On the invertibility of the XOR rotations of a binary word
Author(s)
Rivest, Ronald L.
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Alternative title
The invertibility of the XOR of rotations of a binary word
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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.)
Date issued
2010-12Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer ScienceJournal
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
ISSN
0020-7160
1029-0265