Efficient arithmetic for lattice-based cryptography on GPU using the CUDA platform

Akleylek, Sedat; Tok, Zaliha Yüce

doi:10.1109/siu.2014.6830364

Cited by 12 publications

(2 citation statements)

References 5 publications

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“…We choose p ¼ 49201153 satisfying p 1 ðmod 2nÞ. We implement parallelized schoolbook method, CUDA Fast Fourier Transform (cuFFT) based multiplication (one can also call this Number Theoretic Transform) [9] and interleaved Montgomery modular multiplication method. We generate the random data on the GPU.…”

Section: Resultsmentioning

confidence: 99%

Efficient interleaved Montgomery modular multiplication for lattice-based cryptography

Akleylek

Tok

2014

IEICE Electron. Express

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In this paper, we give modified version of interleaved Montgomery modular multiplication method for lattice-based cryptography. With the proposed algorithms, we improve the multiplication complexity and embed the conversion operation into the algorithm with almost free cost. We implement the proposed methods for the quotient ring (Z/qZ)[x]/ (x n − 1) and (Z/pZ)[x]/(x n + 1) on the GPU (NVIDIA Quadro 600) using the CUDA platform. NTRUEncrypt is accelerated approximately 35% on the GPU by using the proposed method. We receive at least 19% improvement with the proposed method for the polynomial multiplication in (Z/pZ)[x]/ (x n + 1), where n ∈ f1024, 2048, 4096g.

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Section: Resultsmentioning

confidence: 99%

Efficient interleaved Montgomery modular multiplication for lattice-based cryptography

Akleylek

Tok

2014

IEICE Electron. Express

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“…That is, the multiplications are performed using exactly N coefficients, and all arithmetic operations are performed with integer variables. This optimization technique is frequently used for lattice-based PQC algorithms [34], [40]- [42], [56], but it is not applicable to NTRUEncrypt, as NTRUEncrypt is based on Z q [X]/(X N − 1), where q = 2048. However, in an environment where NTT is available, the proposed method and index-based multiplication must compete against NTT, which is more efficient than the original FFT.…”

Section: Application Of Proposed Methodsmentioning

confidence: 99%

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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Accelerating Number Theoretic Transform in GPU Platform for qTESLA Scheme

Lee

Akleylek

Yap

et al. 2019

Information Security Practice and Experience

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Efficient arithmetic for lattice-based cryptography on GPU using the CUDA platform

Cited by 12 publications

References 5 publications

Efficient interleaved Montgomery modular multiplication for lattice-based cryptography

Efficient interleaved Montgomery modular multiplication for lattice-based cryptography

Efficient and Secure Implementation of NTRUEncrypt Using Signed Sliding Window Method

Accelerating Number Theoretic Transform in GPU Platform for qTESLA Scheme

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