Image compression and encryption using chinese remainder theorem

  • Tejas DusejaEmail author
  • Maroti Deshmukh


The proposed encryption technique uses Chinese Remainder Theorem (CRT) and hash map to generate and distribute secret co-prime keys to participants. It utilizes the fact that CRT gives a unique solution for the set of congruent equations if and only if the modulus values are relatively co-prime to each other i.e., Greatest Common Divisor (GCD) of moduli is equal to 1. In this paper, we have proposed secret image sharing scheme using CRT and obtained results on grayscale images of different dimensions. The proposed technique not only increases randomness in encrypted image but also compresses the image, resulting in easy storage and fast transmission. As compression ratio is dependent on shared keys, all shared keys are essential for recovering image without any noise, absence of any key gives an image which is deviated from our original image. For r participants, r pixels are encrypted and compressed simultaneously at a time using CRT which gives one encrypted unique value corresponding to those r pixels. As this encrypted value can be greater than 255, hash map is used to store this value. The experimental results show that the encrypted image is compressed, is not disclosing any secret information and recovery of original image is loss-less.


Compression Chinese remainder theorem Extended Euclidean algorithm Prime numbers Security 



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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.National Institute of Technology, UttarakhandSrinagarIndia

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