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Efficient interleaved Montgomery modular multiplication for lattice-based cryptography

Sedat Akleylek, Zaliha Yüce Tok
2014 IEICE Electronics Express  
In this paper, we give modified version of interleaved Montgomery modular multiplication method for lattice-based cryptography.  ...  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.  ...  He perfomed this study while he was a postdoctoral researcher at Cryptography and Computer Algebra Group, TU Darmstadt.  ... 
doi:10.1587/elex.11.20140960 fatcat:hogmem5upncvrkblx5lg56l2za

Efficient Parallel Implementations of LWE-Based Post-Quantum Cryptosystems on Graphics Processing Units

SangWoo An, Seog Chung Seo
2020 Mathematics  
In the case of NewHope, we present a parallel processing technique for polynomial-based operations.  ...  For each algorithm, we present a part that can perform parallel processing of major operations with a large computational load using the characteristics of the GPU.  ...  Background Overview of Lattice-Based Cryptography Lattice-based cryptography refers to an algorithm that bases the basic components of cryptography on a computational lattice problem.  ... 
doi:10.3390/math8101781 fatcat:visl2xkcynelzcngizoiqvyo6e

TensorCrypto [article]

Wai-Kong Lee, Hwajeong Seo, Zhenfei Zhang, Seongoun Hwang
2021 IACR Cryptology ePrint Archive  
In this paper, we show that for the first time, tensor core can be used to accelerate state-of-the-art lattice-based cryptosystems.  ...  With the introduction of tensor core, the matrix multiplication at low precision can be computed much faster than using conventional integer and floating point units in NVIDIA GPU.  ...  Lattice-based Cryptography Lattice-based cryptographic constructions are based on the hardness of Shortest Vector Problem (SVP) which is approximating the minimal Euclidian length of a lattice vector.  ... 
dblp:journals/iacr/LeeSZH21 fatcat:jxxglxovu5gw3nnhgbqwl7ft64

TensorCrypto: High Throughput Acceleration of Lattice-based Cryptography Using Tensor Core on GPU

Wai-Kong Lee, Hwajeong Seo, Zhenfei Zhang, Seong Oun Hwang
2022 IEEE Access  
In this paper, we show that for the first time, tensor core can be used to accelerate state-of-the-art lattice-based cryptosystems.  ...  The proposed tensorcore-based polynomial convolution technique was applied to NTRU, one of the finalists in NIST postquantum cryptography (PQC) standardization.  ...  LATTICE-BASED CRYPTOGRAPHY Lattice-based cryptographic constructions are based on the hardness of Shortest Vector Problem (SVP) which approximates the minimal Euclidean length of a lattice vector.  ... 
doi:10.1109/access.2022.3152217 fatcat:b3zkaen3pbg2pf5evcmu3a6nx4

Efficient NewHope Cryptography Based Facial Security System on a GPU

Phap Duong-Ngoc, Tuy Nguyen Tan, Hanho Lee
2020 IEEE Access  
For more information, see https://creativecommons.org/licenses/by/4.0/ VOLUME 8, 2020 P. Duong-Ngoc et al.: Efficient NewHope Cryptography-Based Facial Security System on a GPU FIGURE 1.  ...  The proposed facial security system was successfully accelerated using data-parallel computing model on the recently launched Nvidia GTX 2080Ti Graphics Processing Unit (GPU).  ...  We also concentrated on accelerating the NTT-based multiplication and color images processing, taking full advantage of parallel architecture on GPU platform.  ... 
doi:10.1109/access.2020.3000316 fatcat:q65ylsrh25fvbedbdk77fduzy4

