Digital Cryptography Implementation using Neurocomputational Model

with Autoencoder Architecture

Francisco Quinga Socasi

, Ronny Velastegui

, Luis Zhinin-Vera

, Rafael Valencia-Ramos

Francisco Ortega-Zamorano

and Oscar Chang

School of Mathematical and Computational Sciences, Yachay Tech University, 100650, Urcuqui, Ecuador

Keywords:

Cryptography, Artiﬁcial Neural Network, Autoencoder, ASCII Characters.

Abstract:

An Autoencoder is an artiﬁcial neural network used for unsupervised learning and for dimensionality re-

duction. In this work, an Autoencoder has been used to encrypt and decrypt digital information. So, it is

implemented to code and decode characters represented in an 8-bit format, which corresponds to the size of

ASCII representation. The Back-propagation algorithm has been used in order to perform the learning process

with two different variant depends on when the discretization procedure is carried out, during (model I) or after

(model II) the learning phase. Several tests were conducted to determine the best Autoencoder architectures

to encrypt and decrypt, taking into account that a good encrypt method corresponds to a process that generate

a new code with uniqueness and a good decrypt method successfully recovers the input data. A network that

obtains a 100% in the two process is considered a good digital cryptography implementation. Some of the

proposed architecture obtain a 100% in the processes to encrypt 52 ASCII characters (Letter characters) and

95 ASCII characters (printable characters), recovering all the data.

1 INTRODUCTION

Cryptography is a science that allows to write mes-

sages so that only authorized people can read them.

The goal of cryptography is keep the integrity, conﬁ-

dentiality, and authenticity of the information. Mes-

sages are encrypted and decrypted around a key. This

key is considered as the unique way to read an en-

crypted message. There are many techniques to en-

crypt information that are classiﬁed depending on

what type of key is used: secret key, public key and

hash function. However, in all the cases the message

that we want to encrypt is called plain text, and the

encrypted text is denominated cipher text (Stallings,

1998).

Advanced Encryption Standard (AES) is one of

the most used encryption algorithms today. Since

2002, AES is a worldwide standard for information

encryption/decryption. This algorithm allows to en-

crypt blocks of information of 128 bits, using a sym-

metric key of 128, 192 or 256 bits (Forouzan, 2007).

https://orcid.org/0000-0003-3213-4460

https://orcid.org/0000-0001-8628-9930

https://orcid.org/0000-0002-6505-614X

https://orcid.org/0000-0002-1036-1817

https://orcid.org/0000-0002-4397-2905

https://orcid.org/0000-0002-4336-7545

Artiﬁcial neural networks could be deﬁned as net-

works massively interconnected in parallel of simple

elements and with hierarchical organization, which

try to interact with the objects of the real world in

the same way as the biological nervous system does

(Matich, 2001).

An Autoencoder is a feed-forward multilayer neu-

ral network that learns to reproduce the same informa-

tion that it receives input, in the output. So, is a multi-

layer neural network consisting of: an input layer, an

output layer (both with an equal number of neurons),

and one or more intermediate layers, also called hid-

den layers. At ﬁrst glance, it seems that it is a useless

network since it simply replicates the information it

receives. But, in reality, the key lies in the internal

structure and general architecture of the said network

(Tan, 1998).

In recent years, investigations on neural networks

linked to cryptography have increased considerably.

Due to the nature of artiﬁcial neural networks, and to

their great combination of weights and connections, it

is possible to hide and compress information in their

structure (Lonkar and Charniya, 2014).

So, neural networks coupled with cryptography

give us a novel approach to encrypt and decrypt in-

formation.

In this paper, an Autoencoder to encrypt and de-

crypt digital information has been used. This infor-

Socasi, F., Velastegui, R., Zhinin-Vera, L., Valencia-Ramos, R., Ortega-Zamorano, F. and Chang, O.

Digital Cryptography Implementation using Neurocomputational Model with Autoencoder Architecture.

