Paper 2025/1244
A New Bijective Pairing Alternative for Encoding Natural Numbers
Abstract
Pairing functions uniquely encode pairs of natural numbers into single values, a fundamental operation in mathematics and computer science. This paper presents an alternative approach inspired by geometric visualization—viewing pairs as arrangements of square blocks with missing tiles. Our method achieves packing efficiency comparable to the classical Cantor pairing function and matches the time complexity of both Cantor and Szudzik functions. Encoding is performed in constant time using simple arithmetic operations, while decoding requires square root computations, resulting in efficient inversion. By combining algebraic rigor with intuitive geometric insight, this approach offers a practical and accessible alternative for applications involving data encoding, spatial structures, and combinatorial problems.
Metadata
- Available format(s)
-
PDF
- Publication info
- Preprint.
- Keywords
- Bijective pairing functionPairing function alternativeNatural number encodingInteger pair mappingLossless coordinate encodingInvertible mappingAlgorithmic efficiencyDiscrete mathematicsData structure indexingSpace-filling functions
- Contact author(s)
- manideep9949466287 @ gmail com
- History
- 2025-07-24: revised
- 2025-07-05: received
- See all versions
- Short URL
- https://ia.cr/2025/1244
- License
-
CC BY-NC
BibTeX
@misc{cryptoeprint:2025/1244,
author = {Manideep Thotakura},
title = {A New Bijective Pairing Alternative for Encoding Natural Numbers},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/1244},
year = {2025},
url = {https://eprint.iacr.org/2025/1244}
}
