An Improved Rao–Nam Cryptosystem Based on Fractional Order Hyperchaotic System and EDF–QC–LDPC

2019 ◽  
Vol 29 (09) ◽  
pp. 1950122 ◽  
Author(s):  
Jie Liu ◽  
Xiaojun Tong ◽  
Zhu Wang ◽  
Jing Ma ◽  
Longteng Yi
Keyword(s):  
Error Correction ◽  
Fractional Order ◽  
High Capacity ◽  
Pseudorandom Sequence ◽  
Hyperchaotic System ◽  
Difference Family ◽  
Parity Check ◽  
Chosen Plaintext Attack ◽  
Low Density Parity Check ◽  
Security And Reliability

A Rao–Nam cryptosystem based on error correction code is proposed to provide both security and reliability. Since its security is drastically constrained by the limited error syndromes, in this paper, an improved Rao–Nam cryptosystem based on fractional order hyperchaotic system and Extended Difference Family–Quasi-Cyclic–Low-Density Parity-Check (EDF–QC–LDPC) codes is proposed to improve the security. A four-dimensional fractional order hyperchaotic system is constructed and is used to generate an excellent pseudorandom sequence. By replacing error syndromes with the pseudorandom sequence and permuting the coded message dynamically, the security of the Rao–Nam cryptosystem is enhanced greatly. The ability of the improved Rao–Nam cryptosystem against known attacks is analyzed and the error correction performance with different parameters is simulated. The results show that the proposed cryptosystem has a significant advantage of resisting the chosen-plaintext attack. Moreover, the proposed cryptosystem retains high capacity of error correction.

Method of Combining Cryptography and LDPC Coding for Enhanced Privacy

2021 ◽  
Vol 13 (4) ◽  
pp. 51-70
Author(s):  
Bradley Comar
Keyword(s):  
Error Correction ◽  
Pseudorandom Number ◽  
Low Density ◽  
Parity Check ◽  
Pseudorandom Number Generators ◽  
Low Density Parity Check

This paper describes a method of combining cryptographic encoding and low density parity check (LDPC) encoding for the purpose of enhancing privacy. This method uses pseudorandom number generators (PRNGs) to create parity check matrices that are constantly updated. The generated cyphertext is at least as private as a standard additive (XORing) cryptosystem, and also has error correcting capability. The eavesdropper, Eve, has the expanded burden of having to perform cryptanalysis and error correction simultaneously.

scholarly journals Flag fault-tolerant error correction with arbitrary distance codes

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 53 ◽  
Author(s):  
Christopher Chamberland ◽  
Michael E. Beverland
Keyword(s):  
Error Correction ◽  
Fault Tolerant ◽  
Quantum Error Correction ◽  
Quantum Codes ◽  
Parity Check ◽  
Code Length ◽  
Stabilizer Codes ◽  
Low Density Parity Check ◽  
Quantum Error ◽  
First Time

In this paper we introduce a general fault-tolerant quantum error correction protocol using flag circuits for measuring stabilizers of arbitrary distance codes. In addition to extending flag error correction beyond distance-three codes for the first time, our protocol also applies to a broader class of distance-three codes than was previously known. Flag circuits use extra ancilla qubits to signal when errors resulting fromvfaults in the circuit have weight greater thanv. The flag error correction protocol is applicable to stabilizer codes of arbitrary distance which satisfy a set of conditions and uses fewer qubits than other schemes such as Shor, Steane and Knill error correction. We give examples of infinite code families which satisfy these conditions and analyze the behaviour of distance-three and -five examples numerically. Requiring fewer resources than Shor error correction, flag error correction could potentially be used in low-overhead fault-tolerant error correction protocols using low density parity check quantum codes of large code length.

Nonbinary Low-Density Parity Check Decoding Algorithm Research-Based Majority Logic Decoding

2020 ◽  
Vol 34 (12) ◽  
pp. 2058016
Author(s):  
Zhong-xun Wang ◽  
Yang Xi ◽  
Zhan-kai Bao
Keyword(s):  
Error Correction ◽  
Iterative Decoding ◽  
Hamming Distance ◽  
Low Density ◽  
Parity Check ◽  
Soft Decision ◽  
Decoding Algorithm ◽  
Majority Logic ◽  
Low Density Parity Check ◽  
Majority Logic Decoding

In the nonbinary low-density parity check (NB-LDPC) codes decoding algorithms, the iterative hard reliability based on majority logic decoding (IHRB-MLGD) algorithm has poor error correction performance. The essential reason is that the hard information is used in the initialization and iterative processes. For the problem of partial loss of information, when the reliability is assigned during initialization, the error correction performance is improved by modifying the assignment of reliability at initialization. The initialization process is determined by the probability of occurrence of the number of erroneous bits in the symbol and the Hamming distance. In addition, the IHRB-MLGD decoding algorithm uses the hard decision in the iterative decoding process. The improved algorithm adds soft decision information in the iterative process, which improves the error correction performance while only slightly increasing the decoding complexity, and improves the reliability accumulation process which makes the algorithm more stable. The simulation results indicate that the proposed algorithm has a better decoding performance than IHRB algorithm.

scholarly journals A Novel Image Encryption Algorithm Based on a Fractional-Order Hyperchaotic System and DNA Computing

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Taiyong Li ◽  
Minggao Yang ◽  
Jiang Wu ◽  
Xin Jing
Keyword(s):  
Image Encryption ◽  
Fractional Order ◽  
Dna Computing ◽  
Lorenz System ◽  
Effective Diffusion ◽  
Encryption Algorithm ◽  
Pseudorandom Sequence ◽  
Hyperchaotic System ◽  
Diffusion Scheme ◽  
Hyperchaotic Lorenz System

In the era of the Internet, image encryption plays an important role in information security. Chaotic systems and DNA operations have been proven to be powerful for image encryption. To further enhance the security of image, in this paper, we propose a novel algorithm that combines the fractional-order hyperchaotic Lorenz system and DNA computing (FOHCLDNA) for image encryption. Specifically, the algorithm consists of four parts: firstly, we use a fractional-order hyperchaotic Lorenz system to generate a pseudorandom sequence that will be utilized during the whole encryption process; secondly, a simple but effective diffusion scheme is performed to spread the little change in one pixel to all the other pixels; thirdly, the plain image is encoded by DNA rules and corresponding DNA operations are performed; finally, global permutation and 2D and 3D permutation are performed on pixels, bits, and acid bases. The extensive experimental results on eight publicly available testing images demonstrate that the encryption algorithm can achieve state-of-the-art performance in terms of security and robustness when compared with some existing methods, showing that the FOHCLDNA is promising for image encryption.

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