• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Homomorphic Error-Control Codes for Linear Network Coding in Packet Networks

    2017-04-09 05:53:16XiaodongHanFeiGao
    China Communications 2017年9期

    Xiaodong Han, Fei Gao*

    Department of Information and Electronic Engineering, Beijing Institute of Technology, Beijing 100081, China

    * The corresponding author, email: gaofei@bit.edu.cn

    I. INTRODUCTION

    Network coding allows participating nodes in a network to encode incoming data packets instead of simply forwarding them, which makes it possible to achieve the maximum information flow in the multicast networks[1-3]. Moreover, linear coding is enough to achieve the maximum flow upper bound in multicast network with one or more sources[4]. Random linear network coding is even more powerful because the intermediate nodes in the network can perform linear encoding by randomly choosing their local encoding coefficients without any knowledge of the network topology to achieve the multicast capacity [5].Due to these great advantages, linear network coding and random linear network coding are useful in many areas: for example, they can be used in networks to disseminate information efficiently [6, 7], or in distributed data storage system to save storage space [1, 8], and so on.

    Regardless of the benefits that network coding offers to the network, when the network is composed of channels that are error-prone,network coding performs as a double-edged sword. Explicitly speaking, although encoding the data packets at every intermediate node provides some degree of performance gain,the erroneous packets injected to the network at the intermediate nodes may flow in the network and combine with other packets, so that the problem of deducing the source packets at some intended sink nodes may become a challenging task. To overcome this drawback, network error correction code has been proposed and studied [9-12].

    This paper studies homomorphism network error-control design.Specially, it focuses on binary field design since most prevailing code for communication is in binary field instead of high order finite field.

    Several approaches have been proposed to design codes that can correct network errors in network coding. Cai and Yeung have introduced network error correction codes and built a series of correction bounds by generalizing classic coding theory to network setting [9,10]. Zhang, Balli et al. have further studied these codes in [11, 13], where they defined the minimum rank of network error correction codes based on error space and deduced the correction capabilities of random linear network codes. On the other hand, Kotter, Kschischang, and Silva [12, 14] have introduced rank metric codes, where the codewords are defined as subspaces of some ambient space.

    While these information-theoretic multicast network error correction codes are elegant,they are designed to correct errors at sink nodes. Due to lack of sparsity, the encoding at the source node and decoding at the sink nodes with network error correcting codes proposed in the literature are computationally complex; and since such error correction is operated at receivers, bandwidth consumed by corrupted packets at intermediate nodes will not be reclaimed or reduced. Also, correction at the sink nodes can’t benefit from parallel or distributed computation. Furthermore,network coding is highly susceptible to pollution attacks in which malicious nodes modify packets by design so as to prevent message recovery, so that homomorphic signatures for network coding are used to validate the integrity of signed data and suit binary field distributed storage system [6, 15-20]. With homomorphic signatures, a data packet at any intermediate node that fails to pass the verification will be immediately discarded, regardless the reason for the packet corruption is due to malicious attack or random channel error.As a consequence, it is rather unlikely for an error packet to reach the destination, thus error correction only at the sink nodes becomes infeasible. For conventional method with network coding homomorphic signatures verification, it is readily caused that packets are not integrity so as to sinks unable to receive least correct linearly independent packet lead to decode incapable, further waste resource to retransmission. Moreover, the homomorphism in linear network coding can maintain integrity without destroying packets.

    Link by link error correction code solves such problems. However, in classic link by link error correction code, each intermediate node has to pack and unpack the data. Such operations lead to extra bandwidth overhead and latency. Therefore we are motivated to study the homomorphic network error correction code. We will show that, if the source node in linear network coding encodes the source packets with a unified linear block code, then every packet flowing in the network deduced by the source packets satisfies the same encoding constraints as the source packets. The homomorphic checksum manner not only detects error but also correction within the capability of codes. It prevents to consuming extra bandwidth and latency caused by compute-and-forward. It reduces the computational complexity meanwhile improves accuracy of correction.

