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Faster Homomorphic Discrete Fourier Transforms and Improved FHE Bootstrapping
Discrete Fourier Transform Homomorphic Encryption Bootstrapping
2018/11/12
In this work, we propose a faster homomorphic linear transform algorithm for structured matrices such as the discrete Fourier transform (DFT) and linear transformations in bootstrapping.
Constructing low-weight dth-order correlation-immune Boolean functions through the Fourier-Hadamard transform
Correlation-immune Fourier-Hadamard transform Low Hamming weight
2018/1/27
The correlation immunity of Boolean functions is a property related to cryptography, to error correcting codes, to orthogonal arrays (in combinatorics, which was also a domain of interest of S. Golomb...
We present a methodology to evaluate a Discrete Fourier Transform (DFT) on data which has been encrypted using a Somewhat Homomorphic Encryption (SHE) scheme, which is over 200 times faster than other...
Finding Significant Fourier Coefficients: Clarifications, Simplifications, Applications and Limitations
Significant Fourier transform Goldreich-Levin algorithm Kushilevitz-Mansour algorithm
2016/7/13
Ideas from Fourier analysis have been used in cryptography for three decades. Akavia, Goldwasser
and Safra unified some of these ideas to give a complete algorithm that finds significant
Fourier coe...
The Fourier Entropy-Influence conjecture holds for a log-density 1 class of cryptographic Boolean functions
Boolean functions Fourier and Walsh-Hadamard transforms entropy
2016/1/26
We consider the Fourier Entropy-Influence (FEI) conjecture in
the context of cryptographic Boolean functions. We show that the FEI conjecture
is true for the functions satisfying the strict avalanch...
Fast Fourier Orthogonalization
Fast Fourier Transform Gram-Schmidt Orthogonalization Nearest Plane Algorithm
2015/12/22
The classical Fast Fourier Transform (FFT) allows to compute
in quasi-linear time the product of two polynomials, in the circular
convolution ring R[x]/(x
d − 1) — a task that naively require...
Practical Signatures from the Partial Fourier Recovery Problem
lattice techniques digital signatures
2014/3/6
Abstract. We present PASSSign, a variant of the prior PASS and PASS-2 proposals, as a candidate for a practical post-quantum signature scheme. Its hardness is based on the problem of recovering a ring...
On the (Im)Possibility of Tamper-Resilient Cryptography: Using Fourier Analysis in Computer Viruses
Tampering Randomness Fourier Analysis Encryption.
2013/4/18
We initiate a study of the security of cryptographic primitives in the presence of efficient tampering attacks to the randomness of honest parties. More precisely, we consider p-tampering attackers th...
提出一种新的修正离散Chirp-Fourier变换(MDCFT)域盲水印方案，其包括水印嵌入和水印检测2部分。该方案把Chirp水印信息嵌入图像经二维修正离散Chirp-Fourier变换后的系数上，对其进行反变换，得到含水印图像，利用二维MDCFT对水印信息进行盲检测。由于DCFT可通过FFT实现，与其他时/频域水印算法相比，其实现更为方便。仿真试验表明，该算法透明性好，检测速度快，植入的数字水...