Resistance to Statistical Attacks of Parastrophic Quasigroup Transformation

Verica Bakeva,Aleksandra Popovska-Mitrovikj,Vesna Dimitrova

doi:10.14569/ijacsa.2015.060935

Verica Bakeva, Aleksandra Popovska-Mitrovikj + Show 1 more

Open Access

https://doi.org/10.14569/ijacsa.2015.060935

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Abstract

The resistance to statistical kind of attacks of encrypted messages is a very important property for designing cryptographic primitives. In this paper, the parastrophic quasigroup PE-transformation, proposed elsewhere, is considered and the proof that it has this cryptographic property is given. Namely, it is proven that if PE-transformation is used for design of an encryption function then after n applications of it on arbitrary message the distribution of m-tuples (m = 1; 2; : : : ; n) is uniform. These uniform distributions imply the resistance to statistical attack of the encrypted messages. For illustration of theoretical results, some experimental results are presented as well.

Highlights

Quasigroups and quasigroup transformations are very useful for construction of cryptographic primitives, error detecting and error correcting codes
In this paper we proved that after n applications of P Etransformation on an arbitrary message the distribution of mtuples (m = 1, . . . , n) is uniform and we cannot distinguish classes of probabilities in the distribution of (n + 1)-tuples
This means that if P E-transformation is used as encryption function the obtained cipher messages are resistant to statistical kind of attacks when the number n of applications of P Etransformation is enough large

Summary

INTRODUCTION

Quasigroups and quasigroup transformations are very useful for construction of cryptographic primitives, error detecting and error correcting codes. The quasigroup string transformations E and their properties were considered in several papers. = an an pi2 = · · · = an piν elements Using these will be merged in results, the authors one class proposed an algorithm for cryptanalysis. In paper [4], Krapez gave an idea for a new quasigroup string transformation based on parastrophes of quasigroups. In [3], authors showed that the parastrophic quasigroup transformation has good properties for application in cryptography. To complete the proof of goodness of parastrophic quasigroup transformation for cryptography, it is needed to prove that Theorem 1 holds for that transformation, too.

PARASTROPHIC TRANSFORMATION

THEORETICAL PROOF FOR RESISTANCE TO

EXPERIMENTAL RESULTS

CONCLUSION