On the invertibility of the XOR rotations of a binary word
Name
Rivest-OnTheInvertibilityOfTheXOROfVariousRotationsOfABinaryWord (1).pdf
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112.82 KB
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Author(s)
Rivest, Ronald L.
Alternative Title
The invertibility of the XOR of rotations of a binary word
Date Issued
December 2010
Journal
International Journal of Computer Mathematics
Publisher
Taylor & Francis Group
Citation
Rivest, Ronald. “The Invertibility of the XOR of Rotations of a Binary Word.” International Journal of Computer Mathematics (2011) 88.2 : 1–4.
Version
Author's final manuscript
Abstract
We prove the following result regarding operations on a binary word whose length is a power of two: computing the exclusive-or of a number of rotated versions of the word is an invertible (one-to-one) operation if and only if the number of versions combined is odd. (This result is not new; there is at least one earlier proof, due to Thomsen [Cryptographic hash functions, PhD thesis, Technical University of Denmark, 28 November 2008]. Our proof may be new.)
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1080/00207161003596708
