Designs, Codes and Cryptography

, Volume 45, Issue 3, pp 347–357

Generalized mix functions and orthogonal equitable rectangles



Ristenpart and Rogaway defined “mix” functions, which are used to mix inputs from two sets of equal size, and produce outputs from the same two sets, in an optimal way. These functions have a cryptographic application in the context of extending the domain of a block cipher. It was observed that mix functions could be constructed from orthogonal latin squares. In this article, we give a simple, scalable construction for mix functions. We also consider a generalization of mix functions, in which the two sets need not be of equal size. These generalized mix functions turn out to be equivalent to an interesting type of combinatorial design which has not previously been studied. We term these “orthogonal equitable rectangles” and we construct them for all possible parameter situations, with a small number of exceptions and possible exceptions.


Orthogonal latin square Equitable rectangle Block cipher 

AMS Classifications

05B15 94A60 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.David R. Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada

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