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{{Short description|Branch of cryptography}}
'''Neural cryptography''' is a branch of [[cryptography]] dedicated to analyzing the application of [[stochastic]] algorithms, especially [[artificial neural network]] algorithms, for use in [[encryption]] and [[cryptanalysis]].
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== Applications ==
In 1995, Sebastien Dourlens applied neural networks to cryptanalyze [[Data Encryption Standard|DES]] by allowing the networks to learn how to invert the S-tables of the DES. The bias in DES studied through Differential Cryptanalysis by [[Adi Shamir]] is highlighted. The experiment shows about 50% of the key bits can be found, allowing the complete key to be found in a short time. Hardware application with multi micro-controllers have been proposed due to the easy implementation of multilayer neural networks in hardware.
One example of a public-key protocol is given by Khalil Shihab {{Citation needed|date=May 2025}}. He describes the decryption scheme and the public key creation that are based on a [[backpropagation]] neural network. The encryption scheme and the private key creation process are based on Boolean algebra. This technique has the advantage of small time and memory complexities. A disadvantage is the property of backpropagation algorithms: because of huge training sets, the learning phase of a neural network is very long. Therefore, the use of this protocol is only theoretical so far.
== Neural key exchange protocol ==
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## Compute the value of the output neuron
## Compare the values of both tree parity machines
### Outputs are the same:
### Outputs are different:
After the full synchronization is achieved (the weights w<sub>ij</sub> of both tree parity machines are same), {{var|A}} and {{var|B}} can use their weights as keys.<br>
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For conventional cryptographic systems, we can improve the security of the protocol by increasing of the key length. In the case of neural cryptography, we improve it by increasing of the synaptic depth {{var|L}} of the neural networks. Changing this parameter increases the cost of a successful attack exponentially, while the effort for the users grows polynomially. Therefore, breaking the security of neural key exchange belongs to the complexity class NP.
Alexander Klimov, Anton Mityaguine, and Adi Shamir say that the original neural synchronization scheme can be broken by at least three different attacks—geometric, probabilistic analysis, and using genetic algorithms. Even though this particular implementation is insecure, the ideas behind chaotic synchronization could potentially lead to a secure implementation.<ref name="Klimov">{{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|doi-access=free }}</ref>
=== 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 |s2cid=122126162 }}</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 |pages=066117 |issn=1539-3755 |doi=10.1103/PhysRevE.81.066117|pmid=20866488 |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 |pages=025101 |issn=1539-3755 |doi=10.1103/PhysRevE.85.025101|pmid=22463268 |arxiv=1111.5792 |bibcode=2012PhRvE..85b5101S |s2cid=17187463 }}</ref>
=== Security against quantum computers ===
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<references />
* [https://www.researchgate.net/publication/340226157_Neuro-Cryptographie_Appliquee_et_Neuro-Cryptanalyse_du_DES Neuro-Cryptography] 1995 - The first definition of the Neuro-Cryptography (AI Neural-Cryptography) applied to DES cryptanalysis by Sebastien Dourlens, France.
* [https://web.archive.org/web/20070613172058/http://theorie.physik.uni-wuerzburg.de/~ruttor/neurocrypt.html Neural Cryptography] - Description of one kind of neural cryptography at the [[University of Würzburg]], Germany.
* {{cite conference |last1=Kinzel |first1=W. |last2=Kanter |first2=I. |date=2002 |title=Neural cryptography |book-title=Proceedings of the 9th International Conference on Neural Information Processing |conference=ICONIP '02 |pages=1351–1354 |doi=10.1109/ICONIP.2002.1202841|arxiv=cond-mat/0208453 }} - One of the leading papers that introduce the concept of using synchronized neural networks to achieve a public key authentication system.
* {{cite journal |last1=Li |first1=Li-Hua |last2=Lin |first2=Luon-Chang |last3=Hwang |first3=Min-Shiang |date=November 2001 |title=A remote password authentication scheme for multiserver architecture using neural networks |journal=IEEE Transactions on Neural Networks |volume=12 |issue=6 |pages=1498–1504 |issn=1045-9227 |doi=10.1109/72.963786|pmid=18249979 }} - Possible practical application of Neural Cryptography.
* {{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|doi-access=free }} - 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 |pages=036121 |issn=1539-3755 |doi=10.1103/PhysRevE.73.036121|pmid=16605612 |arxiv=cond-mat/0512022 |bibcode=2006PhRvE..73c6121R |s2cid=27786815 }}
* {{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 | url-status=dead | archiveurl=https://web.archive.org/web/20070712012959/http://www.scipub.org/fulltext/jcs/jcs29710-715.pdf | archivedate=2007-07-12 }}
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