Authenticated Encryption Based on Chaotic Neural Networks and Duplex Construction
<p>The <span class="html-italic">Duplex</span> construction.</p> "> Figure 2
<p>Structure of the proposed <span class="html-italic">CNN-Duplex</span> for <span class="html-italic">AEADS</span>—Encryption process.</p> "> Figure 3
<p>Structure of the proposed <span class="html-italic">CNN-Duplex</span> for <span class="html-italic">AEADS</span>—Decryption process.</p> "> Figure 4
<p>Detailed structure of the <span class="html-italic">i</span>th <span class="html-italic">Chaotic compression function</span> of the proposed <span class="html-italic">CNN-Duplex</span> based on a one-layered <span class="html-italic">NL</span> for <span class="html-italic">AEADS</span>.</p> "> Figure 5
<p>Detailed structure of the <span class="html-italic">k</span>th input neuron for the first choice of the proposed <span class="html-italic">CNN-Duplex</span>.</p> "> Figure 6
<p>Detailed structure of the <span class="html-italic">k</span>th input neuron for the second choice of the proposed <span class="html-italic">CNN-Duplex</span>.</p> "> Figure 7
<p>Detailed structure of <span class="html-italic">NL</span> Functions block.</p> "> Figure 8
<p><span class="html-italic">NIST</span> test for one of ciphertext results.</p> "> Figure 9
<p>Results of Lena image. (<b>a</b>) Lena image, (<b>b</b>) Ciphered Lena, (<b>c</b>) Histogram of Lena image, and (<b>d</b>) Histogram of ciphered Lena.</p> "> Figure 10
<p>Results of Boat image. (<b>a</b>) Boat image, (<b>b</b>) Ciphered Boat, (<b>c</b>) Histogram of Boat image, and (<b>d</b>) Histogram of ciphered Boat.</p> "> Figure 11
<p>Results of Camera man image. (<b>a</b>) Camera man image, (<b>b</b>) Ciphered Camera man, (<b>c</b>) Histogram of Camera man image, and (<b>d</b>) Histogram of ciphered Camera man.</p> ">
Abstract
:1. Introduction
1.1. Research Background
- FKS (Full-State Keyed Sponge);
- IKS (Inner keyed-Sponge);
- OKS (Outer keyed-Sponge).
1.2. Research Significance
2. Related Works
3. Description of the Proposed AEADS Based on the Keyed MDS-CNNR Structure
Algorithm 1 The initialization function |
|
Algorithm 2 The duplexing function |
|
- An Initial Value IV, and a secret key K;
- An Associated Data (AD) that will be authenticated but not encrypted;
- A message M that will be both authenticated and encrypted.
Algorithm 3 The Authenticated Encryption function |
|
- The same Initial Value IV and the same secret key K taken from the encryption process;
- The same Associated Data AD used in the encryption process;
- The ciphertext C to be decrypted;
- The authentication tag T used to check the integrity of the Associated Data AD and the authenticity of the message M.
Algorithm 4 The Authenticated Encryption function |
|
4. Performance Analysis of the Proposed AEADS
4.1. Cryptanalytic Analysis
4.1.1. Key Space
4.1.2. Key Security and Sensitivity
- Condition 1: We use the original secret key K.
- Condition 2: We change the value of initial condition in the secret key K.
- Condition 3: We change the value of parameter Ks in the secret key K.
- Condition 4: We change the value of initial condition in the secret key K.
- Condition 5: We change the value of control parameter in the secret key K.
4.1.3. Message Sensitivity
- Condition 1: The initial message M is the one used in Section 4.1.2.
- Condition 2: We change the first character "W" to "X" in the input message.
- Condition 3: We change the word "With" to "Without" in the input message.
- Condition 4: We change the dot (".") to comma (",") at the end of the input message.
- Condition 5: We add a "blank space" at the end of the input message.
- Condition 6: We swap the first block of the input message
4.1.4. Collision Resistance Analysis
4.1.5. The Diffusion Effect
- bits: Mean number of bits changed;
- %: Mean changed probability (mean of );
- bits: Minimum number of bits changed;
- bits: Maximum number of bits changed;
- : Standard variance of the changed bit number;
- %: Standard variance of the changed probability.