    The remainder of this paper is organized as follows. In Section 2, homomorphic linear error-control code over binary field and its extensions in packet-based linear network coding is studied. In Section 3, three examples about the applications of the proposed homomorphic code are demonstrated to show the practical utility of the homomorphism. Further, we presentation simulation and analysis in Section 4.Finally, conclusions are drawn in Section 5.

    II. HOMOMORPHIC LINEAR BLOCK CODING NETWORK CODING

    Consider a linear network multicast network coding on a communication network with a source node, a set of intermediate nodes and a few sink nodes. At first, assume that the networkhas a unique source node.The notation V is the vertex set consisting of nodes of the network and E is the edge set whose elements are the communication channels of the network. Assume that the network coding is defined over a finite fieldwhere q and k is a positive integer. That is, we focus on the network coding over the binary extension Galois fieldswhich are widely used in the classic error-correction codes. Furthermore, we assume that the transmission of the data through the network is packet-based.The network coding can be either random or non-random.

    To show the homomorphism of the linear network coding, here is a simple example.Take an intermediate node from the network.Assume that the node has two incoming edges and one outgoing edge, as shown in figure 1. The data packet transmitted by the incoming edges areandrespectively.Here the superscript T stands for a transpose and K is the information length. Attached on each incoming edge, there is a checksum of the packet. The checksums of the data packets are transmitted through the network along with the data packets, always experiencing the same network encoding as the data packets. Define the checksum of a vectorwhereare a group of predetermined coefficients overAssume that the local encoding coefficients of the two incoming edges areandrespectively. Since the checksums ofandexperience the same network coding, the checksum of the outgoing edge generated by the local encoding will beOn the other hand, the data packet transmitted by the outgoing edge iswhose checksumcan be verified to beThus for allandthe homomorphic propertyis satisfied. In other words, the checksums of the data packets are homomorphic with respect to the linear network coding.

    Based on such an observation, we now investigate the homomorphism of the general linear network coding. Assume that there is an ω-dimension linear network coding on the communication networkover the finite field. The source messages are ω packetseach with lengthwhere for allDefine a linear block codeof blocklength N and rateby a generator matrixof dimension[21, 22]. The source node maps each source packetto a codewordAs known, such a code can also be described by a parity-check matrixof dimension, where. Each row of the parity-check matrix describes a linear constraint satisfied by all codewords. Note that the elements ofandtake values from Fq.The source node then sends the ω codewordsonAccording to[1-3], if the network coding is linear, a data packet transmitted over channelcan be described by (1):

    Fig. 1 Homomorphic checksums for linear network coding

    The last equality follows fromEq. (2) indicates that, for an error-free linear network coding, a data packettransmitted by any channelwill be a codeword of the linear block code. In other words,a data packet over channelsatisfies the same parity-check constraints as the source linear code of generator matrixand parity-check matrix. As seen, linear network coding does not change the encoding constraints of the linear block coded packets flowing in the network. Thus we call the linear block code is homomorphic with respect to linear network coding.

    2.1 Linearly homomorphic block coding

    Theorem 2.1: Define a linear network coding overon a unique source node networkIf the source nodeencodes each one of its K-length ω-dimensional source packets to a N-length codeword by anlinear block code of generator matrixand parity-check matrix, whereandareandq-ary matrices respectively,then a data packet over an edgesatisfies the same encoding constraints as the source linear block code of generator matrixand parity-check matrix.

    According with the definition of ring homomorphism in abstract algebra,where A is a ring, ifandis called the homomorphism of the ring. While the linear network coding does not change its linear block coding constraint rules, so the transmitted data packets are in accordance with the linear homomorphism check rules.

    From Eq. (2), the parity-check matrix can be used to detect or correct errors in the received vector:

    where r is the output vector of channelwhich may be noise polluted. The vector z is referred to as the syndrome. If no malicious attack exists in the network, when the syndrome vector is null, we assume there have been no errors. Malicious attack can be detected by homomorphic signatures for network coding[6, 15, 16], which validates our assumption.Otherwise, when the syndrome is not null, we decode the received vector by finding the most likely error vectorthat explains the observed syndrome given the assumed properties of the channel.

