The permutation parity machine is a binary variant of the tree parity machine.<ref name="Reyes">{{cite webjournal |urllast1=http://iopscienceReyes |first1=O.iop M. |last2=Kopitzke |first2=I. |last3=Zimmermann |first3=K.org/1751-8121/42/19/195002H. |date=April 2009 |title=Permutation Parity Machines for Neural Synchronization |author1journal=OscarJournal Mauricioof ReyesPhysics A: Mathematical and Theoretical |author2volume=Ingo Kopitzke42 |author3issue=Karl-Heinz Zimmermann19 |pages=195002 |last-author-ampissn=yes1751-8113 |doi=10.1088/1751-8113/42/19/195002}}</ref>
It consists of one input layer, one hidden layer and one output layer. The number of neurons in the output layer depends on the number of hidden units K. Each hidden neuron has N binary input neurons:
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Other configurations of the output layer for K>2 are also possible.<ref name="Reyes" />
This machine has proven to be robust enough against some attacks<ref name="Reyes2">{{cite webjournal |urllast1=http://pre.aps.org/abstract/PRE/v81/i6/e066117Reyes |first1=Oscar Mauricio |last2=Zimmermann |first2=Karl-Heinz |date=June 2010 |title=Permutation Parityparity Machinesmachines for Neuralneural Cryptographycryptography |author1journal=OscarPhysical MauricioReview ReyesE |volume=81 |author2issue=Karl-Heinz Zimmermann6 |lastauthorampissn=yes1539-3755 |doi=10.1103/PhysRevE.81.066117}}</ref> so it could work as a cryptographic mean, but a recent implementation of a probabilistic attack has shown that a key-exchange protocol based on PPM can be violated.<ref name="Seoane">{{cite webjournal |urllast1=http://preSeoane |first1=Luís F.aps.org/abstract/PRE/v85/i2/e025101 |last2=Ruttor |first2=Andreas |date=February 2012 |title=Successful attack on permutation-parity-machine-based neural cryptography |author1journal=LuísPhysical F.Review SeoaneE |volume=85 |author2issue=Andreas Ruttor2 |lastauthorampissn=yes1539-3755 |doi=10.1103/PhysRevE.85.025101}}</ref>
