1. PRESENTED BY
T A B I S H F A W A D 1 3 - M S - E E - 0 1 4
R I Z W A N A L I 1 3 - M S - E E - 0 1 9
“Comparison of image
Encryption using different
transforms/techniques”
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2. Contents
 Introduction
 Discrete cosine transforms
 Discrete Wavelet transforms
 Security Analysis
 Proposed Algorithm
 Security table
 Conclusion
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3. Introduction
 Encryption is the conversion of data or information from its original
form to some other form that basically hides the information in it.
 The protection of image data from unauthorized access is important.
 Encryption is employed to increase the data security.
 Decryption is the inverse process of Encryption.
 In decryption, Original image is recovered from the encrypted image.
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4. Discrete Cosine Transform
 The Discrete Cosine Transform (DCT) is a widely used transform
coding technique.
 The DCT represents an image as a sum of sinusoids of varying
magnitudes and frequencies.
 The role of the DCT is to decompose the original signal into its DC and
AC components.
 DCT is a linear transformation it transforms the function f(i) into a
function f (u). (1Dimensional DCT)
 The role of the IDCT is to reconstruct the original signal.
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5. Cosine Basis Function
 The basis functions should be orthogonal
𝐵𝑝 𝑖 . 𝐵𝑞 𝑖 = 0 𝑖𝑓 𝑝#𝑞
 The basis functions should be orthonormal if they are orthogonal
𝐵𝑝 𝑖 . 𝐵𝑞 𝑖 = 1 𝑖𝑓 𝑝 = 𝑞
cos 2i + 1/16 ∗ 𝑝𝜋 . (cos 2i + 1/16 . qπ = 0
𝑀−1
𝑖=0
𝑖𝑓 𝑝 # 𝑞
(
C p
2
∗ cos 2i +
1
16
∗ pπ ∗
C q
2
∗ cos 2i +
1
16
∗ qπ = 1 𝑖𝑓 𝑝 = 𝑞
𝑀−1
𝑖=0
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6. 2D DCT & IDCT
 DCT
𝐹 𝑢, 𝑣 =
2𝐶 𝑢 𝐶 𝑣
𝑀 ∗ 𝑁 .
.
𝑀−1
𝑖=0
cos 2𝑖 + 1 /2𝑀 ∗
𝑁−1
𝑗=0
𝑢𝜋 ∗
cos 2𝑗 + 1
2𝑁
∗ 𝑣𝜋 𝑓(𝑖, 𝑗)
 IDCT
𝑓 𝑖, 𝑗 =
2𝐶 𝑢 𝐶 𝑣
𝑀 ∗ 𝑁 .
.
𝑀−1
𝑢=0
cos 2𝑖 + 1 /2𝑀 ∗
𝑁−1
𝑣=0
𝑢𝜋 ∗
cos 2𝑗 + 1
2𝑁
∗ 𝑣𝜋 𝑓(𝑢, 𝑣)
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7. Wavelet Transform
 In multi resolution analysis (MRA), a scaling function is used to
create a series of approximations of an the image.
 Each differing by the factor of 2 in resolution from its nearest
neighbouring approximations.
 It seeks to represents a signal with good resolution in both time
and frequency by using a set of basis functions called wavelets
{𝛷 𝑘(𝑥)}.
 Wavelets are used to encode the difference in information
between adjacent approximations.
𝑓 𝑥 = ⍺ 𝑘 ∗ 𝛷 𝑘(𝑥)
𝑀−1
𝑘
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8. Discrete Wavelet transform
 DWT is a mathematical tool for decomposing an image.
 The DWT splits the signal into high and low frequency parts.
 The low frequency part is split again into high and low frequency parts.
 For each level of decomposition we first perform the DWT in the
vertical direction followed by the DWT in the horizontal direction.
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9. Wavelet Decomposition
 For 2nd level of decomposition, there are 4 sub-bands
LL1, LH1, HL1, and HH1.
 For each successive level of decomposition, the LL sub band of the
previous level is used as the input.
 To perform second level decomposition, the DWT is applied to LL1
band which decomposes the LL1 band into the four sub- bands LL2,
LH2, HL2, and HH2.
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10. Wavelet Functions
𝛹𝑗,𝑘 𝑥 = 2
𝑗
2 𝛹 2 𝑗 𝑥 − 𝑘
𝑊𝑖 = 𝑠𝑝𝑎𝑛{𝛹𝑗,𝑘(𝑥)}
f (x) = ⍺ 𝑘 𝛹𝑗,𝑘(𝑥)𝑘
Orthogonality and orthonormality condition must be met.
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11. Discrete wavelet transform
 Forward DWT
𝑊𝛷 𝑗𝑜, 𝑘 =
1
𝑀
𝑓(𝑛)𝛷𝑗𝑜,𝑘(𝑛)
𝑛
𝑊 𝛹 𝑗, 𝑘 =
1
𝑀
𝑓(𝑛)𝛹𝑗,𝑘(𝑛)𝑛 j ≥ jo
 Inverse DWT
𝑓 𝑛 = 1/ 𝑀 𝑊𝛷 𝑗𝑜, 𝑘𝑘 𝛷𝑗𝑜,𝑘(𝑛) +1/ 𝑀 𝑊 𝛹 𝑗, 𝑘𝑘 𝛹𝑗,𝑘(𝑛)
𝑤ℎ𝑒𝑟𝑒 𝑀 = 2 𝑗
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12. Security Analysis
 Correlation
Correlation is used to determine the similarity between images, Mathematically,
𝐶𝑜𝑟𝑟 = 𝑖 − µ 𝑗 𝑗 − µ 𝑗 𝑝(𝑖, 𝑗)/𝜕𝑖 𝜕𝑗
 Mean Square Error
MSE is used to measure the difference between values implied by an
estimator and the true values of the quantity being estimated, Mathematically,
𝑀𝑆𝐸 =
1
𝑀 ∗ 𝑁
[𝐶1 𝑖, 𝑗 − 𝐶2(𝑖, 𝑗)]2
𝑁
𝑗=0
𝑀
𝑖=0
 PSNR
Mathematically,
PSNR=10 ∗ 𝑙𝑜𝑔10 𝑀𝐴𝑋2
/MSE
 Histogram testing
Histogram testing is used to check the quality of Encryption.
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13. Proposed Algorithm
Discrete Cosine transform
CorrelationPSNRMSE
Discrete Wavelet transform
MSE PSNR Correlation
Image Size (M*N)
Histogram
testing
Histogram
testing
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14. Security table (Comparison)
Correlation MSE PSNR
-0.0161 -0.0882 18.6475dB
Discrete Cosine Transform
Decomposition
level
Correlation MSE PSNR
L1 0.0046 1.0773 17.8076dB
L2 0.0049 1.0779 17.8092dB
L3 0.0049 -1.3339 16.8795dB
L4 0.0034 0.8831 18.6705dB
Discrete Wavelet Transform
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15. Conclusion
We applied DCT & DWT on a 256*256 size image.
DWT has been a better transform and is a better
decomposition technique.
Each Level of decomposition has a different
correlation and PSNR.
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