Sparse polynomial multiplication for lattice-based cryptography with small complexity

Akleylek, Sedat; Alkım, Erdem; Tok, Zaliha Yüce

doi:10.1007/s11227-015-1570-1

Cited by 8 publications

(6 citation statements)

References 16 publications

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“…The new method also improves the speed by simplifying the overall computational procedure. The idea of considering both positive and negative coefficients for pattern searching was first proposed in [22] in the context of ideal lattices over a quotient ring…”

Section: Signed Sliding Window Methods For Ntruencryptmentioning

confidence: 99%

“…where p is prime and N is a power of 2. In [22], however, side-channel countermeasures were not considered, and the convolution algorithm (Algorithm 3 in [22]) performed the computations in a separable fashion, as in [20].…”

Section: Signed Sliding Window Methods For Ntruencryptmentioning

confidence: 99%

“…However, it can be covered by a slight modification of Algorithm 3. The application of the index-based multipli-cation and sliding window method to a ring Z q [X]/(X N +1) was studied in [22]. We expect that the proposed method may also be applicable to the NTRU Prime key encapsulation mechanism [36] with a proper modification to support its ring structure Z[X]/(X N −X −1), as NTRU Prime also requires multiplication with ternary polynomials.…”

Section: Application Of Proposed Methodsmentioning

confidence: 99%

“…This improvement enables us to apply side-channel countermeasures to sliding window-based convolutions. The idea of considering both positive and negative coefficients for pattern searching was proposed in [22] for ideal lattices. However, side-channel countermeasures were not considered in [22].…”

Section: Introductionmentioning

confidence: 99%

“…The idea of considering both positive and negative coefficients for pattern searching was proposed in [22] for ideal lattices. However, side-channel countermeasures were not considered in [22]. To the best of our knowledge, the proposed method is the first method that provides a sliding window-based convolution with side-channel resistance.…”

Section: Introductionmentioning

confidence: 99%

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Efficient and Secure Implementation of NTRUEncrypt Using Signed Sliding Window Method

Kim

Lee

2020

IEEE Access

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NTRUEncrypt is a public key cryptosystem based on hard problems over lattices. The dominant operation in NTRUEncrypt is convolution, i.e., multiplication over a quotient ring of polynomials. Based on the fact that a convolution has a highly regular structure, Lee et al. proposed the sliding window method for fast convolution of binary polynomials in 2013, which was then extended to ternary polynomials for ideal lattices by Akleylek, Alkim, and Tok in 2016. These sliding window methods reduce the cost of a convolution operation using look-up tables that store partial computation results related to repeated coefficient patterns. In this paper, we propose a signed sliding window method with side-channel resistance for NTRUEncrypt. The proposed method considers both positive and negative nonzero coefficients when constructing look-up tables. The new method not only accelerates convolution but also enables the application of power analysis countermeasures effectively. According to the experimental results, the constant-time implementation of the proposed method with timing and power analysis countermeasures accelerates the previously developed secure convolution method by up to 20%.

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Section: Signed Sliding Window Methods For Ntruencryptmentioning

confidence: 99%

Section: Signed Sliding Window Methods For Ntruencryptmentioning

confidence: 99%

Section: Application Of Proposed Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient and Secure Implementation of NTRUEncrypt Using Signed Sliding Window Method

Kim

Lee

2020

IEEE Access

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Post‐quantum cryptography techniques for secure communication in resource‐constrained Internet of Things devices: A comprehensive survey

Kumari

Singh

et al. 2022

Softw Pract Exp

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As the number and characteristics of smart devices change, the concept of the Internet of Things (IoT) emerges. The IoT provides the connected devices with a variety of resources that enable effective communication. At this point, several security issues arise to get the sensitive information behind every communication in the IoT. To provide users with security and privacy, cryptographic schemes are adopted, the most popular being public key cryptographic systems (PKC). However, with the advent of quantum computing, the level of security that can be provided by the PKC schemes is a big question. Another important issue is that the IoT environment is resource-constrained, which necessitates the implementation of lightweight cryptographic algorithms for better security. In response to these issues, the post-quantum cryptographic (PQC) schemes are one of the significant developments contributing to IoT security in the post-quantum world. This article examines the key security issues in the IoT environment and examines the effective solutions found in the literature. The problems in IoT in the quantum era are discussed and appropriate solutions by PKC schemes under limited resources in IoT are focused. As the lattice-based cryptosystems are more effective, the importance of these schemes

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LizarMong: Excellent Key Encapsulation Mechanism Based on RLWE and RLWR

Jung

Lee

et al. 2020

Lecture Notes in Computer Science

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Sparse polynomial multiplication for lattice-based cryptography with small complexity

Cited by 8 publications

References 16 publications

Efficient and Secure Implementation of NTRUEncrypt Using Signed Sliding Window Method

Efficient and Secure Implementation of NTRUEncrypt Using Signed Sliding Window Method

Post‐quantum cryptography techniques for secure communication in resource‐constrained Internet of Things devices: A comprehensive survey

LizarMong: Excellent Key Encapsulation Mechanism Based on RLWE and RLWR

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