SIKE on GPU: Accelerating Supersingular Isogeny-Based Key Encapsulation Mechanism on Graphic Processing Units

Seo, Seog Chung

doi:10.1109/access.2021.3106551

Cited by 8 publications

(4 citation statements)

References 17 publications

(32 reference statements)

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“…There have been multiple pieces of research on PQC implementation in a GPU environment [13][14][15][16][17][18]. Gupta et al (2020) [13] proposed the techniques that allow PQC-based KEM algorithms such as FrodoKEM, NewHope, and CRYSTALS-Kyber to run fast on GPU.…”

Section: Related Workmentioning

confidence: 99%

“…Furthermore, Seong et al (2021) [15] introduced a parallel operation structure for the server to efficiently process the key exchange protocol in a multi-client environment via the NTRU algorithm. Moreover, PQC-based KEM algorithms such as Saber, SIKE, and NTRU have been examined on GPU [16][17][18]. Although certain studies have implemented latticebased PQC in GPU environments, these only focused on the optimization of polynomial multiplication such as parallelizing the NTT-based polynomial multiplications [13,14], and [16].…”

Section: Related Workmentioning

confidence: 99%

“…Many studies [10][11][12] demonstrated that optimized cryptographic software with GPUs can achieve an impressive throughput enhancement compared with conventional software operating on the central processing unit (CPU). Certain studies [13][14][15][16][17][18] have been conducted on PQC to improve its performance using GPUs.…”

Section: Introductionmentioning

confidence: 99%

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Accelerating Falcon Post-Quantum Digital Signature Algorithm on Graphic Processing Units

Seo¹,

An²,

Choi³

2023

Computers, Materials &Amp; Continua

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Since 2016, the National Institute of Standards and Technology (NIST) has been performing a competition to standardize post-quantum cryptography (PQC). Although Falcon has been selected in the competition as one of the standard PQC algorithms because of its advantages in short key and signature sizes, its performance overhead is larger than that of other lattice-based cryptosystems. This study presents multiple methodologies to accelerate the performance of Falcon using graphics processing units (GPUs) for server-side use. Direct GPU porting significantly degrades performance because the Falcon reference codes require recursive functions in its sampling process. Thus, an iterative sampling approach for efficient parallel processing is presented. In this study, the Falcon software applied a fine-grained execution model and reported the optimal number of threads in a thread block. Moreover, the polynomial multiplication performance was optimized by parallelizing the number-theoretic transform (NTT)-based polynomial multiplication and the fast Fourier transform (FFT)-based multiplication. Furthermore, dummy-based parallel execution methods have been introduced to handle the thread divergence effects. The presented Falcon software on RTX 3090 NVIDA GPU based on the proposed methods with Falcon-512 and Falcon-1024 parameters outperform at 35.14, 28.84, and 34.64 times and 33.31, 27.45, and 34.40 times, respectively, better than the central processing unit (CPU) reference implementation using Advanced Vector Extensions 2 (AVX2) instructions on a Ryzen 9 5900X running at 3.7 GHz in key generation, signing, and verification, respectively. Therefore, the proposed Falcon software can be used in servers managing multiple concurrent clients for efficient certificate verification and be used as an outsourced key generation and signature generation server for Signature as a Service (SaS).

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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Accelerating Falcon Post-Quantum Digital Signature Algorithm on Graphic Processing Units

Seo¹,

An²,

Choi³

2023

Computers, Materials &Amp; Continua

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“…Similar to AVX, research on cryptographic algorithm optimization using GPU architecture has been published. In the case of NIST PQC optimization research using GPU, various approaches were proposed, including a PQC internal function parallel method and a PQC internal function acceleration method using GPU Tensor Core [24][25][26][27][28][29][30]. In addition, research on ECC using GPU architecture is continuously being conducted [31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Parallel Implementation of Lightweight Secure Hash Algorithm on CPU and GPU Environments