4.2. Statistical Tests
4.2.1. NIST Test
4.2.2. Histogram and Chi-Square Analysis
4.2.3. Entropy Analysis
4.2.4. Correlation Analysis
5. Performance Comparison with Other AE Algorithms
5.1. Characteristic Comparison
5.2. Security Comparison
6. Conclusions and Future Work
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Stallings, W. Cryptography and Network Security: Principles and Practice; Pearson: Upper Saddle River, NJ, USA, 2017. [Google Scholar]
- Abdoun, N.; El Assad, S.; Taha, M.A.; Assaf, R.; Deforges, O.; Khalil, M. Hash Function based on Efficient Chaotic Neural Network. In Proceedings of the 2015 10th International Conference for Internet Technology and Secured Transactions (ICITST), London, UK, 14–16 December 2015; pp. 32–37. [Google Scholar]
- Abdoun, N.; El Assad, S.; Taha, M.A.; Assaf, R.; Déforges, O.; Khalil, M. Secure hash algorithm based on efficient chaotic neural network. In Proceedings of the 2016 International Conference on Communications (COMM), Bucharest, Romania, 9–10 June 2016. [Google Scholar]
- McGrew, D.; Paterson, K. Authenticated Encryption with AES-CBC and HMAC-SHA. Internet Engineering Task Force (IETF). 2012. Available online: https://datatracker.ietf.org/doc/html/draft-mcgrew-aead-aes-cbc-hmac-sha2-01 (accessed on 10 November 2021).
- Rajashree, S.; Sukumar, R. CBC (Cipher Block Chaining)-Based Authenticated Encryption for Securing Sensor Data in Smart Home. In Smart IoT for Research and Industry; Springer: Cham, Switzerland, 2022; pp. 189–204. [Google Scholar]
- Kavun, E.B.; Mihajloska, H.; Yalçin, T. A Survey on Authenticated Encryption–ASIC Designer’s Perspective. ACM Comput. Surv. (CSUR) 2017, 50, 1–21. [Google Scholar] [CrossRef]
- Bertoni, G.; Daemen, J.; Peeters, M.; Van Assche, G. Duplexing the sponge: Single-pass authenticated encryption and other applications. In Proceedings of the International Workshop on Selected Areas in Cryptography, Toronto, ON, Canada, 11–12 August 2011; pp. 320–337. [Google Scholar]
- Dobraunig, C.; Eichlseder, M.; Mendel, F.; Schläffer, M. Ascon v1.2. Submission to the CAESAR Competition. Available online: https://competitions.cr.yp.to/round3/asconv12.pdf (accessed on 9 November 2021).
- Bao, Z.; Chakraborti, A.; Datta, N.; Guo, J.; Nandi, M.; Peyrin, T.; Yasuda, K. PHOTON-beetle authenticated encryption and hash family. NIST Lightweight Compet. Round 2019, 1, 115. [Google Scholar]
- Bhattacharjee, A.; List, E.; Lpez, C.; Nandi, M. The Oribatida Family of Lightweight Authenticated Encryption Schemes; Indian Statistical Institute Kolkata: Kolkata, India; p. 2019.
- Khan, S.; Lee, W.K.; Hwang, S.O. Scalable and Efficient Hardware Architectures for Authenticated Encryption in IoT Applications. IEEE Internet Things J. 2021, 8, 11260–11275. [Google Scholar] [CrossRef]
- Bertoni, G.; Daemen, J.; Peeters, M.; Van Assche, G. Cryptographic Sponges. 2011. Available online: http://sponge.noekeon.org (accessed on 10 August 2021).