DOI: 10.5220/0009154908650872

In Proceedings of the 12th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2020) - Volume 2, pages 865-872

ISBN: 978-989-758-395-7; ISSN: 2184-433X

865

mation is represented in an 8-bit format, which cor-

responds to an ASCII (American Standard Code for

Information Interchange) character.

Because the optimal architecture of the neural net-

works depends in its great majority of its speciﬁc ap-

plication (Rojas, 1996), we will compare two pro-

posed models of architectures and try to ﬁnd the best

it as a model of encryption / decryption.

For this, we will perform a series of tests in which

we will vary some parameters such as: number of in-

ternal neurons, among others. And we will observe

the accuracy of the entire network after each test. And

so, we will choose the network with the greatest ac-

curacy.

2 RELATED WORK

Neural networks can accurately identify a nonlin-

ear system model from the inputs and outputs of a

complex system, and do not need to know the exact

relationship between inputs and outputs (Charniya,

2013). All this makes the use of an ANN viable, in the

process of encryption and decryption of data. Artiﬁ-

cial Neural Networks offer a very powerful and gen-

eral framework for representing the nonlinear map-

ping of several input variables to several output vari-

ables. Based on this concept, an encryption system by

using a key that changes permanently was developed.

In Volna’s work, the topology is very important issue

to achieve a correct function of the system, therefore

a multilayer topology was implemented, considered

the more indicated topology in this case. Also for the

encryption and decryption process, it was carried out

using a Back-propagation; technique compatible with

the topology (Volna et al., 2012).

Neural networks can be used to generate common

secret key (Jogdand, 2011). The neural cryptography,

exist two networks that receive an identical input vec-

tor, generate an output bit and are trained based on

the output bit. Both networks and their weight vec-

tors exhibit a novel phenomenon, where the networks

synchronize to a state with identical time-dependent

weights. The generated secret key over a public chan-

nel is used for encrypting and decrypting the informa-

tion being sent on the channel.

A watermarking technique to hides information in

images to diminish copyright violations and falsiﬁ-

cation is proposed (Wang et al., 2006). Basically, it

embeds a little image that represent a signature into

another image. This paper uses techniques as human

visual system (HVS) and discrete wavelet transform

(DWT) to decompose the host image in L-levels. This

is the reason for the Wavelet Domain in the tittle. The

method is embed the watermark into the wavelet co-

efﬁcients chosen by HVS (brightness, weight factor).

This uses neural network to memorize the relation-

ship between the watermark W and the wavelet coef-

ﬁcients I. The topology is a 8, 5 and 1 layer for input,

hidden and output layer respectively. When the net-

work is trained it is capable of recover the watermark

image. The experiment introduces different ranges of

noise into the hos image and see the capability of re-

cover the watermark image.

The application of interacting neural networks for

key exchange over a public channel is showed (Kinzel

and Kanter, 2016). It seems that two neural networks

mutely trained, achieve a synchronization state where

its time dependent synaptic weights are exactly the

same. Neural cryptography uses a topology called

tree parity machine which consist of one output neu-

ron, K hidden neurons and K*N input neurons. The

hidden values are equal to the sign function of dot

product of input and weights while the output value

is the multiplication of hidden values. The training

process is carried out comparing the outputs of the

corresponding tree parity machines of two partners

A and B. It has not been proved that no exits an al-

gorithm for success attack, but this approach is very

hard to crack by brute force. Even though an attacker

knows the input/output relation and knows the algo-

rithm, he is not able to recover the secret common key

that A and B uses for encryption. Neural networks are

the unique algorithm for key generation over a public

channel that is not based on number theory. Its main

advantages over traditional approaches are: it simple,

low computations for training and a new key is gener-

ated for each message exchange.