    Theorem 2.1 provides us flexible ways to perform network error corrections. The error-correction can be performed link by link,point to point from the source to a sink node,or a mixture of the two ways. In the mixed way, an intermediate network node without enough computation capability can simply forward its network coding packets to its subsequent nodes which may decode the received packets.

    As stated, the linear block code for error detection and correction in Theorem 2.1 is defined over finite fieldover which the linear network coding is performed. Hence, the source can use any q-ary linear block codes,such as Reed-solomon codes [21], low-density parity-check (LDPC) codes over[23, 24],and so on. Great advantage of these codes is having efficient encoding and decoding algorithms that allow the computation of the error vector with low complexity. Moreover,due to the algebraic structure or the sparse nature of the parity-check matrix, a linear error detection or correction code can be defined by a group of parameters. Thus in order to decode the packets, one can reconstruct the parity-check matrix based on the parameters at any node of the network, avoiding the multicast of a large-sized parity-check matrix.

    As known, the most well-known and the most widely-used error correction codes as Turbo codes and LDPC codes are binary based. Therefore it is natural for us to ask whether a binary linear block code is homomorphic in network coding. To answer this question, confine all the elements ofandwithinLet the data packet transmitted over channelbeNote the network coding is performed overand. For an elementwe write out its binary extension asforLetforThen from Theorem 2.1, we have (4)

    2.2 Linearly homomorphic block coding over binary field

    Corollary 2.2: Define a linear network coding overon a unique source node networkwhereand L is a positive integer. If the source nodeencodes each one of its K-length ω-dimensional source packets to a N-length codeword by alinear block code of generator matrixand parity-check matrix, whereandareandbinary matrices respectively, then each sub-code of the packet transmitted oversatisfies the same encoding constraints as the source binary linear block code defined by generator matrixand parity-check matrix. In fact, Corollary 2.2 is rather straightforward because the binary fieldis a subfield of the extension fieldwhen

    Corollary 2.2 means that a binary linear block code will be homomorphic in linear network coding when the network coding is defined over a binary extension fieldA binary homomorphic network error-control code is very useful, since all the classic binary linear block codes, such as terminated convolutional code [21], Turbo code [26, 27], LDPC code[22, 28], polar code [29], and so on, along with their efficient encoding and decoding algorithms can be applied to network coding for error detection and correction. Thus we have simply built a bridge between the network error correction and the classic channel coding theory which are rather mature.

    At this point, we have studied the homomorphic linear network error-control codes for unique source multicast. The extension of the homomorphic code from unique source to multiple sources is straight-forward. That is,if we replace the unique source by multiple sources in Theorem 2.1 and Corollary 2.2, the conclusions keep valid. For brevity, we omit further details.

    III. APPLICATION EXAMPLES

    In this section, a combinational use of homomorphic linear code with homomorphic signatures, McEliece public-key cryptosystem and unequal error protection are demonstrated respectively, which verifies the practical utility of the homomorphic linear code.

    3.1 Homomorphic linear code with homomorphic signatures

    A secure way to prevent pollution attack in network coding is to use homomorphic signatures. Several homomorphic signatures for network coding are available, as in [6, 16].However, these homomorphic signatures make use of groups in which the discrete logarithm problem is hard. They require the network coding coefficients to live in a fieldwhere q is very large. In particular, these schemes can’t support linear operations over small fields such asand its extensions, which means that they are not compatible with the homomorphic error-control codes we are studying here. In [15], linearly homomorphic signatures over binary fields have been proposed. This scheme is defined overso it is compatible with our homomorphic error-control codes.

    We now combine the network error correction with homomorphic signatures for reliable and secure multicast. Concretely, our codes work as follows. Assume a linear multicast on the networkoverhas ω-dimension, whereThe source packets are ω vectors :With binary extension, the source message can be described as the following matrix form:

    Let α be a primitive element of Fq. Then Fqcan be either expressed asIt is observed that forcan be expressed as Eq. (7)

    Substitution of Eq. (7) and Eq. (8) into Eq.(1) yields:

    3.2 Homomorphic McEliece publickey cryptosystem

    In this sub-section we illustrate the homomorphic properties of McEliece public-key cryptosystem with respect to linear network coding.As known, the McEliece cryptosystem is built on linear error-correcting block codes, thus we use such a code to design a homomorphic public-key cryptography for network coding.

