Multimedia Tools and Applications

, Volume 78, Issue 2, pp 1511–1546 | Cite as

Multi-bit robust image steganography based on modular arithmetic

  • Biswajita DattaEmail author
  • Sudipta Roy
  • Subhranil Roy
  • Samir Kumar Bandyopadhyay


The main objective is to design a robust algorithm which can hide multiple target bits without direct replacement of the bits of cover image and at the same time maintain perceptibility of carrier medium by reducing the distortion rate by intensity adjustment. The method uses the strength of modular arithmetic for embedding target data and at the same time able to solve the overlapping problem. In this double layer security technique first the target bits are converted into another number system and then these converted digits are embedded by adjusting the pixel intensities in such a way so that modulo operation retrieve data correctly at the receiver side. The proposed technique is tested on different class of images and analyzed based on different parameters. The histograms are distorted significantly for more than four bit insertion and the average PSNR is 34.7 for four multi-bit insertion with 100% payload. Different standard LSB detectors like SP, WS etc. are fail to detect hidden bits and at the same time the statistical attack on stego media unable to get success on stego images. The performance of the proposed technique is measured by Stirmark Benchmark 4.0 whereas the security strength is calculated through KL divergence which establishes it as a more secure algorithm. The Average Embedding Capacity of this technique is four. The work shows better performances than many state-of-the-art-works. The method reduces the distortion rate to half of the standard multi-bit LSB technique. This helps to retain imperceptibility with the increase of capacity through multi-bit insertion. The robustness is introduced in this spatial domain technique by embedding target data without direct replacement of cover bits. This algorithm uses the NP-complete nature of modulo operation to increase security and at the same time introduces parallelism to reduce time complexity.


Image steganography Radix conversion Modulo operator Multi-bit steganography Embedding capacity Robustness 



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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Biswajita Datta
    • 1
    Email author
  • Sudipta Roy
    • 2
    • 3
  • Subhranil Roy
    • 1
  • Samir Kumar Bandyopadhyay
    • 3
  1. 1.Department of Computer Science & EngineeringSt. Thomas’ College of Engineering and TechnologyKolkataIndia
  2. 2.Department of Computer Science & EngineeringUniversity of CalcuttaKolkataIndia
  3. 3.Department of Computer Science & EngineeringCalcutta University Technology Campus, Calcutta UniversityKolkataIndia

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