitionmentioning

confidence: 99%

“…The private key components, ( f , g), meet (8), (9), (33), (34) and (52), where qLen, mgLen meet (38) and (43) The public key component, h, is defined by (10). Message, m, meets (33), and random integer, r, is selected from the range defined in (46), (47) and (50).…”

Section: Rcpkc2 Proposalmentioning

confidence: 99%

“…NTRU and its known variants [7,8,[19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38], shown in Section 2, work with degree N polynomials. The main problem NTRU faces is that it is susceptible to the lattice basis reduction attack (LBRA) using the Gaussian lattice reduction (GLR) algorithm for two-dimensional lattices and the LLL algorithm for higher dimensions [39].…”

Section: Introductionmentioning

confidence: 99%

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NTRU-Like Random Congruential Public-Key Cryptosystem for Wireless Sensor Networks

Ibrahim

Chefranov

Hamad

et al. 2020

Sensors

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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 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.

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