NTRU cryptosystem: Recent developments and emerging mathematical problems in finite polynomial rings

Steinfeld, Ron

doi:10.1515/9783110317916.179

Cited by 13 publications

(6 citation statements)

References 68 publications

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“…Before we deal with the analysis of security infrastructure, it should be noted that the proposed method is based on algebraic infrastructure in the classic version of the NTRU. We can easily define the proposed authentication method based on its optimized versions .…”

Section: Analysis Of the Proposed Schemementioning

confidence: 99%

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Quantum-resistance authentication in centralized cognitive radio networks

Bakhtiari

Hosseinzadeh

2016

Security Comm. Networks

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This paper presents a new method for mutual authentication in centralized cognitive radio networks. In doing so, we analyzed the proposed scheme in terms of security and performance. As for security, we analyzed the proposed scheme from a mathematical standpoint, validated the authentication method using automated validation of Internet security protocols and applications, provided formal verification using the BAN logic, and demonstrated the resistance of the propounded model against different attacks. The performance analysis considered the cost of computation, costs of storage and communication, and also the number of cryptographic operations. This scheme has some advantages over the existing methods: First, it uses the existing and free facilities in the physical layer and medium access control and does not need independent resources; second, the proposed scheme enjoys a high speed because its operations work at the hardware level with less computational complexity compared with the conventional methods; third, the proposed model is well consistent with the underlying conditions in radio environments and is resistant against relevant attacks; and fourth, unlike the conventional methods, it provides quantum resistance, and its security is based on the hardness of the shortest vector problem in lattices.

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Section: Analysis Of the Proposed Schemementioning

confidence: 99%

“…Moreover, given the NP‐hard nature of the SVP problem, this is impossible unless there occurs a rare event in mathematics and the complexity theory. The latest research regarding NTRU security shows that the cyclic structure in the NTRU lattice is not useful for the simplicity of the NTRU .…”

Section: Analysis Of the Proposed Schemementioning

confidence: 99%

Quantum-resistance authentication in centralized cognitive radio networks

Bakhtiari

Hosseinzadeh

2016

Security Comm. Networks

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“…It has been shown that fully homomorphic encryption (FHE) [21] schemes can be designed from NTRU [36], [41], [42]. The design, analysis and implementation of FHE is an active research area at the moment.…”

Section: Concl Usionmentioning

confidence: 99%

Analytical study of implementation issues of NTRU

Gauravaram

Narumanchi

Emmadi

2014

2014 International Conference on Advances in Computing, Communications and Informatics (ICACCI)

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N th -Dimensional Truncated Polynomial Ring (NTRU) is a lattice-based public-key cryptosystem that offers encryption and digital signature solutions. It was designed by Silverman, Hoffstein and Pipher. The NTRU cryptosystem was patented by NTRU Cryptosystems Inc. (which was later acquired by Security Innovations) and available as IEEE 1363.1 and X9.98 standards. NTRU is resistant to attacks based on Quantum computing, to which the standard RSA and ECC public-key cryptosystems are vulnerable to. In addition, NTRU has higher performance advantages over these cryptosystems.Considering this importance of NTRU, it is highly recommended to adopt NTRU as part of a cipher suite along with widely used cryptosystems for internet security protocols and applications. In this paper, we present our analytical study on the implementation of NTRU encryption scheme which serves as a guideline for security practitioners who are novice to latticebased cryptography or even cryptography. In particular, we show some non-trivial issues that should be considered towards a secure and efficient NTRU implementation.

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“…[9,10,14]) and is believed to remain secure in the presence of quantum computers. See the survey [23] for a complete description of the NTRU cryptosystem and its applications. In this paper, we consider the overstretched NTRU variant in the cyclotomic field K = Q[x]/(x n +1), with n a power of 2.…”

Section: Introductionmentioning

confidence: 99%

Characterizing overstretched NTRU attacks

Micheli

Heninger

Shani

2020

Journal of Mathematical Cryptology

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AbstractOverstretched NTRU is a variant of NTRU with a large modulus. Recent lattice subfield and subring attacks have broken suggested parameters for several schemes. There are a number of conflicting claims in the literature over which attack has the best performance. These claims are typically based on experiments more than analysis. In this paper, we argue that comparisons should focus on the lattice dimension used in the attack. We give evidence, both analytically and experimentally, that the subring attack finds shorter vectors and thus is expected to succeed with a smaller dimension lattice than the subfield attack for the same problem parameters, and also to succeed with a smaller modulus when the lattice dimension is fixed.

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NTRU cryptosystem: Recent developments and emerging mathematical problems in finite polynomial rings

Cited by 13 publications

References 68 publications

Quantum-resistance authentication in centralized cognitive radio networks

Quantum-resistance authentication in centralized cognitive radio networks

Analytical study of implementation issues of NTRU

Characterizing overstretched NTRU attacks

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