Likewise, the applications of mutual learning neu-

ral networks that get synchronization of their time de-

pendent weights is showed (Klein et al., 2005). It

suggests that synchronization is novel approach for

the generation of a secure cryptographic secret-key

using a public channel. For a further insights over

the synchronization, the process is analytically de-

scribed using statistical physics methods. This works

describes the learning process in a simple network,

where two perceptrons receive a common and change

their weights according to their mutual output, and the

learning process in a tree parity machines. In addition,

a new technique that combines neural networks with

chaos synchronization. This seems to be the most se-

cure against attackers. Finally, this works explains the

different kind of attacker techniques and suggest that

using a big enough weight space the systems becomes

more secure.

Another ﬁeld in which neural networks have been

applied together with cryptography is Steganalysis.

ICAART 2020 - 12th International Conference on Agents and Artiﬁcial Intelligence

866

Artiﬁcial Neural Network is utilized as the classiﬁer

(Shi et al., 2005). This paper concludes that ANN per-

forms better in Steganalysis than Bayes classiﬁer due

to its powerful learning capability. Steganalysis is the

art and science to detect whether a given medium has

hidden message in it.

Pseudo random number generator is another ap-

proach for neural networks in cryptography. Ran-

domness increases the security of cryptosystem. The

result of many tests claim that the resulting genera-

tor is well suited for practical implementation of efﬁ-

cient stream cipher cryptosystems (Cheng and Chan,

1998). The pseudo random number generator takes

the advantage of multi-layer perception (MLP) neu-

ral networks. In over-ﬁtting process, the network

will not be able to predict the input pattern when re-

ceiving unknown input patterns and will give unpre-

dictable results (Karras and Zorkadis, 2003). MLP

neural network can be used as strong independent ran-

dom generator and can also be used as a method of

strengthening the current existing generators by tak-

ing the pseudo random numbers output by linear com-

putational generators as input to the neural networks

(Hadke and Kale, 2016).

3 AUTOENCODER FOR

ENCRYPTION AND

DECRYPTION OF ASCII CODE

3.1 Autoencoder Architecture

The architecture of an artiﬁcial neural network with

Autoencoder is composed by a ﬁrst layer in which the

input data is presented, and an output layer in which

the presented data is recovered. Both layers have to

be implemented with equal number of neural units,

i.e.neurons, and one or more intermediate layers, also

called hidden layers (Buduma, 2015). In addition,

in order to use the Autoencoder for encryption / en-

cryption purposes, the architecture must be symmet-

ric. Also, the central inner layer must be of discrete

output, and the same size as the input and output lay-

ers. This architecture is shown in the Figure 1.

When entering information in the network, it must

ﬁnd a way to transfer it through each hidden layer.

Once the information reaches the central hidden layer,

we obtain a discrete exit of the same size as the en-

trance. So at this point, we have made an encryption

of our information. After the information is in the

central layer (where the information is currently en-

crypted), this information continues through the rest

of the network, and in the end, we will obtain our orig-

Discrete Code Layer

Input: “c”

Output: “c”

Hidden layer

with n neurons

Hidden layer

with n neurons

Figure 1: Autoencoder architecture of the proposed method.

inal information. So, we have made a decryption of

information. Therefore, once trained the network, we

can divide it into two parts, the ﬁrst is the encryptor,

and the second is the decryptor.

3.2 Back-Propagation Algorithm

The Back-Propagation algorithm is a supervised

learning method for training multilayer artiﬁcial neu-

ral networks, and even if the algorithm is very well

known, we summarize in this section the main equa-

tions in relationship to the implementation of the

Back-Propagation algorithm, as they are important in

order to understand the current work.