GPU Implementation of Quantum Secure ABC Cryptosystem on Cuda

Sedat Akleylek, Ramazan Koyutürk, Hakan Kutucu
2021 International Workshop on Intelligent Information Technologies & Systems of Information Security  
We review the theoretical structure of the ABC cryptosystem and implement it on the GPU by using the NVIDIA CUDA technology.  ...  In this paper, we consider the ABC cryptosystem based on multivariate polynomial systems which is one of the post-quantum cryptosystems.  ...  Acknowledgement The first and second authors were partially supported by TÜBİTAK under grant no. EEEAG-116E279.  ... 
dblp:conf/intelitsis/AkleylekKK21 fatcat:aee4p77z4jh4rd6vji3ma3euva

DPCrypto: Acceleration of Post-quantum Cryptographic Algorithms using Dot-Product Instruction on GPUs [article]

Wai-Kong Lee, Hwajeong Seo, Seong Oun Hwang, Angshuman Karmakar, Jose Maria Bermudo Mera, Ramachandra Achar
2021 IACR Cryptology ePrint Archive  
In this paper, we show that the dot-product instruction can also be used to accelerate matrix-multiplication and polynomial convolution operations, which are commonly found in post-quantum lattice-based  ...  Since matrix-multiplication and polynomial convolution operations are the most time-consuming operations in lattice-based cryptographic schemes, our proposed techniques are likely to benefit other similar  ...  The main performance bottleneck in FrodoKEM comes from the matrix multiplication. Saber Saber is a lattice-based KEM which is based on module-lattices.  ... 
dblp:journals/iacr/LeeSHKMA21 fatcat:fztagcxp7jezhbrnttnn7pttpu

Parallel Shortest Lattice Vector Enumeration on Graphics Cards [chapter]

Jens Hermans, Michael Schneider, Johannes Buchmann, Frederik Vercauteren, Bart Preneel
2010 Lecture Notes in Computer Science  
To illustrate the algorithm, it was implemented on graphics cards using CUDA, a programming framework for NVIDIA graphics cards.  ...  Our implementation is almost 5 times faster in high lattice dimensions. Exhaustive search is one of the main building blocks for lattice basis reduction in cryptanalysis.  ...  We thankÖzgür Dagdelen for creating some of the initial ideas of parallelizing lattice enumeration and Benjamin Milde, Chen-Mou Cheng, and Bo-Yin Yang for the nice discussions and helpful ideas.  ... 
doi:10.1007/978-3-642-12678-9_4 fatcat:ewdokfhpmnakfk7rr5f2lchdxa

Efficient Number Theoretic Transform Implementation on GPU for Homomorphic Encryption [article]

Ozgun Ozerk, Can Elgezen, Ahmet Can Mert, Erdinç Öztürk, Erkay Savas
2021 IACR Cryptology ePrint Archive  
Lattice-based cryptography forms the mathematical basis for homomorphic encryption, which allows computation directly on encrypted data.  ...  (BFV) homomorphic encryption scheme implemented in Microsoft's SEAL homomorphic encryption library on GPU, all of which heavily depend on the NTT-based polynomial multiplication.  ...  NTT-based polynomial multiplication is, on the other hand, highly utilized in lattice-based cryptosystems and it reduces the O(n 2 ) computational complexity of the schoolbook polynomial multiplication  ... 
dblp:journals/iacr/OzerkEMOS21 fatcat:eljo7c73qjd27hlfahxgfmmliu

Lattice Enumeration on GPUs for fplll [article]

Simon Pohmann, Marc Stevens, Jens Zumbrägel
2021 IACR Cryptology ePrint Archive  
For this, we use the CUDA technology that provides an abstract language for programming GPUs.  ...  As this algorithm allows efficient parallel implementations, it is likely that implementing it on modern graphics processing units (GPUs) can significantly improve performance.  ...  Gram-Schmidt orthogonalization The CUDA programming model CUDA is a language extension of C++ that allows writing code for execution on GPUs [Nic+08] .  ... 
dblp:journals/iacr/PohmannSZ21 fatcat:bbt6mk6ucnad3axtwwe6djgfai

