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几种常见的量子图像加密方法及其MATLAB实现

news 2026/3/26 23:23:10

几种常见的量子图像加密方法及其MATLAB实现。量子图像加密通常包括量子图像表示和量子操作两个部分。

1. 量子图像表示基础

Novel Enhanced Quantum Representation (NEQR)

function quantum_image = NEQR_encode(image)% 将灰度图像编码为量子态% 输入：8位灰度图像 (0-255)% 输出：量子态表示[h, w] = size(image);quantum_image = zeros(2^(ceil(log2(h)) + ceil(log2(w)) + 8), 1);for i = 1:hfor j = 1:w% 位置坐标编码y_bin = dec2bin(i-1, ceil(log2(h)));x_bin = dec2bin(j-1, ceil(log2(w)));% 颜色值编码color_bin = dec2bin(image(i,j), 8);% 组合编码pos = bin2dec([y_bin x_bin]);quantum_image(pos*256 + bin2dec(color_bin) + 1) = 1;endend
end

2. 基本量子图像加密算法

基于量子Arnold变换的图像加密

function encrypted_img = quantum_arnold_encrypt(image, iterations)% 量子Arnold变换加密% 输入：图像，迭代次数% 输出：加密后的图像[h, w] = size(image);encrypted_img = zeros(size(image));% 构建Arnold变换矩阵A = [1, 1; 1, 2]; % Arnold变换矩阵for iter = 1:iterationsfor i = 1:hfor j = 1:w% 量子态位置变换pos = [i-1; j-1];new_pos = mod(A * pos, [h; w]);% 更新像素位置encrypted_img(new_pos(1)+1, new_pos(2)+1) = image(i, j);endendimage = encrypted_img;end
end

3. 量子位平面加密算法

function [encrypted_img, key] = quantum_bitplane_encrypt(img)% 量子位平面加密% 输入：灰度图像% 输出：加密图像和密钥% 获取图像尺寸[h, w] = size(img);% 提取位平面bitplanes = zeros(h, w, 8);for k = 1:8bitplanes(:,:,k) = bitget(img, k);end% 生成随机置换密钥key = randperm(8);% 位平面置换（模拟量子置换门）encrypted_bitplanes = zeros(h, w, 8);for k = 1:8encrypted_bitplanes(:,:,k) = bitplanes(:,:,key(k));end% 重组图像encrypted_img = zeros(h, w);for k = 1:8encrypted_img = encrypted_img + encrypted_bitplanes(:,:,k) * 2^(k-1);end
end

4. 基于量子混沌的加密算法

function [encrypted_img, key_stream] = quantum_chaos_encrypt(img, x0, mu, n_skip)% 基于Logistic混沌系统的量子图像加密% 输入：图像，初始值x0，参数mu，跳过步数n_skip% 输出：加密图像和密钥流[h, w] = size(img);total_pixels = h * w;% 生成混沌序列N = total_pixels + n_skip;chaos_seq = zeros(1, N);chaos_seq(1) = x0;for i = 2:Nchaos_seq(i) = mu * chaos_seq(i-1) * (1 - chaos_seq(i-1));end% 跳过前n_skip个值key_stream = chaos_seq(n_skip+1:end);% 将图像转换为一维向量img_vector = double(img(:));% 量子异或操作（模拟）encrypted_vector = zeros(total_pixels, 1);for i = 1:total_pixels% 将混沌序列量化为0-255key_byte = mod(floor(key_stream(i) * 10^10), 256);% 量子异或门操作（经典模拟）encrypted_vector(i) = bitxor(uint8(img_vector(i)), uint8(key_byte));end% 重塑为图像encrypted_img = reshape(encrypted_vector, h, w);
end