Choi,

Seo

2024

Electronics

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Currently, cryptographic hash functions are widely used in various applications, including message authentication codes, cryptographic random generators, digital signatures, key derivation functions, and post-quantum algorithms. Notably, they play a vital role in establishing secure communication between servers and clients. Specifically, servers often need to compute a large number of hash functions simultaneously to provide smooth services to connected clients. In this paper, we present highly optimized parallel implementations of Lightweight Secure Hash (LSH), a hash algorithm developed in Korea, on server sides. To optimize LSH performance, we leverage two parallel architectures: AVX-512 on high-end CPUs and NVIDIA GPUs. In essence, we introduce a word-level parallel processing design suitable for AVX-512 instruction sets and a data parallel processing design appropriate for the NVIDIA CUDA platform. In the former approach, we parallelize the core functions of LSH using AVX-512 registers and instructions. As a result, our first implementation achieves a performance improvement of up to 50.37% compared to the latest LSH AVX-2 implementation. In the latter approach, we optimize the core operation of LSH with CUDA PTX assembly and apply a coalesced memory access pattern. Furthermore, we determine the optimal number of blocks/threads configuration and CUDA streams for RTX 2080Ti and RTX 3090. Consequently, in the RTX 3090 architecture, our optimized CUDA implementation achieves about a 180.62% performance improvement compared with the initially ported LSH implementation to the CUDA platform. As far as we know, this is the first work on optimizing LSH with AVX-512 and NVIDIA GPU. The proposed implementation methodologies can be used alone or together in a server environment to achieve the maximum throughput of LSH computation.

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Accelerating Falcon on ARMv8

2022

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Falcon is one of the promising digital-signature algorithms in NIST's ongoing Post-Quantum Cryptography (PQC) standardization finalist. Computational efficiency regarding software and hardware is also the main criteria for PQC standardization. In this paper, we present an efficient Falcon software implementation on ARMv8 environment. Until now, most of the software optimization on PQC algorithms have been conducted on 32-bit ARM (Cortex-M4) and typical CPUs (Intel and AMD CPUs). However, ARMv8 including Cortex-A30, 50, and 70 series have been widely used for various IoT (Internet of Things) applications, Edge computing devices, and OBUs (On Board Units) in autonomous driving cars. For optimizing the performance of Falcon, we take full advantage of NEON engine which is a kind of parallel processing unit in ARMv8 MCU. The main computation in Falcon belongs to polynomial multiplications in Complex number domain and Integer domain. Typically, FFT (Fast Fourier Transformation)-based multiplication method and NTT (Number Theoriteic Transform)-based multiplication method have been widely used for efficient polynomial multiplications in Complex number domain and Integer domain, respectively. Thus, in order to enhance the overall performance of Falcon, we improve the FFT-based multiplication method and NTT-based multiplication method by utilizing NEON engine in ARMv8. Specifically, we parallelize the overall process (FFT/NTT transformation, pointwise multiplication, and inverse FFT/NTT transformation) of FFT-based polynomial multiplication method and NTT-based polynomial multiplication method with strategically utilizing the NEON engine and vector instructions. Furthermore, we minimize the number of redundant memory accesses during FFT/NTT-based polynomial multiplication by making the most of available registers in NEON engine. Through the proposed parallel FFT/NTT-based polynomial multiplications, the proposed Falcon software provides 15.1% (resp. 18.1%), 16.5% (resp. 17.1%), and 65.4% (resp. 69.4%) of performance improvement in keypair generation, signing, and verification at security level 1 (resp. 5) compared with the reference Falcon implementation submitted to the final round of NIST PQC competition. Furthermore, as far as we know, this is the first optimized implementation of Falcon on ARMv8 environment.

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SIKE on GPU: Accelerating Supersingular Isogeny-Based Key Encapsulation Mechanism on Graphic Processing Units

Cited by 8 publications

References 17 publications

Accelerating Falcon Post-Quantum Digital Signature Algorithm on Graphic Processing Units

Accelerating Falcon Post-Quantum Digital Signature Algorithm on Graphic Processing Units

Parallel Implementation of Lightweight Secure Hash Algorithm on CPU and GPU Environments

Accelerating Falcon on ARMv8

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