Let’s consider a neural network architecture com-

prising several hidden layers. If we consider the neu-

rons belonging to a hidden or output layer, the activa-

tion of these units, denoted by y

, can be written as:

= g





∑

j=1

i j

· s





= g(h) , (1)

where w

i j

are the synaptic weights between neuron i

in the current layer and the neurons of the previous

layer with activation s

. In the previous equation, we

have introduced h as the synaptic potential of a neu-

ron. The activation function used, g, is the logistic

function given by the following equation:

g(x) =

1 + e

−βx

, (2)

The objective of the BP supervised learning algorithm

is to minimize the difference between given outputs

(targets) for a set of input data and the output of the

network. This error depends on the values of the

synaptic weights, and so these should be adjusted in

Digital Cryptography Implementation using Neurocomputational Model with Autoencoder Architecture

867

order to minimize the error. The error function com-

puted for all output neurons can be deﬁned as:

E =

∑

k=1

∑

i=1

(k) − y

(k))

, (3)

where the ﬁrst sum is on the p patterns of the data set

and the second sum is on the M output neurons. z

(k)

is the target value for output neuron i for pattern k, and

(k) is the corresponding response output of the net-

work. By using the method of gradient descent, the

BP attempts to minimize this error in an iterative pro-

cess by updating the synaptic weights upon the pre-

sentation of a given pattern. The synaptic weights be-

tween two last layers of neurons are updated as:

∆w

i j

(k) = −η

∂E

∂w

i j

(k)

= η[z

(k) − y

(k)]g

(k),

(4)

where η is the learning rate that has to be set in

advance (a parameter of the algorithm), g

is the

derivative of the sigmoid function and h is the synap-

tic potential previously deﬁned, while the rest of

the weights are modiﬁed according to similar equa-

tions by the introduction of a set of values called the

“deltas” (δ), that propagate the error from the last

layer into the inner ones, that are computed accord-

ing to Eqs. 5 and 6.

The delta values for the neurons of the last of the

N hidden layers are computed as:

= (S

)

− S

], (5)

The delta values for the rest of the hidden layer

neurons are computed according to:

= (S

)

∑

i j

l+1

, (6)

3.3 Discretization Methods of the

Middle Layer

Two different methods of discretization of the middle

layer have be implemented in order to analyze the bet-

ter implementation for the autoencoder with encryp-

tion use.

3.3.1 Model I

In Model I, the learning algorithm Back-Propagation

is used, but with the difference that the output of the

central layer is always given in discrete values (by

rounding).

3.3.2 Model II

In Model II, the normal Back-Propagation learning al-

gorithm is used. So, during training, the output of

the central layer is always given in continuous val-

ues. The discretization of the central layer is done

only once the training has been completed.

4 EXPERIMENTAL STUDY

The architecture employed for the autoencoder meth-

ods has been with 8 input neurons in order to represent

ASCII characters, n neurons in the ﬁrst hidden layer,

8 neurons in the second hidden layer to represent the

codiﬁcation of the data, n neurons in the third hidden

layer, and ﬁnally 8 neurons in the output layer to re-

covered the initial data. The architecture is shown in

Figure 1, taking into account, that n has been changed

to analyze the best architecture.

Cryptographic tests using two sets of input data

have been performed. The ﬁrst input set contains 52

patterns, that is, 52 ASCII characters (letter charac-

ters). While the second input set is of a larger size,

since it consists of 95 ASCII characters (printable

characters).

Table 1 shows the results in terms of Accuracy and

Uniqueness of the resultant binary code for Model I,

using an input data set of 52 patterns. The ﬁrst column

correspond to the number (n) of neurons in the second

and fourth layer, for purposes of this investigation, n

can take one of these values: 7, 8, 9, 10. The “Beta”

ﬁeld is the gain value of the transfer function used, in

this research it is the sigmoid function. For this inves-

tigation, the possible values that “Beta” can take are:

5, 10, 15, 20, 25. The ﬁeld “Min MSE” corresponds

to the minimum mean squared error reached during

the training process of this network. Then, “Epoch”

corresponds to the epoch number in which the value

speciﬁed in “Min MSE” was reached ﬁrst. Then, the

ﬁeld “Accuracy” corresponds to the accuracy of the

architecture in the recovery of the 52 patterns. There-

fore, this ﬁeld “Accuracy” is the most important in our

table, since only architectures that achieve a 100%

of “Accuracy” will be considered valid architectures

for cryptographic purposes. Architectures that do not

achieve an Accuracy of 100% will be called simply

invalid. Finally, the ﬁeld “Uniq.Cod.Layer” is derived

directly from the ﬁeld “Accuracy”, and means the per-

centage of uniqueness of outputs with respect to the

input.