A Parallel Evolutionary Search for Shortest Vector Problem

Gholam Reza Moghissi, ICT Department, Malek-Ashtar University of Technology, Tehran, Iran, Ali Payandeh
2019 International Journal of Information Technology and Computer Science  
The hardness assumption of approximate shortest vector problem (SVP) within the polynomial factor in polynomial time reduced to the security of many lattice-based cryptographic primitives, so solving this  ...  The main drawback for these test results is the notsufficient tuning of various parameters for showing the potential strength of our contribution.  ...  The security in lattice based cryptography come from the hardness of the lattice problems, where SVP (Shortest Vector Problem) is the determinative one.  ... 
doi:10.5815/ijitcs.2019.08.02 fatcat:cf7tygpwxbeyfnhyf2z7udltay

Accelerating Polynomial Multiplication for Homomorphic Encryption on GPUs [article]

Kaustubh Shivdikar, Gilbert Jonatan, Evelio Mora, Neal Livesay, Rashmi Agrawal, Ajay Joshi, Jose Abellan, John Kim, David Kaeli
2022 arXiv   pre-print
For lattice-based HE to become viable for real-world systems, it is necessary for the key bottlenecks - particularly polynomial multiplication - to be highly efficient.  ...  In this paper, we present a characterization of GPU-based implementations of polynomial multiplication.  ...  A closely related operation to cyclic convolution is negacyclic convolution, which is widely known as polynomial multiplication in the context of lattice-based cryptography [47] .  ... 
arXiv:2209.01290v1 fatcat:f63oxa6g5fgwxphxb5yewzh72i

Post Quantum Cryptographic Keys Generated with Physical Unclonable Functions

Bertrand Cambou, Michael Gowanlock, Bahattin Yildiz, Dina Ghanaimiandoab, Kaitlyn Lee, Stefan Nelson, Christopher Philabaum, Alyssa Stenberg, Jordan Wright
2021 Applied Sciences  
This paper describes practical ways to generate keys from physical unclonable functions, for both lattice and code-based cryptography.  ...  Lattice and code cryptography can replace existing schemes such as elliptic curve cryptography because of their resistance to quantum computers.  ...  NTRU Cryptography Cryptographic algorithms such as FALCON, which uses NTRU (Nth degree of TRUncated polynomial ring) arithmetic, are also based on lattice cryptography.  ... 
doi:10.3390/app11062801 fatcat:qiz5udgplzdzxj7o3gk3le56hq

Comparison of RISC-V and transport triggered architectures for a post-quantum cryptography application [article]

Latif Akçay, Berna Örs Yalçin
2020 IACR Cryptology ePrint Archive  
Cryptography is one of the basic phenomena of security systems. However, some of the widely used publickey cryptography algorithms can be broken by using quantum computers.  ...  Therefore, many post-quantum cryptography algorithms are proposed in recent years to handle this issue. NTRU is one of the most important of these quantum-safe algorithms.  ...  NTRU public key cryptosystem NTRU is a lattice-based approach for public key cryptography and mainly uses polynomial addition and multiplication.  ... 
dblp:journals/iacr/AkcayO20 fatcat:j3xlehr4ojalzevnthue2kqvwq

Efficient computation of spherical harmonic transform using parallel architecture of CUDA

Weiyu Huang, Zubair Khalid, Rodney A. Kennedy
2011 2011 5th International Conference on Signal Processing and Communication Systems (ICSPCS)  
For corroboration, we provide the simulation results using CUDA which indicate the reduction in computational complexity  ...  We investigate the possibility of parallel computation of spherical harmonic transform using Compute Unified Device Architecture (CUDA) with no communication between parallel kernels.  ...  Bradley Treeby for discussions on integration of CUDA with the Matlab and optimization procedures.  ... 
doi:10.1109/icspcs.2011.6140886 dblp:conf/icspcs/HuangKK11 fatcat:yivirn74wreptlyfytesww53eq
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