- Bertoni, G.; Daemen, J.; Peeters, M.; Van Assche, G. Permutation-based encryption, authentication and authenticated encryption. Dir. Authenticated Ciphers 2012, 159–170. [Google Scholar]
- Borowski, M. Cryptographic Applications of the Duplex Construction. Ann. Univ. Mariae Curie-Sklodowska Sect. AI 2014, 14, 37–48. [Google Scholar] [CrossRef] [Green Version]
- Chang, D. Sufficient Conditions on Padding Schemes of Sponge Construction and Sponge-Based Authenticated-Encryption Scheme. In Proceedings of the International Conference on Cryptology in India, Kolkata, India, 9–12 December 2012; pp. 545–563. [Google Scholar]
- Morawiecki, P.; Gaj, K.; Homsirikamol, E.; Matusiewicz, K.; Pieprzyk, J.; Rogawski, M.; Srebrny, M.; Wójcik, M. ICEPOLE: High-speed, hardware-oriented authenticated encryption. In Proceedings of the International Workshop on Cryptographic Hardware and Embedded Systems, Busan, Korea, 23–26 September 2014; pp. 392–413. [Google Scholar]
- Abdoun, N.; El Assad, S.; Hammoud, K.; Assaf, R.; Khalil, M.; Deforges, O. New keyed chaotic neural network hash function based on sponge construction. In Proceedings of the 2017 12th International Conference for Internet Technology and Secured Transactions (ICITST), Cambridge, UK, 11–14 December 2017; pp. 35–38. [Google Scholar]
- Abdoun, N.; El Assad, S.; Assaf, R.; Déforges, O.; Khalil, M.; Belghith, S. Design and Implementation of Robust Keyed Hash Functions Based on Chaotic Neural Network; Electronics; Universite de Nantes: Nantes, France, 2018. [Google Scholar]
- De la Fraga, L.G.; Mancillas-López, C.; Tlelo-Cuautle, E. Designing an authenticated Hash function with a 2D chaotic map. Nonlinear Dyn. 2021, 104, 4569–4580. [Google Scholar] [CrossRef]
- Abdoun, N.; El Assad, S.; Deforges, O.; Assaf, R.; Khalil, M. Design and security analysis of two robust keyed hash functions based on chaotic neural networks. J. Ambient. Intell. Humaniz. Comput. 2019, 11, 2137–2161. [Google Scholar] [CrossRef]
- Field, M.; Golubitsky, M. Symmetric Chaos: A pictorial exploration of an order imposed by symmetry within chaotic systems. Comput. Phys. 1990, 4, 470–479. [Google Scholar] [CrossRef]
- Zhang, F.; Liang, Z.Y.; Yang, B.L.; Zhao, X.J.; Guo, S.Z.; Ren, K. Survey of design and security evaluation of authenticated encryption algorithms in the CAESAR competition. Front. Inf. Technol. Electron. Eng. 2018, 19, 1475–1499. [Google Scholar] [CrossRef]
- Li, Z.; Bi, W.; Dong, X.; Wang, X. Improved conditional cube attacks on Keccak keyed modes with MILP method. In Proceedings of the International Conference on the Theory and Application of Cryptology and Information Security, Hong Kong, China, 3–7 December 2017; pp. 99–127. [Google Scholar]
- Bertoni, G.; Daemen, J.; Peeters, M.; Van Assche, G.; Van Keer, R. Keyak v2. CAESAR Submission. 2015. [Google Scholar]
- Jean, J.; Nikolić, I.; Peyrin, T.; Seurin, Y. The Deoxys AEAD Family. J. Cryptol. 2021, 34, 31. [Google Scholar] [CrossRef]
- Zhang, P.; Yuan, Q. Lightweight Authenticated Encryption Mode with Enhancing Security Guarantees. In Proceedings of the 2021 IEEE 6th International Conference on Computer and Communication Systems (ICCCS), Chengdu, China, 23–26 April 2021; pp. 689–694. [Google Scholar]
- Pan, X.; Li, F. Public-key authenticated encryption with keyword search achieving both multi-ciphertext and multi-trapdoor indistinguishability. J. Syst. Archit. 2021, 115, 102075. [Google Scholar] [CrossRef]
- Dobraunig, C.; Eichlseder, M.; Mendel, F.; Schläffer, M. Ascon v1.2: Lightweight Authenticated Encryption and Hashing. J. Cryptol. 2021, 34, 33. [Google Scholar] [CrossRef]
- Rogaway, P. Advances in Cryptology, Proceedings of the CRYPTO 2011: 31st Annual Cryptology Conference, Santa Barbara, CA, USA, 14–18 August 2011; Springer Science & Business Media: Boston, MA, USA, 2011; Volume 6841. [Google Scholar]
