Secret sharing based on quantum Fourier transform

Secret sharing plays a fundamental role in both secure multi-party computation and modern cryptography. We present a new quantum secret sharing scheme based on quantum Fourier transform. This scheme enjoys the property that each share of a secret is disguised with true randomness, rather than classical pseudorandomness. Moreover, under the only assumption that a top priority for all participants (secret sharers and recovers) is to obtain the right result, our scheme is able to achieve provable security against a computationally unbounded attacker.     

基于量子傅里叶变换算法的量子乘法器

乘法运算是许多量子算法中的基本运算之一.为了实现量子乘法运算并且尽可能少地使用辅助量子比特,提出了一种基于量子傅里叶变换算法的量子乘法器.在量子傅里叶加法电路基础上,设计了量子移位电路,并实现了两个n位二进制无符号数相乘的量子电路,其时间复杂度为O(n3).使用IBM提供的开源量子计算工具包Qiskit分别验证了两个2...     

Analysis and improvement of the watermark strategy for quantum images based on quantum Fourier transform

We investigate the quantum watermark strategy for quantum images based on quantum Fourier transform proposed by Zhang et al.(Quantum Inf Process 12(2):793–803, 2013). It is aimed to embed the watermark image into the Fourier coefficients of the quantum carrier image without affecting the carrier image’s visual effect. However, in our opinion the protocol is not clearly described and several steps are ambiguous. Moreover, we argue that the watermarking algorithm claimed by the authors is incorrect. At last, a possible improvement strategy is presented.     

基于IBM量子计算云服务的量子傅里叶变换实现

Shor算法能够相对经典大整数分解算法实现指数加速,从而直接威胁到了RSA密码体制,而量子傅里叶变换是Shor算法中的一个关键变换,也能够相对经典离散傅里叶变换实现指数加速,从而引起了广泛关注。主要针对量子傅里叶变换的实现方案进行研究。首先介绍了IBM公司量子计算云服务的编程基础,随后设计了3比特量子傅里叶变换的量子线路,最后在IBM公司5超导量子比特的量子计算芯片上进行了实验验证。     

Quantum arithmetic with the quantum Fourier transform

The quantum Fourier transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing quantum Fourier transform adders and multipliers and comment some simple variations that extend their capabilities. These modified circuits can perform modular and non-modular arithmetic operations and work with signed integers. Among the operations, we discuss a quantum method to compute the weighted average of a series of inputs in the transform domain. One of the circuits, the controlled weighted sum, can be interpreted as a circuit to compute the inner product of two data vectors.     

Novel image encryption/decryption based on quantum Fourier transform and double phase encoding

A novel gray-level image encryption/decryption scheme is proposed, which is based on quantum Fourier transform and double random-phase encoding technique. The biggest contribution of our work lies in that it is the first time that the double random-phase encoding technique is generalized to quantum scenarios. As the encryption keys, two phase coding operations are applied in the quantum image spatial domain and the Fourier transform domain respectively. Only applying the correct keys, the original image can be retrieved successfully. Because all operations in quantum computation must be invertible, decryption is the inverse of the encryption process. A detailed theoretical analysis is given to clarify its robustness, computational complexity and advantages over its classical counterparts. It paves the way for introducing more optical information processing techniques into quantum scenarios.     

The amplified quantum Fourier transform: solving the local period problem

This paper creates and analyzes a new quantum algorithm called the Amplified Quantum Fourier Transform (QFT) for solving the following problem: The Local Period Problem: Let L = {0,1 . . . N?1} be a set of N labels and let A be a subset of M labels of period P, i.e. a subset of the form $$A=\{j:j=s+rP,r=0,1\ldots M-1\}$$ where ${P\leq \sqrt{N}}$ and ${M \ll N}$ , and where M is assumed known. Given an oracle f : L→ {0,1} which is 1 on A and 0 elsewhere, find the local period P and the offset s. The first part of this paper defines the Amplified QFT algorithm. The second part of the paper summarizes the main results and compares the new algorithm against the QFT and QHS algorithms when solving the local period problem. It is shown that the new algorithm is, on average, quadratically faster than both the QFT and QHS algorithms.     

一种基于分数阶Fourier域的数字水印

提出了一种分数阶Fourier域的水印嵌入算法。将一复伪随机序列作为水印信息嵌入到图像的分数阶Fourier域中。分数阶Fourier变换的变换角度(α,β)为水印增加了两个自由度,增强了水印的安全性。仿真结果验证了该算法的有效性。     

基于短时傅里叶变换的敏感语音提取

在纯净语音条件下,提出了一种基于短时傅里叶变换的敏感语音提取,该提取利用3种FIR数字滤波器对纯净语音在不同频率范围的特征语音进行选取,从而产生不同的音效.待处理的声音文件可以是自己录制的一段语音,也可以是任意格式的音频文件,通过DSP和编译软件实现敏感语音提取,并在数字处理芯片TMS320C5402上实现.     

基于频域小波变换的Fourier去卷积法研究

将小波变换用于对频域信号的处理,提出了用频域小波变换获得的模糊项作为线性函数的Fourier去卷积法.与其他FSD方法相比较,本文提出的方法对不同类型峰形信号如HPLC信号均具有良好的分辨效果.由于不用选择线性函数,该方法还具有通用性较强,操作简便等优点.重叠峰分辨效果好的主要原因是由于从Fourier变换得到的模与其经小波变换获得的模糊项具有相似的线性和峰宽,能较大程度与原始谱峰相符.该方法有望用于不同类型重叠峰信号的分辨.     

