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Related Concept Videos

Convolution Properties II01:17

Convolution Properties II

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...
Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

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...

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Related Experiment Video

Updated: Jul 10, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

Four-pixel sum-preserving encryption using the chaotic map for high thumbnail-preserving image security.

Chia-Hung Kao1,2, Guan-Zhen Chen3, Yi-You Hou4

  • 1Department of Engineering Science, National Cheng Kung University, Tainan, 701, Taiwan. n98134015@gs.ncku.edu.tw.

Scientific Reports
|July 8, 2026
PubMed
Summary

This study introduces a novel four-pixel sum-preserving encryption (4px-SPE) method to enhance thumbnail-preserving encryption (TPE) security. This approach effectively protects image privacy in cloud services while ensuring thumbnail usability.

Keywords:
Chaotic mapFour-pixel encryptionSecurity analysisSum-preserving encryption (SPE)Thumbnail-preserving encryption (TPE)

Related Experiment Videos

Last Updated: Jul 10, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

Area of Science:

  • Computer Science
  • Cryptography
  • Image Processing

Background:

  • Cloud photo-sharing services risk user privacy through exposed thumbnails.
  • Thumbnail-preserving encryption (TPE) aims to encrypt images while retaining thumbnail functionality.
  • Existing sum-preserving encryption (SPE) methods have limitations with block alignment and plaintext residuals.

Purpose of the Study:

  • To develop an improved SPE method for TPE that addresses limitations of existing techniques.
  • To enhance image privacy in cloud environments without compromising thumbnail usability.
  • To propose a secure and efficient TPE framework using a novel SPE mapping.

Main Methods:

  • Introduced a four-pixel SPE (4px-SPE) mapping, a piecewise bijection on 8-bit pixel quadruples, preserving the four-pixel sum and ensuring perfect invertibility.
  • Integrated the 4px-SPE into a permutation-substitution TPE framework.
  • Utilized a 256-bit master key with deterministic, hash-based key derivation for generating per-image/block keys and permutations, avoiding plaintext-derived material.

Main Results:

  • Validated the 4px-SPE mapping's invertibility through mathematical proof and exhaustive verification of all possible quadruples.
  • Experimental results on grayscale and color images demonstrated high entropy and lossless recovery.
  • The proposed TPE framework successfully maintained thumbnail usability while enhancing image privacy.

Conclusions:

  • The novel 4px-SPE mapping provides a secure and efficient solution for thumbnail-preserving encryption.
  • This method effectively mitigates privacy risks associated with cloud-based photo sharing.
  • The integration into a permutation-substitution TPE framework offers a robust approach to image privacy and thumbnail utility.