Results 11 to 20 of about 6,241 (212)
NTT Multiplication for NTT-unfriendly Rings
Transactions on Cryptographic Hardware and Embedded Systems, 2021 In this paper, we show how multiplication for polynomial rings used in the NIST PQC finalists Saber and NTRU can be efficiently implemented using the Number-theoretic transform (NTT).
Chi-Ming Marvin Chung +5 more
doaj +1 more source
Multiplicity of zeros of polynomials [PDF]
Journal of Approximation Theory, 2021 The paper grew out of the known result of \textit{P. Erdős} and \textit{P. Túran} [Ann. Math. (2) 41, 162--173 (1940; Zbl 0023.02201)] on zero distributions and bounds for their multiplicities of monic polynomials with all their zeros in \([-1,1]\). Theorem 1.1.
openaire +2 more sources
IEEE Access, 2022 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.
Youngbeom Kim +2 more
doaj +1 more source
Polynomial multiplication on embedded vector architectures
Transactions on Cryptographic Hardware and Embedded Systems, 2021 High-degree, low-precision polynomial arithmetic is a fundamental computational primitive underlying structured lattice based cryptography. Its algorithmic properties and suitability for implementation on different compute platforms is an active area of ...
Hanno Becker +4 more
doaj +1 more source
IEEE Access, 2022 Polynomial multiplication is one of the heaviest operations for a lattice-based public key algorithm in Post-Quantum Cryptography (PQC). Many studies have been done to accelerate polynomial multiplication with newly developed hardware accelerators or ...
Jong-Yeon Park +4 more
doaj +1 more source
Fast Multiplication for Skew Polynomials [PDF]
Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation, 2017 We describe an algorithm for fast multiplication of skew polynomials. It is based on fast modular multiplication of such skew polynomials, for which we give an algorithm relying on evaluation and interpolation on normal bases. Our algorithms improve the best known complexity for these problems, and reach the optimal asymptotic complexity bound for ...
Caruso, Xavier, Le Borgne, Jérémy
openaire +3 more sources
Computing Sparse Multiples of Polynomials [PDF]
Algorithmica, 2010 We consider the problem of finding a sparse multiple of a polynomial. Given f in F[x] of degree d over a field F, and a desired sparsity t, our goal is to determine if there exists a multiple h in F[x] of f such that h has at most t non-zero terms, and if so, to find such an h.
Mark Giesbrecht +2 more
openaire +4 more sources
FourierPIM: High-throughput in-memory Fast Fourier Transform and polynomial multiplication
Memories - Materials, Devices, Circuits and Systems, 2023 The Discrete Fourier Transform (DFT) is essential for various applications ranging from signal processing to convolution and polynomial multiplication. The groundbreaking Fast Fourier Transform (FFT) algorithm reduces DFT time complexity from the naive O(
Orian Leitersdorf +4 more
doaj +1 more source
Multiplication Rules for Polynomials [PDF]
Proceedings of the American Mathematical Society, 1978 It is proved that the polynomial solutions of the functional equation \[ F ( z )
openaire +2 more sources
Configurable Mixed-Radix Number Theoretic Transform Architecture for Lattice-Based Cryptography
IEEE Access, 2022 Lattice-based cryptography continues to dominate in the second-round finalists of the National Institute of Standards and Technology post-quantum cryptography standardization process. Computational efficiency is primarily considered to evaluate promising
Phap Duong-Ngoc, Hanho Lee
doaj +1 more source