High-Speed RLWE-Oriented Polynomial Multiplier Utilizing Karatsuba Algorithm

Wong, Zheng-Yan; Wong, Denis C. K.; Lee, Wai-Kong; Mok, Kai-Ming

doi:10.1109/tcsii.2020.3049002

Cited by 17 publications

(4 citation statements)

References 7 publications

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“…In Wong et al (2021), an improved SPMA‐Karatsuba (schoolbook polynomial multiplication method) architecture was developed, along with a unique technique for implementing negacyclic convolution. It is claimed that the suggested design is more than 2.09 times quicker at the expense of 96.06% more hardware resources than the state‐of‐the‐art SPMA architecture.…”

Section: Post‐quantum Based Approaches For Edge Computing Securitymentioning

confidence: 99%

A survey on post‐quantum based approaches for edge computing security

Karakaya,

Ulu

2024

WIREs Computational Stats

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With the development of technology and its integration with scientific realities, computer systems continue to evolve as infrastructure. One of the most important obstacles in front of quantum computers with high‐speed processing is that its existing systems cause security vulnerabilities. Therefore, in order to take advantage of quantum systems, existing systems that are already secure must also be secure in the post‐quantum scenario. One of these systems is edge computing. There are challenges in terms of computational power for the implementation of pre‐ and post‐quantum methods in structures with resource‐constrained devices. This article reviews the post‐quantum security threats of edge devices and systems and the secure methods developed for them. Although there is relatively little research in this field, it remains relevant. In the studies reviewed, lattice‐based approaches are often highlighted for making edge systems quantum‐resistant. Additionally, these studies indicate that there has been an increasing trend in this field in recent years.This article is categorized under: Applications of Computational Statistics > Defense and National Security Algorithms and Computational Methods > Networks and Security

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Section: Post‐quantum Based Approaches For Edge Computing Securitymentioning

confidence: 99%

A survey on post‐quantum based approaches for edge computing security

Karakaya,

Ulu

2024

WIREs Computational Stats

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“…The Karatsuba Algorithm is analyzed by recursive sub-partitioning of the input integers to the base case, typically the single digit. This method is the backbone of the device that will form its products as an intermediary [7]. By recalling the algorithm's procedure, the polynomial's underlying structure is exposed, which eases the multiplication and, therefore, the tedious task.…”

Section: Algorithm Implementationmentioning

confidence: 99%

Efficiency of large integer multiplication algorithms: A comparative study of traditional methods and Karatsuba's algorithm

Zhang

2024

ACE

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The large integer multiplication is the basis of many computer science algorithms, ranging from cryptography to complex calculations in various scientific fields. Contemporary society excessively depends on complex computing tasks. Hence, the need for good algorithms is becoming increasingly apparent as well. This text gives the reader an in-depth knowledge of the multiplication algorithms of large integers by contrasting traditional algorithms with the new Algorithm developed by Karatsuba. This research methodology involves a comparative analysis of the components using an advanced analysis framework that primarily focuses on execution times, efficiency metrics, and resource utilization. Incontrovertibly, the experimental results confirm the Karatsuba algorithm's undoubted hastiness compared to the conventional approaches. This study extends our grasp of the evolution of algorithms in computational optimization, enabling people to get unique and relevant findings that will benefit numerous areas where large integer multiplications are involved. In addition to these findings, the study also highlights the importance of algorithm selection in ensuring computational efficiency and accuracy in large integer multiplications across various applications.

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“…Note that in majority of the lattice-based cryptography, including NTRU, polynomial convolution is the most time consuming operation with a computational O(N 2 ), where N refers to the degree of polynomial. Due to this reason, a number of hardware architectures were proposed recently to accelerate the polynomial convolution on FPGA [23], [24]. Such approaches can drastically reduce the computation time of the underlying lattice-based cryptographic schemes, but they also introduce significant hardware consumption.…”

Section: B Polynomial Convolution In Cryptographymentioning

confidence: 99%

Cryptensor: A Resource-Shared Co-processor to Accelerate Convolutional Neural Network and Polynomial Convolution

See¹,

Ng²,

Tan³

et al. 2022

Preprint

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<p>Practical deployment of convolutional neural net?work (CNN) and cryptography algorithm on constrained devices are challenging due to the huge computation and memory requirement. Developing separate hardware accelerator for AI and cryptography incur large area consumption, which is not desirable in many applications. This paper proposes a viable solution to this issue by expressing the CNN and cryptography as Generic-Matrix-Multiplication (GEMM) operations and map them to the same accelerator for reduced hardware consumption. A novel systolic tensor array (STA) design was proposed to reduce the data movement, effectively reducing the operand registers by 2×. Two novel techniques, input layer extension and polynomial factorization, are proposed to mitigate the under-utilization issue found in existing STA architecture. Additionally, the Tensor Processing Element (TPE) is fused using DSP unit to reduce the Look-Up Table (LUT) and Flip-Flops (FF) consumption for implementing multipliers. On top of that, a novel memory efficient factorization technique is proposed to allow computation of polynomial convolution on the same STA. Experimental results show that Cryptensor achieved 22.3% better throughput for VGG-16 implementation on XC7Z020 FPGA; 95.0% lesser LUT when implementing on XC7Z045 compared to state-of-the-art result. Cryptensor can also flexibly support multiple security levels in NTRU scheme, with no additional hardware. The proposed hardware unifies the computation of two different domains that are critical for IoT applications, which greatly reduces the hardware consumption on edge nodes. </p>

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High-Speed RLWE-Oriented Polynomial Multiplier Utilizing Karatsuba Algorithm

Cited by 17 publications

References 7 publications

A survey on post‐quantum based approaches for edge computing security

A survey on post‐quantum based approaches for edge computing security

Efficiency of large integer multiplication algorithms: A comparative study of traditional methods and Karatsuba's algorithm

Cryptensor: A Resource-Shared Co-processor to Accelerate Convolutional Neural Network and Polynomial Convolution

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