    Let’s begin with the construction of “homomorphic” error vector pattern that will be used in the McEliece cryptosystem for network coding. Assume t is a predetermined positive integer number. For a ω-dimension q-valued linear network coding multicast, we will designbinary vectors that span a linear space, in which every vector has Hamming weight no more than t.

    Assume Alice has D sink nodesin the networkand a node of Bob wishes to broadcast ω K-length q-valued vectors to these sink nodes. One may imagine that Alice runs a company to collect live-view videos from global mobile users. Alice has D severs distributed around the world.Bob witnesses an interesting scene and he is now uploading the live-view video to the servers. The contents transmitted by Bob are invaluable thus they are protected by McEliece cryptosystem [32]. The nodesshare the same keys which are generated as follows. Alice chooses a binarycode C capable of correcting t errors. This code can be generated by agenerator matrixand possesses an efficient decoding algorithm.For example, this code can be the Goppa code of parameters[33]. In addition, Alice chooses a randombinary non-singular matrixand a randompermutation matrix, and computes thematrix. Finally,Alice publishesas her public key and holdsas her private key.

    Assume now Bob has ω vectorsto be broadcasted to the D nodes of Alice. He will then send the messages in the following steps.

    (1) Bob expands the source vectorsto binary vectors by writing out their sub-codes as

    (2) Bob encodes the messageas a binary vector of length K and computesfor

    (4) Bob computes and broadcastsfor

    To conclude the discussions above, if the messages at the source node are encrypted with the McEliece cryptography for linear network coding, then any packet over channelis encrypted or protected by the same cryptography.

    3.3 Unequal error protection

    In some scenarios of multicast network coding, different messages do not have equal rank of importance, thus it is better to protect them separately with unequal error protection(UEP). For example, the global kernel of the packet in network coding needs better protection, since it contains crucial information to recover the original source messages. A global kernel error may affect the decoding at the destination. Another example is when a multi-resolution source code is transmitted over a wireless channel with network coding.Since the coarse resolution contains the basic information to reconstruct at least a crude representation of the intended objects, it should be protected more carefully than the fine resolution.

    As seen in Section 2, the classic linear block code is homomorphic in network coding. An unequal error protection design for the classic linear block code is naturally applicable to network coding error correction thus more detailed explanations is omitted. Interested readers please refer to [34, 35].

    IV. SIMULATION RESULTS AND DISCUSSION

    In this section, we evaluate via simulation the error-correction performance of homomorphic error-control codes for linear network coding over finite fieldFor the butterfly network in figure 2, we made a simulation with homomorphic checksum detection and correction at different nodes in network. We verify the BER(bit error rate) on sink nodesandusing code rate-1/2 Turbo code. Also, we transmit codes from source node to sink nodes with linear network coding scheme over

    All depicts for the simulations set light on the BER of sink nodesandwhich(dB) represents the SNR (Signal to Noise Ratio). As seen, the simulation curves of sink nodesandmatch almost exactly for all the schemes because of sink nodesandare symmetric, therefore we analyze one of them.The interaction of the simulation and theoretical curves nearby Y-axis more and more for different scheme which proposed the correction gains increases significantly. Theory curve is the BER obtained by using classic link by link error correction code (i.e., Turbo code of code rate 1/2). First of all, we can observe that the performance of the scheme for correction at sink nodes only is around 0.2dB better than the theory at the BERin figure 3. Meanwhile, a performance gain of around 0.7dB of the scheme for correction at network coding node (node 3 in network) and 1.8dB of the scheme for correction at each node at the same BER in figure 4 and figure 5. Furthermore, our simulation shows that the performance with the scheme of correction at each node is more optimal than theory value when SNR is more than 1dB in figure 5.