5. 完整的量子图像加密系统

function [encrypted_img, keys] = quantum_image_encryption_system(img, method)% 完整的量子图像加密系统% 输入：原始图像，加密方法% 输出：加密图像和密钥switch methodcase 'Arnold'% Arnold变换加密iterations = 10;encrypted_img = quantum_arnold_encrypt(img, iterations);keys.iterations = iterations;case 'BitPlane'% 位平面加密[encrypted_img, key] = quantum_bitplane_encrypt(img);keys.permutation_key = key;case 'Chaos'% 混沌加密x0 = 0.3; % 初始值mu = 3.99; % 混沌参数n_skip = 1000; % 跳过步数[encrypted_img, key_stream] = quantum_chaos_encrypt(img, x0, mu, n_skip);keys.x0 = x0;keys.mu = mu;keys.n_skip = n_skip;keys.key_stream = key_stream;case 'Hybrid'% 混合加密方法% 步骤1：位平面置换[temp_img, key1] = quantum_bitplane_encrypt(img);% 步骤2：Arnold变换temp_img = quantum_arnold_encrypt(temp_img, 5);% 步骤3：混沌加密[encrypted_img, key2] = quantum_chaos_encrypt(temp_img, 0.3, 3.99, 1000);keys.bitplane_key = key1;keys.arnold_iterations = 5;keys.chaos_params = key2;end
end

6. 解密函数示例

function decrypted_img = quantum_arnold_decrypt(encrypted_img, iterations)% Arnold变换解密[h, w] = size(encrypted_img);decrypted_img = zeros(size(encrypted_img));% Arnold逆变换矩阵A_inv = [2, -1; -1, 1]; % mod [h; w]for iter = 1:iterationsfor i = 1:hfor j = 1:wpos = [i-1; j-1];original_pos = mod(A_inv * pos, [h; w]);decrypted_img(original_pos(1)+1, original_pos(2)+1) = encrypted_img(i, j);endendencrypted_img = decrypted_img;end
end

7. 测试示例

% 主测试程序
clear all; close all; clc;% 读取图像
img = imread('cameraman.tif');
if size(img, 3) == 3img = rgb2gray(img);
end% 选择加密方法
method = 'Hybrid'; % 'Arnold', 'BitPlane', 'Chaos', 'Hybrid'% 执行加密
[encrypted_img, keys] = quantum_image_encryption_system(img, method);% 显示结果
figure('Position', [100, 100, 1200, 400]);
subplot(1,3,1);
imshow(img, []);
title('原始图像');
colorbar;subplot(1,3,2);
imshow(encrypted_img, []);
title('加密图像');
colorbar;subplot(1,3,3);
histogram(double(encrypted_img(:)), 0:255);
title('加密图像直方图');
xlabel('像素值');
ylabel('频数');% 计算评估指标
mse_val = mean((double(img(:)) - double(encrypted_img(:))).^2);
psnr_val = 10 * log10(255^2 / mse_val);
fprintf('PSNR: %.2f dB\n', psnr_val);% 相关性分析
corr_horizontal = corrcoef(double(img(1:end-1,:)), double(img(2:end,:)));
corr_vertical = corrcoef(double(img(:,1:end-1)), double(img(:,2:end)));
fprintf('水平相关性: %.4f\n', corr_horizontal(1,2));
fprintf('垂直相关性: %.4f\n', corr_vertical(1,2));

8. 高级功能：量子FRQI表示

function state = FRQI_encode(image)% Flexible Representation of Quantum Images (FRQI)% 输入：归一化到[0,1]的图像% 输出：量子态向量[h, w] = size(image);n = ceil(log2(h * w)); % 位置量子比特数% 初始化量子态state = zeros(2^n, 1);% 计算每个位置的幅度total = 0;for i = 1:hfor j = 1:widx = (i-1)*w + j;if idx <= 2^ntheta = acos(image(i,j));state(idx) = exp(1i * theta);total = total + abs(state(idx))^2;endendend% 归一化state = state / sqrt(total);
end

参考代码 matlab实现量子图像加密 www.3dddown.com/csb/45759.html