Now, once all the ﬁelds in Table 1 have been de-

ﬁned, it is time to interpret their contents. As we

already know, we are only interested in valid archi-

ICAART 2020 - 12th International Conference on Agents and Artiﬁcial Intelligence

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Table 1: Results of the architectures, 52 inputs, Model I.

Arch. Beta Min MSE Epoch Acc. (%)

Uniq. Cod.

Layer (%)

Arch. 1

5 0.1979 680 78.8% 80.7%

10 0.0426 749 92.3% 98%

(n=10)

15 0.0238 385 100% 100%

20 0.0657 1000 96.1% 98%

25 0.5044 375 44.2% 46.1%

Arch.2

5 0.2338 742 67.3% 82.6%

10 0.1263 123 80.7% 86.5%

(n=9)

15 0.0350 430 96.1% 96.1%

20 0.0842 125 88.4% 96.1%

25 0.4765 48 51.9% 69.2%

Arch. 3

5 0.2863 747 59.6% 71.1%

10 0.0172 325 94.2% 98%

(n=8)

15 0.0541 137 96.1% 96.1%

20 0.2957 109 63.4% 76.9%

25 0.7087 102 34.6% 46.1%

Arch. 4

5 0.2937 574 55.7% 71.1%

10 0.0567 498 88.4% 92.3%

(n=7)

15 0.3983 442 55.7% 59.6%

20 0.3840 68 51.9% 63.4%

25 0.6497 90 34.6% 44.2%

tectures, that is, those that achieve a 100% accuracy.

Thus, in Table 1, we observe that only architecture 1

with “Beta” = 15, is a valid architecture, because the

100% accuracy was obtained in the 385 epoch.

Table 2 shows the results in terms of Accuracy and

Uniqueness of the resultant binary code for Model I,

using an input data set of 95 patterns. Consider that

the columns in Table 2 have the same meaning as the

columns in Table 1.

In Table 2, we can see that in no architecture was

it possible to obtain an Accuracy of 100%. Also, it

can even be noted that these values of accuracy are

much lower than those in Table 1. Therefore, there is

no valid architecture in Table 2.

Table 3 summarizes the results in terms of Accu-

racy and Uniqueness of the resultant binary code for

Model II, using an input data set of 52 patterns. Con-

sider that the columns in Table 3 have the same mean-

ing as the columns in Table 1.

In Table 3, we can see that in 4 architectures it

was possible to obtain an accuracy of 100%. In other

words, using Model II, with 52 inputs, we obtained 4

valid architectures for cryptographic purposes. Two

of them with n = 10, one of them with n = 9, and the

last with n = 8. And all of them with a “Beta” between

15 or 20.

Table 4 shows the results in terms of Accuracy and

Uniqueness of the resultant binary code for Model II,

using an input data set of 95 patterns. Consider that

the columns in Table 4 have the same meaning as the

columns in Table 1.

In Table 4, we can see that in 3 architectures it

was possible to obtain an accuracy of 100%. In other

words, using Model II, with 95 inputs, we obtained

3 valid architectures for cryptographic purposes. One

Table 2: Results of the architectures, 95 inputs, Model I.

Arch. Beta Min MSE Epoch Acc. (%)

Uniq. Cod.

