3.1. Example
Below is a simple example of generating long symmetric keys using the pre–trained VGG16.
[[[[0.0, 0.0, 0.0, 0.0, 6.903665065765381, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 34.10573196411133, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 67.41827392578125, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 31.747112274169922, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 15.003043174743652, 0.0, 0.0, 0.0, 0.0, 0.0, 17.883718490600586, 0.0, 0.0, 31.02227210998535, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 3.426398515701294, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.979990482330322, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 67.9732666015625, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.141775369644165, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 17.164846420288086, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.9679595232009888, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 11.956241607666016, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.2587838172912598, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 6.765922546386719, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 19.34865951538086, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 5.301035404205322, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 10.16125774383545, 0.0, 0.0, 0.0, 17.666433334350586, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 6.217296600341797, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 35.38439178466797, 0.0, 0.0, 0.0, 0.0, 0.0,…]]]]
[[[[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 24.223085403442383, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 10.136581420898438, 9.996827125549316, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 43.26572036743164, 0.0, 0.0, 9.374469757080078, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.680146217346191, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 11.460838317871094, 8.864582061767578, 0.0, 0.0, 12.735118865966797, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.2287561893463135, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 6.5052361488342285, 0.0, 0.0, 0.0, 0.0, 4.149342060089111, 7.862621784210205, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 37.46705627441406, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 3.7152833938598633, 0.0, 0.0, 11.048995018005371, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 13.8164701461792, 1.718098759651184, 0.0, 11.642448425292969, 0.0, 0.0, 0.0, 0.0, 5.835142612457275, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 3.547330379486084, 8.25907039642334, 0.0, 3.026193141937256, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 5.3880109786987305, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.9568023681640625, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 3.869873046875, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.10132180899381638, 0.0, 0.0, 0.0, 0.0, 9.61951732635498, 29.360055923461914, …]]]]
[6.903665065765381, 34.10573196411133, 67.41827392578125, 31.747112274169922, 15.003043174743652, 17.883718490600586, 31.02227210998535, 3.426398515701294, 4.979990482330322, 67.9732666015625, 2.141775369644165, 17.164846420288086, 0.9679595232009888, 11.956241607666016, 2.2587838172912598, 6.765922546386719, 19.34865951538086, 5.301035404205322, 10.16125774383545, 17.666433334350586, 6.217296600341797, 35.38439178466797, 12.481855392456055, 49.49517822265625, 2.6517748832702637, 58.775062561035156, 14.709327697753906, 4.851640224456787, 32.54026794433594, 18.19671058654785, 38.65156936645508, 62.830291748046875, …]
[24.223085403442383, 10.136581420898438, 9.996827125549316, 43.26572036743164, 9.374469757080078, 4.680146217346191, 11.460838317871094, 8.864582061767578, 12.735118865966797, 1.2287561893463135, 6.5052361488342285, 4.149342060089111, 7.862621784210205, 37.46705627441406, 3.7152833938598633, 11.048995018005371, 13.8164701461792, 1.718098759651184, 11.642448425292969, 5.835142612457275, 3.547330379486084, 8.25907039642334, 3.026193141937256, 5.3880109786987305, 1.9568023681640625, 3.869873046875, 0.10132180899381638, 9.61951732635498, 29.360055923461914, 11.005602836608887, 3.671891927719116, 25.473989486694336, 9.130292892456055, 7.472241401672363, 11.316661834716797, 8.249753952026367, 15.941848754882812, 6.701721668243408, 2.259157180786133, 33.08333969116211, …]
Feature | Remove the Dot (.) | Convert to Binary |
6.903665065765381 | 6903665065765381 | 11000100001101101100011000111111001001010101000000101 |
34.10573196411133 | 3410573196411133 | 1100000111011110010111110011110110100100000011111101 |
67.41827392578125 | 6741827392578125 | 10111111100111010100000000010110111110010001001001101 |
31.747112274169922 | 31747112274169922 | 1110000110010011101010010010101101111110001000001000010 |
15.003043174743652 | 15003043174743652 | 110101010011010011000000110010111110101111111001100100 |
… | … | … |
Feature | Remove the Dot (.) | Convert to Binary |
24.223085403442383 | 24223085403442383 | 1010110000011101100010010010000110101100000110011001111 |
10.136581420898438 | 10136581420898438 | 100100000000110010101011000110110101000101100010000110 |
9.996827125549316 | 9996827125549316 | 100011100001000000111110110001101100110000100100000100 |
43.26572036743164 | 4326572036743164 | 1111010111101111111010001101010110000101111111111100 |
9.374469757080078 | 9374469757080078 | 100001010011100000011111010011110101000001001000001110 |
… | … | … |
To equalize the two binary strings, truncate them to the length of the shorter one and perform an XOR operation between the binary string of the first image and the binary string of the second image. The output is a binary string of 150,728 bits, as shown below.
