A Fast Pseudo-Stochastic Sequential Cipher Generator Based on RBMs
📝 Abstract
Based on Restricted Boltzmann Machines (RBMs), an improved pseudo-stochastic sequential cipher generator is proposed. It is effective and efficient because of the two advantages: this generator includes a stochastic neural network that can perform the calculation in parallel, that is to say, all elements are calculated simultaneously; unlimited number of sequential ciphers can be generated simultaneously for multiple encryption schemas. The periodicity and the correlation of the output sequential ciphers meet the requirements for the design of encrypting sequential data. In the experiment, the generated sequential cipher is used to encrypt the image, and better performance is achieved in terms of the key space analysis, the correlation analysis, the sensitivity analysis and the differential attack. The experimental result is promising that could promote the development of image protection in computer security.
💡 Analysis
Based on Restricted Boltzmann Machines (RBMs), an improved pseudo-stochastic sequential cipher generator is proposed. It is effective and efficient because of the two advantages: this generator includes a stochastic neural network that can perform the calculation in parallel, that is to say, all elements are calculated simultaneously; unlimited number of sequential ciphers can be generated simultaneously for multiple encryption schemas. The periodicity and the correlation of the output sequential ciphers meet the requirements for the design of encrypting sequential data. In the experiment, the generated sequential cipher is used to encrypt the image, and better performance is achieved in terms of the key space analysis, the correlation analysis, the sensitivity analysis and the differential attack. The experimental result is promising that could promote the development of image protection in computer security.
📄 Content
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A Fast Pseudo-Stochastic Sequential Cipher Generator Based on RBMs Fei Hu · Xiaofei Xu · Tao Peng · Changjiu Pu · Li Li1
Abstract Based on Restricted Boltzmann Machines (RBMs), an improved pseudo-stochastic sequential cipher generator is proposed. It is effective and efficient because of the two advantages: this generator includes a stochastic neural network that can perform the calculation in parallel, that is to say, all elements are calculated simultaneously; unlimited number of sequential ciphers can be generated simultaneously for multiple encryption schemas. The periodicity and the correlation of the output sequential ciphers meet the requirements for the design of encrypting sequential data. In the experiment, the generated sequential cipher is used to encrypt the image, and better performance is achieved in terms of the key space analysis, the correlation analysis, the sensitivity analysis and the differential attack. The experimental result is promising that could promote the development of image protection in computer security. Keywords Restricted Boltzmann Machines; neural networks; sequence correlation; sequential data encryption
1 Introduction In the field of communication and encryption for sequential data, sequential cipher generation algorithms have been one of the main technology used for military and diplomatic occasions. As a kind of symmetric encryption algorithm, sequential ciphers have the following characteristics: easy to be implemented, simple implementation with hardware, fast in encryption and decryption processing, none or limited error propagation. Shannon proved the one-time pad encryption system was safe [1]. It plays an important role in promoting the development of the sequential ciphering technology. The development of the sequential cipher technology has been attempting to imitate the one-time pad scheme, i.e., the one-time pad encryption system is the prototype of the sequential ciphering system. In order to cipher the sequential data, a stochastic sequence, determined by a cipher code, will be generated at first. The algorithms of generating stochastic sequential ciphers can be roughly divided into two categories: Linear Feedback Shift Register sequential cipher generators (LFSR) and nonlinear sequential cipher generators. LFSR
Fei Hu School of Computer and Information Science, Southwest University, Chongqing, China Network Centre, Chongqing University of Education, Chongqing, China Xiaofei Xu School of Computer and Information Science, Southwest University, Chongqing, China Tao Peng Network Centre, Chongqing University of Education, Chongqing, China Changjiu Pu Network Centre, Chongqing University of Education, Chongqing, China Li Li School of Computer and Information Science, Southwest University, Chongqing, China 1 Corresponding author. E-mail: lily@swu.edu.cn 2
algorithms generate sequential ciphers by maximizing the length of the shift registers and by using a linear feedback function. The theoretical foundation of LFSR algorithms has been mature [2–4]. Sequential ciphers generated by LFSR algorithms are stochastic, however, the resulting sequential ciphers have the risk of being decrypted [5]. As a result, people turn to the nonlinear field instead. The encryption algorithms using nonlinear sequential ciphering technology can be roughly divided in to the following categories: (1) the Nonlinear Feedback Shift Register sequential cipher generator (NFSR), it consists of a shift register and a nonlinear feedback function, and can yields a 2n-length sequence, NFSR has good cryptographic properties, but the generation speed is slow and restricts the development of NFSRs; (2) the nonlinear-combination sequential cipher generator, it consists of multiple LFSRs and nonlinear functions; (3) the clock controlled sequential cipher generator, it controls registers using another registers clock, it is easy to be attacked using logistic analysis; (4) other sequential cipher generators, these generators construct complex networks to generate sequential ciphers by combining above algorithms, e.g. the chaotic theory, the artificial neural network, the DNA encoding technology and the quantum encryption. Probably Lauria was the first to use artificial neural networks (ANNs) in cryptography [6–8]. ANN has the following characteristics that are suitable for cryptography: Nonlinear calculation, associative memory, massively parallel processing and strong fault tolerance. With these characteristics, cryptography has a broad application prospect in the field of Very Large Scale Integration (VLSI) and optical implementations. In [9], Ding et. al. used a discrete Hopfield neural network to make a nonlinear sequential cipher generator. The network can generate sequential ciphers meeting the requirements for the design of encrypting sequential data. By using a
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