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Implementation of number-theoretic transforms
Electronics Letters, 1976 We propose various methods for the implementation of number-theoretic transforms to a prime or prime-power modulus. Such transforms may be performed in a processor or by special hardware. We also give, without proof, the condition for the existence of transforms in an arbitrary ring.
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Highly Efficient Architecture of NewHope-NIST on FPGA using Low-Complexity NTT/INTT
Transactions on Cryptographic Hardware and Embedded Systems, 2020 NewHope-NIST is a promising ring learning with errors (RLWE)-based postquantum cryptography (PQC) for key encapsulation mechanisms. The performance on the field-programmable gate array (FPGA) affects the applicability of NewHope-NIST.
Neng Zhang +5 more
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IEEE Access, 2023 Homomorphic Encryption (HE) allows performing specific algebraic computations on encrypted data without the need for decryption. For this reason, HE is emerging as a strong privacy-preserving solution in cloud computing environments since it allows to ...
Stefano Di Matteo +2 more
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Reduced-Dimension Linear Transform Coding of Correlated Signals in Networks
, 2012 A model, called the linear transform network (LTN), is proposed to analyze the compression and estimation of correlated signals transmitted over directed acyclic graphs (DAGs). An LTN is a DAG network with multiple source and receiver nodes. Source nodes
Gastpar, Michael, Goela, Naveen
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Hardware acceleration of number theoretic transform for zk‐SNARK
Engineering Reports, 2022 AbstractZk‐SNARK unleashes the great potential of ZKP (zero‐knowledge proof) in the blockchain, distributed storage, and so forth. However, the proof‐generation of zk‐SNARK is excessively time intensive, making it a challenge to deploy a high‐performance zk‐SNARK in most real applications.
Haixu Zhao +6 more
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Parallel Accelerating Number Theoretic Transform for Bootstrapping on a Graphics Processing Unit
MathematicsThe bootstrapping procedure has become the main bottleneck affecting the efficiency of all known fully homomorphic encryption (FHE) schemes. The state-of-the-art scheme for efficient bootstrapping, which is called fully homomorphic encryption over the ...
Huixian Li +3 more
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The Background Field Method as a Canonical Transformation
, 2012 We construct explicitly the canonical transformation that controls the full dependence (local and non-local) of the vertex functional of a Yang-Mills theory on a background field.
A. Quadri, D. Binosi, L. F. Abbott
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Transactions on Cryptographic Hardware and Embedded Systems, 2021 Number theoretic transform (NTT) is widely utilized to speed up polynomial multiplication, which is the critical computation bottleneck in a lot of cryptographic algorithms like lattice-based post-quantum cryptography (PQC) and homomorphic encryption (HE)
Xiangren Chen +4 more
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, 2007 Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions.
Tauber, Uwe C.
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The Hamming and Golay Number-Theoretic Transforms [PDF]
Anais de XXXVI Simpósio Brasileiro de Telecomunicações e Processamento de Sinais, 2018 New number-theoretic transforms are derived from known linear block codes over finite fields. In particular, two new such transforms are built from perfect codes, namely the \textit {Hamming number-theoretic transform} and the \textit {Golay number-theoretic transform}. A few properties of these new transforms are presented.
Paschoal, A. J. A. +2 more
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