[0110100000101011010011110001111010001001010010011011000100101110111010111010111111011011100000101011101011101011101111100010000111111101010010101110100000010111000110001111001101011001101101110100100000111101111011111010001111010110001110001100000111111111010111001110101111101100101101101000101011000000100100110110011010110000100111000011111000101011101001110101011111001000111011011101011100011011111101110110111011001011100100110110001011001001001100110011100100111111100100111101111111100101001001000110000101110111111010111101110010001110010100000110000010001100001110001011000011111011010111101111000010101111011011010111001100111100011110011110111100000110011011011010000110011111100101001010010000100101000000010111010101001010101001101111100111110111101101110101000001010000100000011100011110100010101111010001110011110011101100010100101001011010010000111011010001000100100101011101010111001101011100101100101111010110001100111100011010111000101100010001000011101101000101101010001001111110011101011111101110011110000000011010101010011001111101101100010110111110101101101001010011110111001010000000101100000001010100100001010001111101110000110011111011010, …]
3.2. The Sensitivity of the Symmetric Key to Any Alterations Made to One of the Reference Images
An effective method should demonstrate a high degree of sensitivity to even the slightest changes in the base image. For instance, minor modifications such as altering a single bit should lead to substantial differences in the features extracted from the image. These significant changes in the extracted features should, in turn, result in the generation of completely different keys. Here, a simple example shows how changing a single bit in the base image completely changes the features extracted from it.
Base image | single bit in the base image is changed |
| |
[[[[0.0, 0.0, 0.0, 0.0, 6.903665065765381, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 34.10573196411133, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 67.41827392578125, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 31.747112274169922, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 15.003043174743652, 0.0, 0.0, 0.0, 0.0, 0.0, 17.883718490600586, 0.0, 0.0, 31.02227210998535, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 3.426398515701294, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.979990482330322, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 67.9732666015625, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.141775369644165, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 17.164846420288086, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.9679595232009888, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 11.956241607666016, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.2587838172912598, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 6.765922546386719, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 19.34865951538086, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 5.301035404205322, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 10.16125774383545, 0.0, 0.0, 0.0, 17.666433334350586, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 6.217296600341797, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 35.38439178466797, 0.0, 0.0, 0.0, 0.0, 0.0,…]]]]
[[[[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 8.439230918884277, 0.0, 12.917805671691895, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.9626998901367188, 0.0, 0.0, 43.08259963989258, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 3.9462945461273193, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 48.83059310913086, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 12.243735313415527, 27.153099060058594, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,3.810386896133423, 37.272727966308594, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 5.046123504638672, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 26.434804916381836, 2.660520076751709, 0.0, 0.0,7.4828314781188965, 0.0, 0.0, 1.8224953413009644, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 23.51656723022461, 0.0, 6.485126495361328, 0.0, 0.0, 0.0, 0.0, 13.915960311889648, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 6.456112861633301, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 27.75977325439453, 0.0, 0.0, 0.0, 0.0, 14.999650955200195, 0.5237445831298828, 0.0, 0.0, 0.0, 0.0, 0.0, 4.312615871429443, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 28.290889739990234, 0.0, 0.0, 0.0, 1.773626446723938, 22.507610321044922, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.360454559326172, 0.0, 7.555282115936279, 0.0, 0.0, 0.0, 55.96969985961914, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 8.2135591506958, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 6.036996841430664, 0.0, 8.161231994628906, 0.0, 3.563197612762451, 0.0, 0.0, 0.0, 0.0, 34.11822509765625, 0.0, 0.0,…]]]]