- Abdoun, N.; El Assad, S.; Manh Hoang, T.; Deforges, O.; Assaf, R.; Khalil, M. Designing Two Secure Keyed Hash Functions Based on Sponge Construction and the Chaotic Neural Network. Entropy 2020, 22, 1012. [Google Scholar] [CrossRef] [PubMed]
- Rogaway, P. Authenticated-encryption with associated-data. In Proceedings of the 9th ACM Conference on Computer and Communications Security 2002, Washington, DC, USA, 18–22 November 2002; pp. 98–107. [Google Scholar]
- Siegenthaler, T. Decrypting a class of stream ciphers using ciphertext only. IEEE Trans. Comput. 1985, 34, 81–85. [Google Scholar] [CrossRef]
- Lian, S.; Sun, J.; Wang, Z. Security analysis of a chaos-based image encryption algorithm. Phys. A Stat. Mech. Its Appl. 2005, 351, 645–661. [Google Scholar] [CrossRef] [Green Version]
- Taha, M.A.; Assad, S.E.; Queudet, A.; Deforges, O. Design and efficient implementation of a chaos-based stream cipher. Int. J. Internet Technol. Secur. Trans. 2017, 7, 89–114. [Google Scholar] [CrossRef]
- Biham, E.; Shamir, A. Differential cryptanalysis of DES-like cryptosystems. J. Cryptol. 1991, 4, 3–72. [Google Scholar] [CrossRef]
- Wu, Y.; Noonan, J.P.; Agaian, S. NPCR and UACI randomness tests for image encryption. Cyber J. Multidiscip. J. Sci. Technol. J. Sel. Areas Telecommun. (JSAT) 2011, 1, 31–38. [Google Scholar]
- Mar, P.P.; Latt, K.M. New analysis methods on strict avalanche criterion of S-boxes. World Acad. Sci. Eng. Technol. 2008, 2, 899–903. [Google Scholar]
- Wang, X.; Luan, D.; Bao, X. Cryptanalysis of an image encryption algorithm using Chebyshev generator. Digit. Signal Process. 2014, 25, 244–247. [Google Scholar] [CrossRef]
- Xiao, D.; Liao, X.; Deng, S. One-way Hash function construction based on the chaotic map with changeable-parameter. Chaos Solitons Fractals 2005, 24, 65–71. [Google Scholar] [CrossRef]
- Zhang, J.; Wang, X.; Zhang, W. Chaotic keyed hash function based on feedforward–feedback nonlinear digital filter. Phys. Lett. A 2007, 362, 439–448. [Google Scholar] [CrossRef]
- Preneel, B. Analysis and Design of Cryptographic Hash Functions. Ph.D. Thesis, Katholieke Universiteit te Leuven, Leuven, The Netherlands, 1993. [Google Scholar]
- Feistel, H. Cryptography and computer privacy. Sci. Am. 1973, 228, 15–23. [Google Scholar] [CrossRef]
- Shannon, C.E. Communication theory of secrecy systems. Bell Syst. Tech. J. 1949, 28, 656–715. [Google Scholar] [CrossRef]
- Barker, E.B.; Kelsey, J.M. Recommendation for Random Number Generation Using Deterministic Random Bit Generators (Revised); US Department of Commerce, Technology Administration, National Institute of Standards and Technology, Computer Security Division, Information Technology Laboratory: Washington, DC, USA, 2007. [Google Scholar]
- Wu, Y.; Zhou, Y.; Saveriades, G.; Agaian, S.; Noonan, J.P.; Natarajan, P. Local Shannon entropy measure with statistical tests for image randomness. Inf. Sci. 2013, 222, 323–342. [Google Scholar] [CrossRef] [Green Version]
- Song, C.Y.; Qiao, Y.L.; Zhang, X.Z. An image encryption scheme based on new spatiotemporal chaos. Opt.-Int. J. Light Electron Opt. 2013, 124, 3329–3334. [Google Scholar] [CrossRef]
- Simplicio, M.A.; de Oliveira, B.T.; Barreto, P.S.; Margi, C.B.; Carvalho, T.C.; Naslund, M. Comparison of authenticated-encryption schemes in wireless sensor networks. In Proceedings of the 2011 IEEE 36th Conference on Local Computer Networks, Bonn, Germany, 4–7 October 2011; pp. 450–457. [Google Scholar]
- Švenda, P. Basic Comparison of Modes for Authenticated-Encryption (IAPM, XCBC, OCB, CCM, EAX, CWC, GCM, PCFB, CS). 2016, Volume 35. Available online: https://www.fi.muni.cz/~xsvenda/docs/AE_comparison_ipics04.pdf (accessed on 10 August 2021).
