Design of S-boxes based on neural networks*

Abstract

In this paper, we present a framework for the design of S-boxes used in ciphers based on neural networks. It can yield S-boxes with different input and output length. The designed S-boxes satisfy the desired cryptographic properties of non-linearity, completeness, strict avalanche, and output bits independence criteria. We propose a four layer topology, where the number of neurons, located at the input layer, is two times the number of input bits of the designed Sbox and also, the number of neurons, located at the first hidden layer, is as equal as input layer neurons, while its second hidden layer included / neurons, and its output layer included n neurons. The input value of the designed S-boxes consists of n-bit input vector and constant n-bit initial value (IV). We apply a Sigmoid nonlinear function as the activation function of our scheme. The values of weights were obtained through error back propagation learning algorithm, while a training set is used for learning. The used training set consists some different pairs of plaintexts and ciphertexts with AES's S-box. We also implement anS-box based on neural networks with the essential security criteria. The results indicate that the proposed scheme can yield S-boxes with the desired cryptographic properties.

Deep Learning for Cyber Security Applications: A Comprehensive Survey

“…Another study discussed the theoretical aspects of applying NNs to encrypted data [80]. Various experimental studies showed how an artificial agent can learn a secure encryption method and the use of RNN and CNN based methods for S-box and cipher design as well as their classification [82] [83] [84] [85] [86]. Further, cryptonets, a set of NNs with DL was proposed to allow the user to send the encrypted data to the cloud and the models were trained to predict risks without decrypting the data with various experiments to enhance their performance [87] [88].…”

A Comprehensive Tutorial and Survey of Applications of Deep Learning for Cyber Security

“…The detailed experimental analysis on RNN based methods for cipher design was done by [142]. In [143] showed detailed experimental analysis of NNs on the design of S-boxes used in ciphers. Cryptographic Primitive classification based on CNN was done by [144].…”

New S-box calculation approach for Rijndael-AES based on an artificial neural network

“…Due to their importance, S-boxes are chosen and designed to be resistant to cryptanalysis, in literature several proposals with different characteristics are found, some of them based on neural networks, like the framework for the design of S-boxes used in ciphers based on neural networks by Noughabi (Noughabi & Sadeghiyan, 2010) and "a new scheme for implementing s-box based on neural network" by X. Zhang (Zhang, Chen, Chen, & Cao, 2015), others that optimize existing boxes such as the high speed implementation of S. Oukili for the AES Sbox (Oukili, Bri & Kumar, 2016) and low-area S-box implementation of Thomson (Thomson, Siva, & Priya, 2014); even new proposals such as the evolutionary design of S-Box of M. Yang (Yang, Wang, Meng & Han, 2011) and the based on chaotics maps of C. I. Rı̂ncu (Rı̂ncu & Iana, 2014). This article presents a substitution of the S-box for another module that calculates the AES S-box outputs with the use of a neural network and the multiplicative inverse on Galois field 2 8 (GF (2 8 )) of the input value to transform, or S-box input value.…”