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Journal of Mathematical Cryptology

Managing Editor: Magliveras, Spyros S. / Steinwandt, Rainer / Trung, Tran

Editorial Board: Blackburn, Simon R. / Blundo, Carlo / Burmester, Mike / Cramer, Ronald / Gilman, Robert / Gonzalez Vasco, Maria Isabel / Grosek, Otokar / Helleseth, Tor / Kim, Kwangjo / Koblitz, Neal / Kurosawa, Kaoru / Lauter, Kristin / Lange, Tanja / Menezes, Alfred / Nguyen, Phong Q. / Pieprzyk, Josef / Rötteler, Martin / Safavi-Naini, Rei / Shparlinski, Igor E. / Stinson, Doug / Takagi, Tsuyoshi / Williams, Hugh C. / Yung, Moti

CiteScore 2018: 1.41

SCImago Journal Rank (SJR) 2018: 0.342
Source Normalized Impact per Paper (SNIP) 2018: 1.076

Mathematical Citation Quotient (MCQ) 2018: 0.75

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Volume 7, Issue 2


Using carry-truncated addition to analyze add-rotate-xor hash algorithms

Rebecca E. Field / Brant C. Jones
Published Online: 2013-03-19 | DOI: https://doi.org/10.1515/jmc-2012-0019


We introduce a truncated addition operation on pairs of N-bit binary numbers that interpolates between ordinary addition mod and bitwise addition in . We use truncated addition to analyze hash functions that are built from the bit operations add, rotate, and xor, such as Blake, Skein, and Cubehash. Any ARX algorithm can be approximated by replacing ordinary addition with truncated addition, and we define a metric on such algorithms which we call the sensitivity. This metric measures the smallest approximation agreeing with the full algorithm a statistically useful portion of the time (we use ). Because truncated addition greatly reduces the complexity of the non-linear operation in ARX algorithms, the approximated algorithms are more susceptible to both collision and pre-image attacks, and we outline a potential collision attack explicitly. We particularize some of these observations to the Skein hash function.

Keywords: Hash algorithms; ARX; new metric on ARX algorithms; practical attacks

About the article

Received: 2012-07-09

Revised: 2012-12-28

Accepted: 2013-03-08

Published Online: 2013-03-19

Published in Print: 2013-09-01

Citation Information: Journal of Mathematical Cryptology, Volume 7, Issue 2, Pages 97–110, ISSN (Online) 1862-2984, ISSN (Print) 1862-2976, DOI: https://doi.org/10.1515/jmc-2012-0019.

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© 2013 by Walter de Gruyter Berlin Boston.Get Permission

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