- Patel, M.; Venkatesan, S.; Weiner, D. Role assignment for data aggregation in wireless sensor networks. In Proceedings of the 21st International Conference on Advanced Information Networking and Applications Workshops (AINAW’07), Niagara Falls, ON, Canada, 21–23 May 2007; Volume 2, pp. 390–395. [Google Scholar]
AEAD | NPCR | UACI | HD % |
---|---|---|---|
Proposed AEADS | 99.67 | 33.43 | 49.8 |
Message Variants | Authenticated Tag in Hexadecimal Format | |||
---|---|---|---|---|
b = 64 bytes | 1 | 5cf839f23ab09f77a0f5efb4b8376f7014a64d4573a0a49d6b622459c7f3066c | – | – |
2 | 2aa99d0a65ba78b1dca34c4737dab62f10da532481ac655b6ad59f334dd57a38 | 133.00 | 51.95 | |
3 | 635f0c9970b9cee82508fc620e4481b1db50e8250ac1b5e1218dc832f499a1a6 | 141.00 | 55.07 | |
4 | 1dad759ec9f258d6022b272a97ffb69d70c543d49d47591f0893c8a8efa93de1 | 133.00 | 51.95 | |
5 | 9b498e512ec5e2e37ea0c0791124170422488f0f2b7c13c044f8c4bd77945cb6 | 138.00 | 53.90 | |
Average | – | 136.25 | 53.22 | |
b = 128 bytes | 1 | c1fb8921581959928cce8d75b42e6c5d4dff037b91e42ca4a904cd8c50d5a2aa | – | – |
2 | 7fc5609746e964392d0ff999124274d627c8bb57de6ef906e1237449d4a9bbc8 | 128.00 | 50.00 | |
3 | 404864221fbfdd28a5cc0af04543a8d9634dbc41d62abf9b36a51db210ab092a | 124.00 | 48.44 | |
4 | d7366dee282cfa69a48c55e381255d3e79505c83a5f6a224805faaf9782aab44 | 128.00 | 50.00 | |
5 | 58d7387465730f264dbb1161ffdcc4d6ba31ab63f2ee6e1a4089bbad0564d418 | 126.00 | 49.21 | |
Average | – | 126.50 | 49.41 |
Message Variants | Authenticated Tag in Hexadecimal Format | |||
---|---|---|---|---|
b = 64 bytes | 1 | 5cf839f23ab09f77a0f5efb4b8376f7014a64d4573a0a49d6b622459c7f3066c | – | – |
2 | af1f98eda7a69b2a1c9b146d60b04e7f3a1c421ead01e913d12ab3018b86bf60 | 135.00 | 52.73 | |
3 | ac3a80e98af6809e94bd50b7c337acfa6987fce4df7534b388ffc8fe224f98e0 | 127.00 | 49.60 | |
4 | 20aaf22ec8f025fbb8da59b6f175dc5587b1e19c60c0603c296fe5df5fabd816 | 114.00 | 44.53 | |
5 | a177b89d7ec17468ff0c4aff348ba20334855f53f5c9bcdb3e4e54273e40a977 | 133.00 | 51.95 | |
6 | 0bdc884523ac64cc5c14150af8068b1b46f83f0067c7b3d7c3d52dc67d2b99dd | 136.00 | 53.13 | |
Average | – | 129.00 | 50.39 | |
b = 128 bytes | 1 | c1fb8921581959928cce8d75b42e6c5d4dff037b91e42ca4a904cd8c50d5a2aa | – | – |
2 | 55d53d2a5f8b2ce215f0ecd097296d26c1511f8f49c21a82cb1b9b749d63e9dd | 124.00 | 48.43 | |
3 | 7e428a69f21099ce7717ae2892e8107160a8ecd18e757d856b8ac3dc99ca3f7c | 127.00 | 49.60 | |
4 | e306a1484f36d072c37c9f33c8e18cbb987710db2ecc56862551450e75c7d96e | 116.00 | 45.31 | |
5 | 2622493df19883b33d23aa780a3fe817f1aa1c79c869ddc8ff759fa704e06bc9 | 121.00 | 47.26 | |
6 | 504ab6f4aa4b2262727bf6a067b83f9679aeada6f2046386e7c7aab0f9d13880 | 137.00 | 53.51 | |
Average | – | 125.00 | 48.82 |
0 | 1 | 2 | 3 | 32 | ||
---|---|---|---|---|---|---|
J | 2048 | 1806.91 | 226.74 | 13.78 | 0.54 | |
1024 | 903.45 | 113.37 | 6.89 | 0.27 | ||
512 | 451.72 | 56.68 | 3.44 | 0.13 |
0 | 1 | 2 | 3 | 4 | 5 | |
---|---|---|---|---|---|---|
b = 64 bytes | 1816 | 218 | 13 | 1 | 0 | 0 |
b = 128 bytes | 1898 | 142 | 8 | 0 | 0 | 0 |
b (bytes) | Minimum | Maximum | Mean | Mean/Character | |
