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=== Permutation parity machine ===
The permutation parity machine is a binary variant of the tree parity machine.<ref name="Reyes">{{cite journal |last1=Reyes |first1=O. M. |last2=Kopitzke |first2=I. |last3=Zimmermann |first3=K.-H. |date=April 2009 |title=Permutation Parity Machines for Neural Synchronization |journal=Journal of Physics A: Mathematical and Theoretical |volume=42 |issue=19 |pages=195002 |issn=1751-8113 |doi=10.1088/1751-8113/42/19/195002|bibcode=2009JPhA...42s5002R }}</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 journal |last1=Reyes |first1=Oscar Mauricio |last2=Zimmermann |first2=Karl-Heinz |date=June 2010 |title=Permutation parity machines for neural cryptography |journal=Physical Review E |volume=81 |issue=6 |issn=1539-3755 |doi=10.1103/PhysRevE.81.066117|bibcode=2010PhRvE..81f6117R }}</ref> so it could be used as a cryptographic mean, but it has been shown to be vulnerable to a probabilistic attack.<ref name="Seoane">{{cite journal |last1=Seoane |first1=Luís F. |last2=Ruttor |first2=Andreas |date=February 2012 |title=Successful attack on permutation-parity-machine-based neural cryptography |journal=Physical Review E |volume=85 |issue=2 |issn=1539-3755 |doi=10.1103/PhysRevE.85.025101|arxiv=1111.5792 |bibcode=2012PhRvE..85b5101S }}</ref>
=== Security against quantum computers ===
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* {{cite conference |last1=Klimov |first1=Alexander |last2=Mityagin |first2=Anton |last3=Shamir |first3=Adi |date=2002 |title=Analysis of Neural Cryptography |url=https://iacr.org/archive/asiacrypt2002/25010286/25010286.pdf |book-title=Advances in Cryptology |conference=ASIACRYPT 2002 |series=[[Lecture Notes in Computer Science|LNCS]] |volume=2501 |pages=288–298 |issn=0302-9743 |doi=10.1007/3-540-36178-2_18 |accessdate=2017-11-15}} - Analysis of neural cryptography in general and focusing on the weakness and possible attacks of using synchronized neural networks.
* [http://www.opus-bayern.de/uni-wuerzburg/volltexte/2007/2361/ Neural Synchronization and Cryptography] - Andreas Ruttor. PhD thesis, Bayerische Julius-Maximilians-Universität Würzburg, 2006.
* {{cite journal |last1=Ruttor |first1=Andreas |last2=Kinzel |first2=Wolfgang |last3=Naeh |first3=Rivka |last4=Kanter |first4=Ido |date=March 2006 |title=Genetic attack on neural cryptography |journal=Physical Review E |volume=73 |issue=3 |issn=1539-3755 |doi=10.1103/PhysRevE.73.036121|arxiv=cond-mat/0512022 |bibcode=2006PhRvE..73c6121R }}
* {{cite journal | author=Khalil Shihab | year=2006 | title=A backpropagation neural network for computer network security | journal=Journal of Computer Science 2 | pages=710–715 | url=http://www.scipub.org/fulltext/jcs/jcs29710-715.pdf | deadurl=yes | archiveurl=https://web.archive.org/web/20070712012959/http://www.scipub.org/fulltext/jcs/jcs29710-715.pdf | archivedate=2007-07-12 | df= }}
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