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Related Concept Videos

Convolution Properties I01:20

Convolution Properties I

421
Convolution computations can be simplified by utilizing their inherent properties.
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:
421
Convolution Properties II01:17

Convolution Properties II

482
The important convolution properties include width, area, differentiation, and integration properties.
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...
482
Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

714
In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
714
Correlation01:09

Correlation

14.2K
In statistics, two variables are said to be correlated if the values of one variable are associated with the other variable. Depending on the relationship between two variables, correlation can be of three types– positive correlation, negative correlation, and zero correlation.
Two variables, for example, a and b, are said to be positively correlated if both variables move in the same direction. In other words, a positive correlation exists between two variables, a and b, if:
14.2K
Deconvolution01:20

Deconvolution

443
Deconvolution, also known as inverse filtering, is the process of extracting the impulse response from known input and output signals. This technique is vital in scenarios where the system's characteristics are unknown, and they must be inferred from the observable signals.
Deconvolution involves several mathematical techniques to derive the impulse response. One common approach is polynomial division. In this method, the input and output sequences are treated as coefficients of...
443
Cross Product01:25

Cross Product

519
The cross product is a fundamental concept in vector algebra that is a vector operation on two different vectors to obtain a third vector. Unlike the scalar product, the cross product results in a vector quantity perpendicular to both the original vectors.
The magnitude of the cross product is obtained by multiplying the magnitude of both the vectors and the sine of the angle between them. This means that a larger angle between the vectors will lead to a greater magnitude of the cross product.
519

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Related Experiment Videos

Plaintext attack on joint transform correlation encryption system by convolutional neural network.

Linfei Chen, BoYan Peng, Wenwen Gan

    Optics Express
    |September 29, 2020
    PubMed
    Summary
    This summary is machine-generated.

    This study demonstrates that joint transform correlation image encryption is vulnerable to convolutional neural network attacks. A trained neural network can directly convert ciphertext to plaintext, bypassing traditional decryption methods.

    Related Experiment Videos

    Area of Science:

    • Optics and Photonics
    • Computer Science
    • Cryptography

    Background:

    • Joint transform correlation (JTC) is a popular image encryption technique due to its real-valued ciphertext and relaxed alignment requirements.
    • Traditional JTC decryption often relies on phase recovery algorithms, which can be complex and sensitive to errors.

    Purpose of the Study:

    • To investigate the vulnerability of JTC image encryption systems to deep learning-based attacks.
    • To develop a novel method for direct ciphertext-to-plaintext conversion using neural networks.

    Main Methods:

    • A convolutional neural network (CNN) was trained on a large dataset of JTC ciphertexts and their corresponding plaintexts.
    • The CNN architecture incorporated sigmoid activation functions and dropout layers for enhanced speed and accuracy.
    • The trained CNN effectively learned to simulate the encryption key.

    Main Results:

    • The trained CNN model demonstrated the ability to directly convert JTC ciphertexts into their original plaintexts.
    • The neural network-based approach proved more efficient than traditional phase recovery methods.
    • The trained equivalent key exhibited notable robustness.

    Conclusions:

    • JTC image encryption systems are susceptible to sophisticated deep learning attacks.
    • CNNs offer a powerful alternative for breaking JTC encryption, providing direct decryption capabilities.
    • The proposed neural network method is feasible and effective, as confirmed by computer simulations.