A note on the fuzzy Xor

Radosław Łukasik

doi:10.2478/amsil-2025-0018

.blurhash-client-img { display: none !important; }

A note on the fuzzy Xor

Annales Mathematicae Silesianae

Volume 40 (2026): Issue 1 (March 2026)

By: Radosław Łukasik

Open Access

|Nov 2025

Abstract

In this paper we will try to answer what conditions must be met by the fuzzy Xor to be used for cryptographic purposes. We will also show that defining the fuzzy Xor using other fuzzy connectives is not suitable for this purpose.

References

M. Baczyński and B. Jayaram, Fuzzy Implications, Studies in Fuzziness and Soft Computing, Vol. 231, Springer-Verlag, Berlin, 2008.
Search in Google Scholar Back to article
B.C. Bedregal, R.H.S. Reiser, and G.P. Dimuro, Xor-implications and E-implications: classes of fuzzy implications based on fuzzy Xor, Electron. Notes Theor. Comput. Sci. 247 (2009), 5–18.
Search in Google Scholar Back to article
B.C. Bedregal, R.H.S. Reiser, and G.P. Dimuro, Revisiting Xor-implications: classes of fuzzy (co)implications based on f-Xor (f-XNor) connectives, Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 21 (2013), no. 6, 899–925.
Search in Google Scholar Back to article
G. Bongiovanni and P. Penna, XOR-based schemes for fast parallel IP lookups, Theory Comput. Syst. 38 (2005), no. 4, 481–501.
Search in Google Scholar Back to article
E.G. Codding and G. Horlick, Application of AND and exclusive-or (XOR) logic operations to the identification of elemental emission spectra measured using a photodiode array direct reading spectrometer, Appl. Spectrosc. 27 (1973), no. 5, 366–370.
Search in Google Scholar Back to article
M.M. Gupta, A. Kandel, W. Bandler, and J.B. Kiszka (Eds.), Approximate Reasoning in Expert Systems, North-Holland Publishing Co., Amsterdam, 1985.
Search in Google Scholar Back to article
Y. Horikawa, Landscapes of basins of local minima in the XOR problem, in: Proceedings of 1993 International Conference on Neural Networks (IJCNN-93-Nagoya, Japan), IEEE, 1993, pp. 1677–1680.
Search in Google Scholar Back to article
L. Kohout and E. Kim, Characterization of interval fuzzy logic systems of connectives by group transformations, Reliab. Comput. 10 (2004), no. 4, 299–334.
Search in Google Scholar Back to article
A.G. Konheim, Computer Security and Cryptography, John Wiley & Sons, Inc., Hoboken, 2007.
Search in Google Scholar Back to article
M. Maeda, M. Suenaga, and H. Miyajima, Qubit neuron according to quantum circuit for XOR problem, Appl. Math. Comput. 185 (2007), no. 2, 1015–1025.
Search in Google Scholar Back to article
C.F. Mela and D.R. Lehmann, Using fuzzy set theoretic techniques to identify preference rules from interactions in the linear model: an empirical study, Fuzzy Sets and Systems 71 (1995), no. 2, 165–181.
Search in Google Scholar Back to article
N.D. Mermin, Quantum Computer Science. An Introduction, Cambridge University Press, Cambridge, 2007.
Search in Google Scholar Back to article
W. Pedrycz and G. Succi, fXOR fuzzy logic networks, Soft Comput. 7 (2002), no. 2, 115–120.
Search in Google Scholar Back to article
C. Shannon, Communication theory of secrecy systems, Bell System Tech. J. 28 (1949), 656–715.
Search in Google Scholar Back to article
W. Stallings, Cryptography and Network Security. Principles and Practice, Prentice Hall, Upper Saddle River, 1999.
Search in Google Scholar Back to article
H. Vandierendonck and K. De Bosschere, XOR-based hash functions, IEEE Trans. Comput. 54 (2005), no. 7, 800–812.
Search in Google Scholar Back to article
H. Vandierendonck, P. Manet, and J.-D. Legat, Application-specific reconfigurable XOR-indexing to eliminate cache conflict misses, in: Proceedings of the Design Automation & Test in Europe Conference, IEEE, 2006, pp. 357–362.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/amsil-2025-0018 | Journal eISSN: 2391-4238 (formerly 0860-2107) | Journal ISSN: 0860-2107

Journal RSS Feed

Language: English

Page range: 125 - 139

Submitted on: Jul 7, 2025

Accepted on: Oct 26, 2025

Published on: Nov 15, 2025

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Keywords:

t-norm,

MSC:

Related subjects:

© 2025 Radosław Łukasik, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 40 (2026): Issue 1 (March 2026)