The Weighted Fractional Fourier Transform and Its Application in Image Encryption

<p>The parameter redundancy of the MPFRFT: (a) original image, (b) encrypted image, (c) image decrypted by the correct key <span class="nowrap"><svg height="8.68572pt" id="M97" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 10.095 8.68572" width="10.095pt" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M743 375C743 570 607 650 407 650H136L130 622C214 612 220 606 204 526L125 122C110 43 105 36 24 27L17 0H250C382 0 482 23 571 76C680 141 743 248 743 375ZM644 379C644 188 520 36 305 36C277 36 249 38 229 46C205 55 202 71 212 126L293 553C300 588 306 600 317 606C330 613 356 617 390 617C547 617 644 537 644 379Z"></path></g></svg>,</span> and (d) image decrypted with the wrong key <span class="nowrap"><svg height="11.4859pt" id="M98" style="vertical-align:-0.04979992pt" version="1.1" viewbox="-0.0498162 -11.4361 13.8905 11.4859" width="13.8905pt" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M743 375C743 570 607 650 407 650H136L130 622C214 612 220 606 204 526L125 122C110 43 105 36 24 27L17 0H250C382 0 482 23 571 76C680 141 743 248 743 375ZM644 379C644 188 520 36 305 36C277 36 249 38 229 46C205 55 202 71 212 126L293 553C300 588 306 600 317 606C330 613 356 617 390 617C547 617 644 537 644 379Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.958,-5.741)"><path d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z"></path></g></svg>.</span></p>

Mathematical Problems in Engineering

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Figure 6

Figure 6: The Weighted Fractional Fourier Transform and Its Application in Image Encryption 