希尔密码。逆矩阵

Question

我有一个任务是编写一个与Hill密码一起工作的程序。并不难让它加密我的信息，但我无法让它解开它。 如果我使用此处的输入数据：http://en.wikipedia.org/wiki/Hill_cipher 它给出了相同的结果。

但是如果我更改了一个密钥 - 它将无法加密该消息。

我认为问题是由错误的矩阵反转造成的，但我不确定。它有点奇怪为什么它可以用一个键正常工作，而不能与另一个键一起工作。

    string alphabet_eng = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";        
    private void button2_Click(object sender, EventArgs e)
    {
        float m11 = 0, m12 = 0, m13 = 0, m21 = 0, m22 = 0, m23 = 0, m31 = 0, m32 = 0, m33 = 0;
        float deter = 0;

        m11 = alphabet_eng.IndexOf(matrix_11.Text);
        m12 = alphabet_eng.IndexOf(matrix_12.Text);
        m13 = alphabet_eng.IndexOf(matrix_13.Text);
        m21 = alphabet_eng.IndexOf(matrix_21.Text);
        m22 = alphabet_eng.IndexOf(matrix_22.Text);
        m23 = alphabet_eng.IndexOf(matrix_23.Text);
        m31 = alphabet_eng.IndexOf(matrix_31.Text);
        m32 = alphabet_eng.IndexOf(matrix_32.Text);
        m33 = alphabet_eng.IndexOf(matrix_33.Text);

        deter = (m11 * m22 * m33 + m12 * m23 * m31 + m13 * m21 * m32) - (m13 * m22 * m31 + m12 * m21 * m33 + m11 * m23 * m32);

        deter %= alphabet_eng.Length;

        if (deter == 0)
        {
            MessageBox.Show("deter = 0");
        }

        float a11 = 0, a12 = 0, a13 = 0, a21 = 0, a22 = 0, a23 = 0, a31 = 0, a32 = 0, a33 = 0;

        a11 = (m22 * m33 - m23 * m32);
        a12 = -1*(m21 * m33 - m23 * m31);
        a13 = (m21 * m32 - m22 * m31);
        a21 = -1 * (m12 * m33 - m13 * m32);
        a22 = (m11 * m33 - m13 * m31);
        a23 = -1 * (m11 * m32 - m12 * m31);
        a31 = (m12 * m23 - m13 * m22);
        a32 = -1 * (m11 * m23 - m13 * m21);
        a33 = (m11 * m22 - m12 * m21);

        float Ta11 = 0, Ta12 = 0, Ta13 = 0, Ta21 = 0, Ta22 = 0, Ta23 = 0, Ta31 = 0, Ta32 = 0, Ta33 = 0;

        Ta11 = a11;
        Ta12 = a21;
        Ta13 = a31;
        Ta21 = a12;
        Ta22 = a22;
        Ta23 = a32;
        Ta31 = a13;
        Ta32 = a23;
        Ta33 = a33;

        Ta11 *= deter;
        Ta12 *= deter;
        Ta13 *= deter;
        Ta21 *= deter;
        Ta22 *= deter;
        Ta23 *= deter;
        Ta31 *= deter;
        Ta32 *= deter;
        Ta33 *= deter;

        Ta11 = normalize_element(Ta11);
        Ta12 = normalize_element(Ta12);
        Ta13 = normalize_element(Ta13);
        Ta21 = normalize_element(Ta21);
        Ta22 = normalize_element(Ta22);
        Ta23 = normalize_element(Ta23);
        Ta31 = normalize_element(Ta31);
        Ta32 = normalize_element(Ta32);
        Ta33 = normalize_element(Ta33);

        Ta11 = Math.Abs(Ta11);
        Ta12 = Math.Abs(Ta12);
        Ta13 = Math.Abs(Ta13);
        Ta21 = Math.Abs(Ta21);
        Ta22 = Math.Abs(Ta22);
        Ta23 = Math.Abs(Ta23);
        Ta31 = Math.Abs(Ta31);
        Ta32 = Math.Abs(Ta32);
        Ta33 = Math.Abs(Ta33);

        Tmatrix_11.Text = Ta11.ToString();
        Tmatrix_12.Text = Ta12.ToString();
        Tmatrix_13.Text = Ta13.ToString();
        Tmatrix_21.Text = Ta21.ToString();
        Tmatrix_22.Text = Ta22.ToString();
        Tmatrix_23.Text = Ta23.ToString();
        Tmatrix_31.Text = Ta31.ToString();
        Tmatrix_32.Text = Ta32.ToString();
        Tmatrix_33.Text = Ta33.ToString();
    }

    float normalize_element(float f)
    {
        if (f >= alphabet_eng.Length)
        {
            while (f >= alphabet_eng.Length)
                f -= alphabet_eng.Length;
        }
        else if ((f + alphabet_eng.Length) < 0)
        {
            while ((f + alphabet_eng.Length) < 0)
                f += alphabet_eng.Length;

            f = alphabet_eng.Length + f;
        }

        return f;
    }

请求你的帮助。