Quantum secret sharing based on quantum error-correcting codes

Quantum secret sharing（QSS） is a procedure of sharing classical information or quantum information by using quantum states. This paper presents how to use a [2k- 1, 1, k] quantum error-correcting code （QECC） to implement a quantum （k, 2k-1） threshold scheme. It also takes advantage of classical enhancement of the [2k-1, 1, k] QECC to establish a QSS scheme which can share classical information and quantum information simultaneously. Because information is encoded into QECC, these schemes can prevent intercept-resend attacks and be implemented on some noisy channels.

An Error-Correcting Code-Based Robust Watermarking Scheme for Stereolithographic Files

Stereolithographic(STL)files have been extensively used in rapid prototyping industries as well as many other fields as watermarking algorithms to secure intellectual property and protect three-dimensional models from theft.However,to the best of our knowledge,few studies have looked at how watermarking can resist attacks that involve vertex-reordering.Here,we present a lossless and robust watermarking scheme for STL files to protect against vertexreordering attacks.Specifically,we designed a novel error-correcting code(ECC)that can correct the error of any one-bit in a bitstream by inserting several check digits.In addition,ECC is designed to make use of redundant information according to the characteristics of STL files,which introduces further robustness for defense against attacks.No modifications are made to the geometric information of the three-dimensional model,which respects the requirements of a highprecision model.The experimental results show that the proposed watermarking scheme can survive numerous kinds of attack,including rotation,scaling and translation(RST),facet reordering,and vertex-reordering attacks.

USING ERROR-CORRECTING ENCODERS TO DESIGN LOCAL-RANDOM SEQUENCE GENERATORS

This paper proved the statement that a good linear block encoder is in fact a good local-random sequence generator. Furthermore, this statement discovers the deep relationship between the error-correcting coding theory and the modern cryptography.

Spatial Image Watermarking by Error-Correction Coding in Gray Codes

In this paper, error-correction coding (ECC) in Gray codes is considered and its performance in the protecting of spatial image watermarks against lossy data compression is demonstrated. For this purpose, the differences between bit patterns of two Gray codewords are analyzed in detail. On the basis of the properties, a method for encoding watermark bits in the Gray codewords that represent signal levels by a single-error-correcting (SEC) code is developed, which is referred to as the Gray-ECC method in this paper. The two codewords of the SEC code corresponding to respective watermark bits are determined so as to minimize the expected amount of distortion caused by the watermark embedding. The stochastic analyses show that an error-correcting capacity of the Gray-ECC method is superior to that of the ECC in natural binary codes for changes in signal codewords. Experiments of the Gray-ECC method were conducted on 8-bit monochrome images to evaluate both the features of watermarked images and the performance of robustness for image distortion resulting from the JPEG DCT-baseline coding scheme. The results demonstrate that, compared with a conventional averaging-based method, the Gray-ECC method yields watermarked images with less amount of signal distortion and also makes the watermark comparably robust for lossy data compression.

ON CLASSICAL BCH CODES AND QUANTUM BCH CODES

It is a regular way of constructing quantum error-correcting codes via codes with self-orthogonal property, and whether a classical Bose-Chaudhuri-Hocquenghem (BCH) code is self-orthogonal can be determined by its designed distance. In this paper, we give the sufficient and necessary condition for arbitrary classical BCH codes with self-orthogonal property through algorithms. We also give a better upper bound of the designed distance of a classical narrow-sense BCH code which contains its Euclidean dual. Besides these, we also give one algorithm to compute the dimension of these codes. The complexity of all algorithms is analyzed. Then the results can be applied to construct a series of quantum BCH codes via the famous CSS constructions.

Self-dual Codes Defined on Factor Graphs

A definition of a self-dual code on graph and a procedure based on factor graphs to judge a self-dual code were presented. Three contributions of this paper were described as follows. To begin with, transform T_ R→L were defined, which was the basis of self-dual codes defined on graphs and played a key role in the paper. The second were that a self-dual code could be defined on factor graph, which was much different from conventional algebraic method. The third was that a factor graph approach to judge a self-dual code was illustrated, which took advantage of duality properties of factor graphs and our proposed transform T_ R→L to offer a convenient and geometrically intuitive process to judge a self-dual code.

Quantum BCH Codes Based on Spectral Techniques

When the time variable in quantum signal processing is discrete, the Fourier transform exists on the vector space of n-tuples over the Galois field F2, which plays an important role in the investigation of quantum signals. By using Fourier transforms, the idea of quantum coding theory can be described in a setting that is much different from that seen that far. Quantum BCH codes can be defined as codes whose quantum states have certain specified consecutive spectral components equal to zero and the error-correcting ability is also described by the number of the consecutive zeros. Moreover, the decoding of quantum codes can be described spectrally with more efficiency.