Layer (%)

Arch.1

5 0.2572 727 50.5% 66.3%

10 0.3064 156 63.1% 70.5%

(n=10)

15 0.3151 54 56.8% 73.6%

20 0.4340 84 51.5% 68.4%

25 0.9769 87 22.1% 35.7%

Arch. 2

5 0.3410 640 46.3% 49.4%

10 0.1566 258 70.5% 80.0%

(n=9)

15 0.2699 146 66.3% 72.6%

20 0.7556 25 25.2% 42.1%

25 1.1362 88 14.7% 20.0%

Arch. 3

5 0.4167 999 41.0% 46.3%

10 0.3639 133 47.3% 61.0%

(n=8)

15 0.4116 61 48.4% 54.7%

20 0.6323 83 33.6% 36.8%

25 0.9375 156 18.9% 29.4%

Arch.4

5 0.4680 787 35.7% 43.1%

10 0.4554 60 37.8% 68.4%

(n=7)

15 0.5182 461 37.8% 43.1%

20 0.7462 306 32.6% 40.0%

25 1.1851 76 11.5% 20.0%

with n = 10, other with n = 9, and the last with n = 8.

And all of them with a “Beta” = 15.

Figure 2 show the evolution of Accuracy with re-

spect to the number of epoch elapsed during training

of Model II, with an input data set of 52 patterns.

With an input data set of 52 patterns, we notice

that four architectures of Model II are valid (this we

had already noted in Table 3), that is, they reach an

accuracy of 100%. Additionally, in this 4 valid archi-

tectures, the maximum accuracy is reached before the

300 epoch.

Figure 3 has the same structure of Figure 2. But

in this case the results represented were obtained with

an input data set of 95 patterns using Model II.

We notice that three architectures of Model II are

valid (this we had already noted in Table 3), that is,

they reach an accuracy of 100%. Additionally, in

this 3 valid architectures the maximum accuracy is

reached before the 300 epoch.

5 DISCUSSION AND

CONCLUSIONS

A new method to encrypt and decrypt digital informa-

tion by autoencoder architecture of a neural network

model has been analyzed. Two architecture models

with different learning algorithms were proposed. Be-

tween both models, clearly the best one for crypto-

graphic purposes is the Model II. Since that model

produced more valid architectures (with 100% of ac-

curacy). This difference between Models I and II, is

due to the learning algorithm used. In the ﬁrst model

a small variation of the back-propagation is used, in

Digital Cryptography Implementation using Neurocomputational Model with Autoencoder Architecture

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Table 3: Results of the architectures, 52 inputs, Model II.

Arch. Beta Min MSE Epoch Acc. (%)

Uniq. Cod.

Layer (%)

Arch. 1

5 0.0019 1000 78.84% 94.23%

10 3.97e-04 1000 78.84% 92.3%

(n=10)

15 1.38e-04 1000 100% 100%

20 8.35e-05 1000 100% 100%

25 0.255 138 69.23% 73.07%

Arch.2

5 0.0027 1000 69.23% 84.61%

10 5.27e-04 1000 73.07% 96.15%

(n=9)

15 1.32e-04 1000 90.38% 94.23%

20 1.39e-04 1000 100% 100%

25 0.3876 548 53.84% 61.53%

Arch. 3

5 0.004 1000 63.46% 86.53%

10 3.00e-04 1000 71.15% 90.38%

(n=8)

15 1.36e-04 1000 92.30% 98.07%

20 9.65e-05 1000 100% 100%

25 0.4008 196 59.61% 65.38%

Arch.4

5 0.0055 1000 65.38% 92.30%

10 8.78e-04 1000 65.38% 88.46%

(n=7)

15 0.0015 1000 86.53% 92.30%

20 1.15e-04 1000 96.15% 98.07%

25 0.3412 159 59.61% 65.38%

Table 4: Results of the architectures, 95 inputs, Model II.

Arch. Beta Min MSE Epoch Acc. (%)

Uniq. Cod.

