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Conceptual Review on Number Theoretic Transform and Comprehensive Review on Its Implementations
IEEE Access, 2023 The Number Theoretic Transform (NTT) is a powerful mathematical tool that has become increasingly important in developing Post Quantum Cryptography (PQC) and Homomorphic Encryption (HE).
Ardianto Satriawan +5 more
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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.
A. J. A. Paschoal +2 more
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New Number Theoretic Transform
A new number theoretic transform is introduced. This transform is defined modulo the Mersenne primes, has long transform length which is a power of two, a fast algorithm, and the inverse transform has within a factor of (1/N) the same form as the forward
Holt AGJ, Boussakta S
core +5 more sources
Hardware Acceleration of Number Theoretic Transform in zk-SNARK [PDF]
Jisuanji kexue yu tansuoThe proof in zk-SNARK has a fixed length and can be verified quickly, promoting the application of zero-knowledge proof in areas such as digital signature, blockchain, distributed storage, and outsourced computing.
ZHAO Haixu, CHAI Zhilei, HUA Pengcheng, WANG Feng, DING Dong
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Adapting Belief Propagation to Counter Shuffling of NTTs
Transactions on Cryptographic Hardware and Embedded Systems, 2022 The Number Theoretic Transform (NTT) is a major building block in recently introduced lattice based post-quantum (PQ) cryptography. The NTT was target of a number of recently proposed Belief Propagation (BP)-based Side Channel Attacks (SCAs). Ravi et al.
Julius Hermelink +3 more
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Long Polynomial Modular Multiplication using Low-Complexity Number Theoretic Transform [PDF]
, 2023 This tutorial aims to establish connections between polynomial modular multiplication over a ring to circular convolution and discrete Fourier transform (DFT).
Parhi, Keshab K., Chiu, Sin-Wei
core +1 more source
Number-Theoretic Transform with Constant Time Computation for Embedded Post-Quantum Cryptography
Acta Electrotechnica et Informatica, 2022 In this article, we describe the principles and advantages of using the Number-Theoretic Transform (NTT) in post-quantum cryptography. We deal with usages of NTT in post-quantum algorithms included in the competition announced by the National Institute ...
Kupcová Eva, Drutarovský Miloš
doaj +1 more source
IEEE Access, 2021 In recent years, public-key cryptography has become a fundamental component of digital infrastructures. Such a scenario has to face a new and increasing threat, represented by quantum computers.
Pietro Nannipieri +5 more
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Number Theoretic Transform (NTT) FPGA Accelerator
, 2020 Post-quantum cryptography has become popular in recent years due to advances in quantum computing. Current cryptographic solutions are vulnerable to post-quantum attacks as they can solve computationally hard problems.
Weber, Scott S. +3 more
core +2 more sources
Introduction to Number Theoretic Transform
CoRRThe Number Theoretic Transform (NTT) can be regarded as a variant of the Discrete Fourier Transform. NTT has been quite a powerful mathematical tool in developing Post-Quantum Cryptography and Homomorphic Encryption. The Fourier Transform essentially decomposes a signal into its frequencies. They are traditionally sine or cosine waves.
Banhirup Sengupta +2 more
openaire +2 more sources