A NOVEL CONSTRUCTION OF QUANTUM LDPC CODES BASED ON CYCLIC CLASSES OF LINES IN EUCLIDEAN GEOMETRIES

The dual-containing (or self-orthogonal) formalism of Calderbank-Shor-Steane (CSS) codes provides a universal connection between a classical linear code and a Quantum Error-Correcting Code (QECC). We propose a novel class of quantum Low Density Parity Check (LDPC) codes constructed from cyclic classes of lines in Euclidean Geometry (EG). The corresponding constructed parity check matrix has quasi-cyclic structure that can be encoded flexibility, and satisfies the requirement of dual-containing quantum code. Taking the advantage of quasi-cyclic structure, we use a structured approach to construct Generalized Parity Check Matrix (GPCM). This new class of quantum codes has higher code rate, more sparse check matrix, and exactly one four-cycle in each pair of two rows. Ex-perimental results show that the proposed quantum codes, such as EG(2,q)II-QECC, EG(3,q)II-QECC, have better performance than that of other methods based on EG, over the depolarizing channel and decoded with iterative decoding based on the sum-product decoding algorithm.

Chinese Remainder Codes

Chinese Remainder Codes are constructed by applying weak block designs and Chinese Remainder Theorem of ring theory. The new type of linear codes take the congruence class in the congruence class ring R/I 1∩I 2∩...∩I n for the information bit, embed R/J i into R/I 1∩I 2∩...∩I n, and asssign the cosets of R/J i as the subring of R/I 1∩I 2∩...∩I n and the cosets of R/J i in R/I 1∩I 2∩...∩I n as check lines. There exist many code classes in Chinese Remainder Codes, which have high code rates. Chinese Remainder Codes are the essential generalization of Sun Zi Codes.

Enhancement of Error-Correction Coding of Spatial Watermarks in Gray Code

This paper demonstrates how channel coding can improve the robustness of spatial image watermarks against signal distortion caused by lossy data compression such as the JPEG scheme by taking advantage of the properties of Gray code. Two error-correction coding (ECC) schemes are used here: One scheme, referred to as the vertical ECC (VECC), is to encode information bits in a pixel by error-correction coding where the Gray code is used to improve the performance. The other scheme, referred to as the horizontal ECC (HECC), is to encode information bits in an image plane. In watermarking, HECC generates a codeword representing watermark bits, and each bit of the codeword is encoded by VECC. Simple single-error-correcting block codes are used in VECC and HECC. Several experiments of these schemes were conducted on test images. The result demonstrates that the error-correcting performance of HECC just depends on that of VECC, and accordingly, HECC enhances the capability of VECC. Consequently, HECC with appropriate codes can achieve stronger robustness to JPEG—caused distortions than non-channel-coding watermarking schemes.

ECC嵌入BCH码的NAND闪存纠错算法

针对现有闪存基于硬件ECC纠错算法的纠错能力差,而基于RS码和BCH码纠错算法的译码耗时长的问题,提出一种适于空间应用的硬件ECC嵌入BCH码的闪存纠错算法.分析了闪存内部组织结构特点及闪存硬件ECC纠错原理,提出了一种嵌入BCH(2084,2048,3)码的闪存纠错算法.采用一种蝶形阵列处理机制来迭代计算BCH校验码.使用地面检测设备对闪存纠错算法进行了试验验证.结果表明,纠错算法能快速稳定、可靠地工作,在Flash单页2 kB/页下,可以纠正24b错误.该纠错提高了空间相机图像存储系统的可靠性.

基于ECC和HFE的纠错密码构造

纠错密码是一种利用纠错码体制来实现纠错和加密双重功能的一种密码体制。大部分已知的纠错密码从变换的角度看是一种对明文的线性变换。从密码分析的角度看,由于不具有非线性变换,密码的混淆能力不强,容易被攻击。利用纠错码(Error-Correction Code,ECC)改造基本HFE(Hidden Field Equations)密码算法,所得的新密码算法具有纠错和加密功能,而且因其具有概率密码特性以及建立在MQ困难问题之上,具有很高的安全强度。

ECC抗功率分析攻击的等功耗编码算法

可以抵抗功率分析攻击的椭圆曲线密码算法往往效率较低。针对该问题,将等功耗编码的思想应用到椭圆曲线密码标量乘法运算过程中,通过消除标量乘运算中的功耗差异,掩盖相关密钥信息,达到抵抗功率分析攻击的目的。理论分析结果表明,与二元法抗功耗攻击算法和NAF窗口法抗功耗攻击算法相比,改进算法的执行效率较高。