Layer (%)

Arch. 1)

5 0.011 1000 61.05% 80%

10 2.56e-04 1000 75.78% 89.47%

(n=10)

15 7.60e-05 1000 100% 100%

20 0.0837 209 89.47% 89.47%

25 0.7764 132 26.31% 32.63%

Arch. 2

5 0.013 1000 49.47% 75.78%

10 2.73e-05 1000 78.94% 88.42%

(n=9)

15 1.35e-04 1000 100% 100%

20 5.04e-05 1000 97.89% 100%

25 1.1049 34 28.42% 35.78%

Arch. 3

5 0.0017 1000 48.42% 73.68%

10 2.40e-04 1000 67.36% 76.84%

(n=8)

15 9.23e-05 1000 100% 100%

20 0.0636 174 91.57% 91.57%

25 0.7255 928 33.68% 35.78%

Arch. 4

5 0.0413 999 38.94% 69.47%

10 0.1268 1000 66.31% 76.84%

(n=7)

15 1.46e-04 1000 91.57% 96.84%

20 0.1685 1000 78.94% 80%

25 0.8556 26 28.42% 42.1%

ICAART 2020 - 12th International Conference on Agents and Artiﬁcial Intelligence

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0 100 200 300 400 500 600 700 800 900 1000

Epoch

100

Accuracy

=10

=15

=20

=25

(a) Architecture 1 (n=10)

0 100 200 300 400 500 600 700 800 900 1000

Epoch

100

Accuracy

=10

=15

=20

=25

(b) Architecture 2 (n=9)

0 100 200 300 400 500 600 700 800 900 1000

Epoch

100

Accuracy

=10

=15

=20

=25

0 100 200 300 400 500 600 700 800 900 1000

Epoch

100

Accuracy

=10

=15

=20

=25

(d) Architecture 4 (n=7)

Figure 2: Accuracy of Model II for every architecture and

52 inputs.

0 100 200 300 400 500 600 700 800 900 1000

Epoch

100

Accuracy

=10

=15

=20

=25

(a) Architecture 1 (n=10)

0 100 200 300 400 500 600 700 800 900 1000

Epoch

100

Accuracy

=10

=15

=20

=25

(b) Architecture 2 (n=9)

0 100 200 300 400 500 600 700 800 900 1000

Epoch

100

Accuracy

=10

=15

=20

=25

0 100 200 300 400 500 600 700 800 900 1000

Epoch

100

Accuracy

=10

=15

=20

=25

(d) Architecture 4 (n=7)

Figure 3: Accuracy of Model II for every architecture and

95 inputs.

Digital Cryptography Implementation using Neurocomputational Model with Autoencoder Architecture

871

which a discretization (rounding) of the outputs of

the intermediate layer is carried out during the train-

ing. This rounding produces a loss of uniqueness and

therefore loss of precision when retrieving patterns.

Once we identify the Model II, as the best model.

It was necessary to choose the best architecture of said

model. This architecture is the one that recovers all

the patterns (accuracy 100%), and that has the small-

est number (n) of neurons.

In Table 4, there are 3 architectures that reach a

100% of precision. Architecture 1 with n = 10, archi-

tecture 2 with n = 9, and architecture 3 with n = 8.

Therefore, architecture 3 is the best architecture valid

(for cryptographic purposes), since it reaches a 100%

of accuracy, with the smallest number of neurons.

It should be noted that an input set of 95 ASCII

characters was used for this research, but this crypto-

graphic method can work with more input characters.

So, if we want that our network to encrypt/decrypt all

256 Extended-ASCII characters, we should only in-

crease neurons in the intermediate layers.

Finally, this method of encryption can be a great

change in current cryptographic methods. For future

works, It would be interesting to analyze this method,

in terms of efﬁciency and strength, and compare it

with other common cryptographic methods such as:

DES, AES, RSA, among others.

ACKNOWLEDGEMENTS

Authors thank to the SDAS Research Group (www.

sdas-group.com) for its valuable support.

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