随机性检测的五项基本检测方法的matlab程序

以下是五项基本检测方法的 Matlab 程序：

1. 频数检测

function [p_value] = frequency_test(bits)
    n = length(bits);
    count = sum(bits);
    p_value = 2*min(count, n-count)/n;
end

2. 块频数检测

function [p_value] = block_frequency_test(bits, block_size)
    n = length(bits);
    num_blocks = floor(n/block_size);
    counts = zeros(num_blocks, 1);
    for i = 1:num_blocks
        block = bits((i-1)*block_size+1:i*block_size);
        counts(i) = sum(block);
    end
    chi2 = ((counts - block_size/2).^2) / (block_size/2);
    p_value = 1 - gammainc(num_blocks/2, chi2/2);
end

3. 游程总数检测

function [p_value] = runs_test(bits)
    n = length(bits);
    runs = 1;
    for i = 2:n
        if bits(i) ~= bits(i-1)
            runs = runs + 1;
        end
    end
    pi = runs / n;
    tau = 2 / sqrt(n);
    if abs(pi - 0.5) >= tau
        p_value = 0;
    else
        vobs = 1;
        for i = 2:n
            if bits(i) ~= bits(i-1)
                vobs = vobs + 1;
            else
                break;
            end
        end
        for i = n:-1:2
            if bits(i) ~= bits(i-1)
                vobs = vobs + 1;
            else
                break;
            end
        end
        mu = (2*n - 1) / 3;
        sigma2 = (16*n - 29) / 90;
        sigma = sqrt(sigma2);
        z = (vobs - mu) / sigma;
        p_value = erfc(abs(z) / sqrt(2));
    end
end

4. 乱数排列检测

function [p_value] = permutation_test(bits)
    n = length(bits);
    pi = sum(bits) / n;
    if abs(pi - 0.5) >= 2/sqrt(n)
        p_value = 0;
    else
        k = 0;
        for i = 2:n
            if bits(i) ~= bits(i-1)
                k = k + 1;
            end
        end
        k = k + 1;
        tau = 2 / sqrt(n);
        if abs(k - 2*n*pi*(1-pi)) >= tau
            p_value = 0;
        else
            p_value = gammainc((n-1)/2, (abs(k - 2*n*pi*(1-pi))/2)^2);
        end
    end
end

5. 矩阵秩检测

function [p_value] = matrix_rank_test(bits, matrix_size)
    n = length(bits);
    num_matrices = floor(n/matrix_size);
    counts = zeros(num_matrices, 1);
    for i = 1:num_matrices
        matrix = reshape(bits((i-1)*matrix_size+1:i*matrix_size), sqrt(matrix_size), sqrt(matrix_size));
        counts(i) = rank(matrix);
    end
    mu = matrix_size*(1/2 + 1/18);
    sigma2 = matrix_size*(13/18 - 7/180)^2 + matrix_size*(1/6 - 1/180);
    sigma = sqrt(sigma2);
    chi2 = ((counts - mu).^2) / sigma2;
    p_value = 1 - gammainc(num_matrices/2, chi2/2);
end