ECC技术在大容量智能Smart Media卡上的应用

分析了Smart Media(SM)智能卡的使用现状,特别是大容量SM卡数据存储系统的关键技术问题。提出利用ECC编码技术在SM卡实现DOS文件系统的ECC编码,从而解决大容量SM卡在实际应用中的关键技术问题。

一种基于ACC和ECC的数字指纹方案

文章将基于欧式几何的ACC算法与纠错码ECC结合,编码下层使用前者,将该算法生成的指纹序列再进行卷积编码,得到最终的用户指纹序列。该方案兼具二者的优点,使生成的指纹具有更好的鲁棒性,能减小误判率,并且在保证抗合谋能力的前提下扩大能容纳的用户数量。

基于排序损失的ECC多标签代码异味检测方法

代码异味是由糟糕的代码或设计问题引起的一种软件特征,严重影响了软件系统的可靠性和可维护性.在软件系统中,一段代码元素可能同时受到多种代码异味的影响,使得软件质量明显下降.多标签分类适用该情况,将高共现的多个代码异味置于同一标签组,可以更好地考虑代码异味的相关性,但现有的多标签代码异味检测方法未考虑同一段代码元素中多种代码异味检测顺序的影响.对此,提出了一种基于排序损失的集成分类器链(ensemble of classifier chains,ECC)多标签代码异味检测方法,该方法选择随机森林作为基础分类器并采取多次迭代ECC的方式,以排序损失最小化为目标,选择一个较优的标签序列集,优化代码异味检测顺序问题,模拟其生成机理,检测一段代码元素是否同时存在长方法长参数列表、复杂类消息链或消息链过大类这3组代码异味.实验采用9个评价指标,结果表明所提出的检测方法优于现有的多标签代码异味检测方法,F1平均值达97.16%.

A Novel Deterministic Quantum Communication Scheme Using Stabilizer Quantum Code

Exploiting the encoding process of the stabilizer quantum code [[n, k, d]], a deterministic quantum communication scheme, in which n - 1 photons are distributed forward and backward in two-way channel, is proposed to transmit the secret messages with unconditional security. The present scheme can be implemented to distribute the secret quantum （or classical） messages with great capacity in imperfect quantum channel since the utilized code encodes k-qubit messages for each scheme run.

Cryptanalysis on AW digital signature scheme based on error-correcting codes

In 1993, Alabhadi and Wicker gave a modification to Xinmei Digital Signature Scheme based on error-correcting codes, which is usually denoted by AW Scheme. In this paper we show that the AW Scheme is actually not secure: anyone holding public keys of the signatory can obtain the equivalent private keys, and then forge digital signatures for arbitrary messages successfully. We also point out that one can hardly construct a digital signature scheme with high-level security due to the difficulty of decomposing large matrixes.

ELIMINATING SPEED PENALTIES IN ECC PROTECTED MEMORY DESIGNS USING “BIT BYPASSING” TECHNIQUES

In deep sub-micron ICs, growing amounts of on-die memory and scaling effects make embedded memories more vulnerable to reliability problems, such as soft errors induced by radiation. Error Correction Code(ECC) along with scrubbing is an efficient method for protecting memories against these errors. However, the latency of coding circuits brings speed penalties in high performance applications. This paper proposed a "bit bypassing" ECC protected memory by buffering the encoded data and adding an identifying address for the input data. The proposed memory design has been fabricated on a 130 nm CMOS process. According to the measurement, the proposed scheme only gives the minimum delay overhead of 22.6%, compared with other corresponding memories. Furthermore, heavy ion testing demonstrated the single event effects performance of the proposed memory achieves error rate reductions by 42.9 to 63.3 times.

Digital Image Watermarking Based on Mixed Error Correcting Code

In this paper, we present a novel technique based on a mixed Error Correcting Code(ECC)-the convolutional code and the repetition code to enhance the robustness of the embedded watermark. Before embedding, the binary watermark is scanned to one-dimension sequence and later inputted into the (3, 1, 2) convolutional encoder and (3, 1) repetition encoder frame by frame, which will improve the error correcting capability of decoder. The output code sequence is scanned to some matrixes as the new watermark messages. The watermarking is selected in low frequency band of the Discrete Wavelet Transform (DWT) and therefore it can resist the destruction of image processing. Experimental results are presented to demonstrate that the robustness of a watermark with mixed ECC is much higher than the traditional one just with repetition coding while suffering JPEG lossy compression, salt and pepper noise and center cutting processing.