基于傅里叶变换的粒子群优化算法

针对标准粒子群算法容易陷入局部收敛的问题,提出了新的优化粒子群方法,从两个方面对其进行优化.为了改进学习因子,利用傅里叶级数的特性定义了一个傅里叶级数进行分析判断;加入随机速度,辅助粒子扩大搜索区域并避免早熟.该算法遵循启发式规则,可根据粒子搜索结果动态调整参数,具有较好的全局搜索性能和搜索精度.最后,采用4种经典测试函数进行测试并比较,选取一个单峰函数和多峰函数进行仿真,仿真结果表明了该算法的可行性.     

基于稀疏快速傅里叶变换的信号压缩处理

随着数据采集能力和采样频率的不断提高,采用传统的奈奎斯特采样定理会获得海量的数据,这给信号的存储和传递带来了极大挑战。提出基于稀疏快速傅里叶变换的信号压缩方法,利用信号在频域的稀疏性,压缩信号所需的存储空间,在保证拥有足够小的误码率的前提下,以高概率重构原始信号。     

Improved quantum circuit modelling based on Heisenberg representation

Heisenberg model allows a more compact representation of certain quantum states and enables efficient modelling of stabilizer gates operation and single-qubit measurement in computational basis on classical computers. Since generic quantum circuit modelling appears intractable on classical computers, the Heisenberg representation that makes the modelling process at least practical for certain circuits is crucial. This paper proposes efficient algorithms to facilitate accurate global phase maintenance for both stabilizer and non-stabilizer gates application that play a vital role in the stabilizer frames data structure, which is based on the Heisenberg representation. The proposed algorithms are critical as maintaining global phase involves compute-intensive operations that are necessary for the modelling of each quantum gate. In addition, the proposed work overcomes the limitations of prior work where the phase factors due to non-stabilizer gates application was not taken into consideration. The verification of the proposed algorithms is made against the golden reference model that is constructed based on the conventional state vector approach.     

A watermark strategy for quantum images based on quantum fourier transform

We present a robust watermark strategy for quantum images. The watermark image is embedded into the fourier coefficients of the quantum carrier image, which will not affect the carrier image’s visual effect. Before being embedded into the carrier image, the watermark image is preprocessed to be seemingly meaningless using quantum circuit, which further ensures the security of the watermark image. The properties of fourier transform ensure that the watermark embedded in the carrier image resists the unavoidable noise and cropping.     

The multiple-parameter fractional Fourier transform

The fractional Fourier transform （FRFT） has multiplicity, which is intrinsic in fractional operator. A new source for the multiplicity of the weight-type fractional Fourier transform （WFRFT） is proposed, which can generalize the weight coefficients of WFRFT to contain two vector parameters m,n ∈ Z^M . Therefore a generalized fractional Fourier transform can be defined, which is denoted by the multiple-parameter fractional Fourier transform （MPFRFT）. It enlarges the multiplicity of the FRFT, which not only includes the conventional FRFT and general multi-fractional Fourier transform as special cases, but also introduces new fractional Fourier transforms. It provides a unified framework for the FRFT, and the method is also available for fractionalizing other linear operators. In addition, numerical simulations of the MPFRFT on the Hermite-Gaussian and rectangular functions have been performed as a simple application of MPFRFT to signal processing.     

基于分数阶傅里叶变换的多项式相位信号参数估计

研究了一种基于分数阶傅里叶变换(FRFT)的多项式相位信号快速估计方法,对于线性调频信号(LFM),即用信号延时相关解调的方法得到调频斜率的粗略估计,从而得到分数阶旋转角度的范围,简化为小范围的一维搜索问题。多项式相位信号的检测通过延时相关解调可转化为LFM信号的检测,再运用FRFT便可进行参数估计。理论分析与仿真结果表明该方法简单,估计性能好。     

傅里叶变换耦合DNA编码的图像加密算法

为提高光学加密系统的安全性与敏感性,设计分阶Fourier变换耦合DNA序列编码的光学图像加密算法.利用SHA-256方法来处理初始明文,形成一个256位密钥,并将其转换为密钥矩阵;引入DNA编码,对明文实施编码操作,得到一个DNA序列矩阵,将其与密钥矩阵完成XOR操作,输出混淆密文;根据256位密钥计算Lorenz系...     

A multiparty quantum proxy group signature scheme for the entangled-state message with quantum Fourier transform

A novel multiparty quantum proxy group signature scheme is proposed based on the discrete quantum Fourier transform in order to improve the efficiency and the security of quantum signature for an n-dimensional quantum message, in which the generation and verification of the signature can be successfully conducted only if all the n participants cooperate with each other and with the message owner’s, the receiver’s and the arbitrator’s help. The quantum parallel algorithm is applied to efficiently compare the restored quantum message to the original quantum message both of which contain a large amount of information. All the operations in signing and verifying phase can be executed in quantum circuits. The analysis shows that our scheme is more efficient than other traditional quantum signature schemes, and a secure quantum proxy group signature can be achieved effectively for a contract that needs the cosigner of multi participants. It has a wide application to E-payment system, Online contract, Online notarization and etc.     

The relationship between the Laplace transform and Fourier transform

In this note, a relationship between the one-sided Laplace transform and the one-sided Fourier transform is discussed.