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  5. Modeling of improved multi-stage 2D RSA algorithm for cryptographic transformations and blind electron digital signature

Modeling of improved multi-stage 2D RSA algorithm for cryptographic transformations and blind electron digital signature

V. Krasilenko, D. Nikitovich, R. Yatskovska, V. Yatskovskyi
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Description: We consider new modifications of the RSA cryptosystem for the 2D case, namely, improved multi-step models and algorithms for cryptographic transformations (CP) of images and text-graphic documents (TGD), taking into account their specifics and adapting to different formats. It is shown that for some special images for their better encryption additional procedures for their closure are needed, along with the multi-step cryptographic transformations. To this end, and to ensure operation with the same keys, it has been proposed to additionally close the document with the public key of the second party before the encryption procedure with the first party and additionally open it with the same key after the reverse decryption procedure by the second party. To test the proposed RSA modifications of the matrix type, a series of experiments was carried out using the Mathcad software environment. Formulas, program modules, their fragments corresponding to the algorithmic steps of the cryptographic transformation procedures, examples of explicit and transformed images, matrix arrays and their digital signatures are suggested. A histogram-entropy analysis was carried out, which showed a significant (by an order of magnitude!) increase in the entropy of cryptograms and digital signatures to 7.98 - 7.99 bits / pixel even for explicit text-graphic documents with low initial entropy. Experiments in the Mathcad software environment on a variety of examples of encryption of special halftone and color images and TGD demonstrated the functionality and advantages of such improved multi-step 2D RSA models, as well as blind electronic digital signatures and systems based on them.


Keywords: cryptographic transformations, 2D RSA system, matrix multi-step models, encryption, decryption, simulation, electronic signature, algorithm, text and graphic document

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Reference:
 Krasylenko, V.H., Nikitovych, D.V., Yatskovska, R.O. and Yatskovskyi, V.I. (2019), “Modeliuvannia pokrashchenykh bahatokrokovykh 2D RSA alhorytmiv dlia kryptohrafichnykh peretvoren ta slipoho elektronnoho tsyfrovoho pidpysu” [Modeling of improved multi-stage 2D RSA algorithm for cryptographic transformations and blind electron digital signature], Information Processing Systems, Vol. 1(156), pp. 92-100. https://doi.org/10.30748/soi.2019.156.12.