Research Article
An Image Encryption Algorithm Based on Hyperchaotic System and Variable-Step Josephus Problem
| Test items | Encrypted cameraman image | Encrypted Lena image | Encrypted white image |
| The frequency (monobit) test | 0.0145 | 0.3445 | 0.0145 | Frequency test within a block | 0.5579 | 0.2092 | 0.5579 | The runs test | 0.9938 | 0.4367 | 0.9938 | Tests for the longest-run-of-ones in a block | 0.2798 | 0.7677 | 0.2798 | The binary matrix rank test | 0.0223 | 0.1924 | 0.0225 | The discrete Fourier transform (spectral) test | 0.9600 | 0.3087 | 0.9600 | The nonoverlapping template matching test | 0.0775 | 0.0478 | 0.0775 | The overlapping template matching test | 0.3450 | 0.5307 | 0.3450 | Maurer’s “universal statistical” test | 0.1878 | 0.0182 | 0.1878 | The serial test | 0.0161 | 0.4132 | 0.0161 | 0.8952 | 0.6253 | 0.8952 | The approximate entropy test | 0.8776 | 0.9952 | 0.8776 | The cumulative sums (CUSUMs) test | 0.4752 | 0.8580 | 0.4752 | 0.9431 | 0.6384 | 0.9431 | The random excursions test | 0.3075 | 0.0178 | 0.3075 | 0.4309 | 0.0364 | 0.4309 | 0.9371 | 0.0595 | 0.9371 | 0.8469 | 0.0869 | 0.8469 | 0.8645 | 0.2959 | 0.8645 | 0.1806 | 0.6863 | 0.1806 | 0.2538 | 0.7197 | 0.2538 | 0.4315 | 0.4917 | 0.4315 | The random excursions variant test | 0.6441 | 0.2875 | 0.6441 | 0.5550 | 0.3591 | 0.5550 | 0.6597 | 0.3490 | 0.6597 | 0.8183 | 0.3757 | 0.8183 | 0.7190 | 0.3885 | 0.7190 | 0.8103 | 0.1848 | 0.8103 | 0.8203 | 0.0682 | 0.8203 | 0.9415 | 0.0334 | 0.9415 | 0.6567 | 0.0097 | 0.6567 | 0.4849 | 0.2926 | 0.4849 | 0.2126 | 0.9798 | 0.2126 | 0.0649 | 0.7537 | 0.0649 | 0.0187 | 0.7909 | 0.0187 | 0.0049 | 0.9650 | 0.0049 | 0.0005 | 0.8222 | 0.0005 | 0.0009 | 0.7611 | 0.0009 | 0.0091 | 0.6836 | 0.0091 | 0.0349 | 0.5373 | 0.0349 |
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