---|---|---|---|---|---|
Proposed AEADS | 64 | 1642 | 3784 | 2665.24 | 83.28 |
128 | 1846 | 3548 | 2668.15 | 83.33 |
b (bytes) | P | ||||||
---|---|---|---|---|---|---|---|
Proposed AEADS | 64 | 128.10 | 50.04 | 101 | 155 | 7.96 | 3.13 |
128 | 128.01 | 50.00 | 104 | 150 | 7.8 | 2.23 |
Images | Experimental Values | Theoretical Values |
---|---|---|
Lena 512 × 512 × 3 | 272.152689 | 293.247835 |
Boat 512 × 512 × 3 | 268.465369 | 293.247835 |
C-man 512 × 512 × 3 | 270.317852 | 293.247835 |
Entropy | Lena | Boat | Camera Man |
---|---|---|---|
Plain image | 7.4504 | 7.6845 | 7.4892 |
Cipher image | 7.9584 | 7.9865 | 7.9582 |
Image | Horizontal | Vertical | Diagonal |
---|---|---|---|
Lena | 0.939403 | 0.971060 | 0.931085 |
Lena encrypted | −0.002674 | −0.009113 | −0.002178 |
Boat | 0.951837 | 0.962357 | 0.915555 |
Boat encrypted | −0.002602 | −0.009819 | 0.002402 |
Camera man | 0.887794 | 0.734230 | 0.888141 |
Camera man encrypted | −0.007750 | −0.006998 | −0.002788 |
Feature | Proposed AEADS | GCM | CCM | OCB |
---|---|---|---|---|
Tag length (bits) | 256 | 0 to n | 16k, | 0 to n |
IV size (bits) | Any | Any (favored: ) | n | n |
Number of passes | One | Two | Two | One |
Provably secure | yes | yes | yes | yes |
Keying material | one key | one key | one key | one key |
Online | no | yes | no | yes |
Endian dependent | yes | yes | yes | no |
Incremental MAC | yes | yes | no | no |
Error propagation | no | no | no | no |
Associated data authentication | yes | yes | yes | no |
Feature | Proposed AEADS | GCM | CCM | OCB |
---|---|---|---|---|
Secure against | yes | yes | yes | yes |
chosen-plaintext attack | ||||
Synchronization between sender and receiver | Same IV | Same IV | Same nonce | Same nonce |
Keying Requirements | One block cipher key | One block cipher key | One block cipher key | One block cipher key |
Message Length Requirements | Any bit string allowed | Arbitrary message up to | Arbitrary message up to | Any bit string allowed |
–256 bits | bits where L = 2, …, 8 | |||
Arbitrary authenticated | Arbitrary authenticated | |||
data up to bits | data up to bits | |||
Underlying Cipher Block Size Requirements (bits) | 512, 1024 | 64, 128 | Only 128 | 128, 192, 256 |
Parallelizability | None | Encryption block level Authentication bit level | None | Fully parallelizable |
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Abdoun, N.; El Assad, S.; Manh Hoang, T.; Deforges, O.; Assaf, R.; Khalil, M. Authenticated Encryption Based on Chaotic Neural Networks and Duplex Construction. Symmetry 2021, 13, 2432. https://doi.org/10.3390/sym13122432
Abdoun N, El Assad S, Manh Hoang T, Deforges O, Assaf R, Khalil M. Authenticated Encryption Based on Chaotic Neural Networks and Duplex Construction. Symmetry. 2021; 13(12):2432. https://doi.org/10.3390/sym13122432
Chicago/Turabian StyleAbdoun, Nabil, Safwan El Assad, Thang Manh Hoang, Olivier Deforges, Rima Assaf, and Mohamad Khalil. 2021. "Authenticated Encryption Based on Chaotic Neural Networks and Duplex Construction" Symmetry 13, no. 12: 2432. https://doi.org/10.3390/sym13122432