An Extensive Study of Flexible Design Methods for the Number Theoretic Transform

Mert, Ahmet Can; Karabulut, Emre; Öztürk, Erdinç; Savaş, Erkay; Aysu, Aydın

doi:10.1109/tc.2020.3017930

Cited by 44 publications

(20 citation statements)

References 39 publications

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“…An extensive and promising analysis of NTT is performed in [3], a follow-up paper from the authors of [2], where it analyzes all available optimizations of hardware in literature and compares parametric designs between hardware and HLS. This paper re-constructs the software code, for optimal use of the HLS tool, using the corresponding HLS pragmas.…”

Section: Number Theoretic Transform (Ntt) a Definitionsmentioning

confidence: 99%

“…The complexity of such a task indicates that the HLS tool design path can be a good alternative to traditional RTL design. Several researchers have shown that such an approach does have merit and can lead to good results as long as the right pragmas are used [1] [2] [3].…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, an NTT design approach for HLS tools is proposed that manages to minimize the dependency between NTT processing elements and increase the access of these element to memory by forcing the HSL tool to use dual port RAMs. After initially testing the configuration capabilities of openCL NTT code (using the highly constrained number of openCL attributes) that did not manage to produce efficient results, we introduce in the paper a reformulation of C/C++ NTT code, initially using the design approach of [3] and then further optimizing this approach by adapting the FFTbased technique described in [6] in the NTT domain. As a result of this effort, two architectures are presented in this paper, the initial and an optimized/proposed architecture.…”

Section: Introductionmentioning

confidence: 99%

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High-Level Synthesis design approach for Number-Theoretic Transform Implementations

El-Kady

Fournaris

Tsakoulis

et al. 2021

2021 IFIP/IEEE 29th International Conference on Very Large Scale Integration (VLSI-SoC)

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Lattice-based cryptography performs polynomial multiplication using the Number Theoretic Transform (NTT), in order to reduce the polynomial multiplication complexity from O(n 2 ) to O(n log n). NTT has been in the center of investigation in cryptography space, as it is applied in many cryptography schemes such as hash functions, homomorphic encryption, keyencapsulation mechanisms, and digital signatures. A common approach for rapid production of hardware designs commences from semi-automatic software production, as supported by the Xilinx High-Level Synthesis (HLS) toolchain or similar tools. Most of the times this approach requires careful modifications (e.g. code modification, loop reordering, loop flattening, removing dependencies, loop pipelining, loop unrolling) in order to achieve a design with performance comparable to a Register-Transfer Level (RTL) hand-crafted design. In this paper a design solution is proposed that solves the data and loop-carry dependencies of the Cooley-Tukey NTT algorithm, by assisting the HLS synthesizer to produce efficient designs, in terms of latency and resources. The proposed work has been evaluated using the Dilithium digital-signature scheme NTT version (n = 256, Q of 23 bits), and is shown to achieve a 20-50% improvement in terms of latency (without really affecting the resources) compared to other existing HLS-based NTT solutions in the literature.

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Section: Number Theoretic Transform (Ntt) a Definitionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

High-Level Synthesis design approach for Number-Theoretic Transform Implementations

El-Kady

Fournaris

Tsakoulis

et al. 2021

2021 IFIP/IEEE 29th International Conference on Very Large Scale Integration (VLSI-SoC)

View full text Add to dashboard Cite

show abstract

“…For the ternary Golay codes, the extended Golay code has parameters G(N = 12, k = 6, d = 6) over GF (3). The new geometric space can be constructed by taking now a new ensemble of "representative complex points" according to:…”

Section: Geometrical Representation Of the Ternary Golay Transformmentioning

confidence: 99%

“…Discrete transforms defined over a finite field are signal processing tools capable of providing Fourier analysis [1], [2], [3] while operating in error-free structure. Because its arithmetic is performed in a finite field, fixed-point implementations can provide exact computation and simple hardware requirements.…”

Section: Introductionmentioning

confidence: 99%

Geometrical Representation for Number-theoretic Transforms

Oliveira¹,

Cintra²

2020

Anais De XXXVIII Simpósio Brasileiro De Telecomunicações E Processamento De Sinais

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This short note introduces a geometric representation for binary (or ternary) sequences. The proposed representation is linked to multivariate data plotting according to the radar chart. As an illustrative example, the binary Hamming transform recently proposed is geometrically interpreted. It is shown that codewords of standard Hamming code H(N = 7, k = 4, d = 3) are invariant vectors under the Hamming transform. These invariant are eigenvectors of the binary Hamming transform. The images are always inscribed in a regular polygon of unity side, resembling triangular rose petals and/or "thorns". A geometric representation of the ternary Golay transform, based on the extended Golay G(N = 12, k = 6, d = 6) code over GF(3) is also showed. This approach is offered as an alternative representation of finite-length sequences over finite prime fields.

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A Monolithic Hardware Implementation of Kyber: Comparing Apples to Apples in PQC Candidates

Bisheh-Niasar

Azarderakhsh

Kermani

2021

Lecture Notes in Computer Science

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An Extensive Study of Flexible Design Methods for the Number Theoretic Transform

Cited by 44 publications

References 39 publications

High-Level Synthesis design approach for Number-Theoretic Transform Implementations

High-Level Synthesis design approach for Number-Theoretic Transform Implementations

Geometrical Representation for Number-theoretic Transforms

A Monolithic Hardware Implementation of Kyber: Comparing Apples to Apples in PQC Candidates

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