游程检验的随机性检测模型

游程检验是一种常用的随机性检测模型，用于评估一串二进制序列的随机性。它基于统计学原理，通过计算序列中连续出现相同数字的游程（run）的长度分布来判断序列的随机性。

在游程检验中，一个游程是指连续出现相同数字的序列片段。例如，在二进制序列"110100111001"中，有4个游程，分别是"11"、"0"、"111"和"00"。游程检验通过统计不同长度的游程出现的频率，然后与理论上的期望频率进行比较，来判断序列的随机性。

常见的游程检验模型包括：

1. 简单游程检验（Simple Runs Test）：该模型统计序列中1和0的游程长度，并与理论上的期望频率进行比较。

2. 长度为3的游程检验（Runs of Three Test）：该模型统计序列中长度为3的游程的频率，并与理论上的期望频率进行比较。

3. 长度为5的游程检验（Runs of Five Test）：该模型统计序列中长度为5的游程的频率，并与理论上的期望频率进行比较。

4. 长度为6以上的游程检验：除了上述模型外，还可以进行更长游程的检验，如长度为6、7、8等的游程检验。

这些游程检验模型可以用于评估随机数生成器的质量，或者判断一串二进制序列是否具有随机性。它们在密码学、随机数生成、数据压缩等领域有广泛的应用。

相关问题

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

伪随机数的随机性基本检测方法的matlab程序

以下是常用的伪随机数的随机性基本检测方法的 Matlab 程序：

1. 频数检测

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

2. 块频数检测

function [p_value] = block_frequency_test(numbers, block_size)
    n = length(numbers);
    num_blocks = floor(n/block_size);
    counts = zeros(num_blocks, 1);
    for i = 1:num_blocks
        block = numbers((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(numbers)
    n = length(numbers);
    runs = 1;
    for i = 2:n
        if numbers(i) ~= numbers(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 numbers(i) ~= numbers(i-1)
                vobs = vobs + 1;
            else
                break;
            end
        end
        for i = n:-1:2
            if numbers(i) ~= numbers(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. 累加和检测

function [p_value] = cumulative_sums_test(numbers)
    n = length(numbers);
    s = cumsum(2*numbers-1);
    a = max(abs(s));
    p_value = erfc(a/sqrt(n)/sqrt(2));
end

5. 近似熵检测

function [p_value] = approximate_entropy_test(numbers, m)
    n = length(numbers);
    c = zeros(n-m+1, 1);
    for i = 1:n-m+1
        block = numbers(i:i+m-1);
        count = 0;
        for j = 1:n-m+1
            if i ~= j
                if isequal(numbers(j:j+m-1), block)
                    count = count + 1;
                end
            end
        end
        c(i) = count / (n-m);
    end
    phi_m = mean(log(c));
    c = zeros(n-m-1, 1);
    for i = 1:n-m-1
        block = numbers(i:i+m);
        count = 0;
        for j = 1:n-m-1
            if i ~= j
                if isequal(numbers(j:j+m), block)
                    count = count + 1;
                end
            end
        end
        c(i) = count / (n-m-1);
    end
    phi_m_plus_1 = mean(log(c));
    p_value = gammainc((n-m)*phi_m - (n-m-1)*phi_m_plus_1, m/2);
end

这些程序可以用于对伪随机数序列进行基本的随机性检测，以评估伪随机数生成器的随机性。请注意，不同的检测方法适用于不同的随机性问题，因此需要根据具体情况选择适当的检测方法。