    In figure 3, the BER performance of the scheme for correction at sink nodes is poorer than the way for classic link by link error correction code in a low SNR regimebecause the error packets are transmitted to destination nodes, which impairs network performance. However, as the SNR increases, the BER improves, and network capacity also increases. While the scheme of link by link error correction code has to pack and unpack, which results in extra bandwidth overhead and lower bandwidth efficiency. Therefore, such scheme can only achieve better capacity in a higher SNR regime

    Since the error packets are corrected at intermediate nodes, the BER of the scheme for error checking and correction at intermediate nodes in figure 4 and figure 5, including the scheme of correction at network coding nodes and each node, can be close to the scheme of link by link error correction code in a low SNR regime, especially for the way of correc-tion at each node. The homomorphic checksum method is simpler and less costly, hence it can achieve the BER at a low SNR regime, which the classic scheme needs 10dB to reach. This indirectly illustrates the relationship between the capacity and the SNR according to Shannon’s theorem as well.

    Fig. 2 butterfly network

    Fig. 3 The scheme of correction at sink nodes

    Fig. 4 The scheme of correction at network coding nodes

    Fig. 5 The scheme of correction at each node

    Compared with simulation results in figure 3 and figure 4, SNR needs more than 3.8dB and 3dB respectively at least is able to make the performance better than theory value. It notes that error performance improves notably for correction at network coding nodes compared with correction at sink nodes only. In other words, our homomorphic error-control codes for linear network coding are able to achieve optimal error performance gain.

    V. CONCLUSIONS

    In this work, the application of classic linear block code in network coding for network error-control has been studied. Concretely, the homomorphism of the classic linear block code in linear network coding has been shown. Therefore, the code is applicable to detect and correct errors not only in a distributed link by link way, but also in a centralized point to point way, where the error correction is performed at the sink node. Moreover, the binary homomorphic linear error-control code is introduced. Great advantage of the homomorphic property of the network error-control code is that, the classic good binary linear block codes, such as Turbo code and LDPC code, can be directly used in network coding to perform network error control. Furthermore,the proposed code has many applications as the combination with the homomorphic signatures for network error correction and malicious attack prevention, the combination with McEliece public-key cryptosystem for secure multicast, and unequal error protection for different priorities and qualities in a unified multicast, and so on.

    ACKNOWLEDGEMENTS

    This work was supported by Natural Science Foundation of China (No. 61271258).

    [1] Chou, P.A., Wu, Y., “Network coding for the internet and wireless networks”, IEEE Signal Process Magazine, vol.24, no.5, pp 77-85, 2007.

    [2] R. Alshwede, N. Cai, S.-Y. R. Li, R. W. Yeung,“Network information flow”. IEEE Transactions on Information Theory. vol.46, no.4, pp 1204-1216, 2000.

    [3] R. W Yeung, S.-Y. R. Li, N. Cai, Z. Zhang, “Network coding theory”. (Now Publishers Inc., Boston),pp 411-483,2006.

    [4] S.-Y. R. Li, R. W. Yeung, N. Cai, “Linear network coding”. IEEE Transactions on Information Theory. vol.49, no.2, pp 371-381, 2003.

    [5] T. Ho, M. Medard, R. Koetter, D. Karger, M. Eff -ros, J. Shi, B. Leong, “A random linear network coding approach to multicast”. IEEE Transactions on Information Theory. vol.52, no.10, pp 4413-4430, 2006.

    [6] P. Krishnan, B. Sundar Rajan, “A Matroidal Framework for Network-Error Correcting Codes”. IEEE Transactions on Information Theory. vol.61, no.2, pp 836-872, 2015.

    [7] M. Yang, Y. Y. Yang, “Applying network coding to peer-to-peer file sharing”. IEEE Transactions on Computers. vol.63, no.8, pp 1-14, 2013.

    [8] X. Li, T. Jiang, Q. Zhang, L. Wang, “Binary linear multicast network coding on acyclic networks:principle and applications in wireless communication networks”. IEEE Journal on Selected Areas in Communications. vol.27, no.5, pp 738-748,2009.

    [9] R. W. Yeung, N. Cai, “Network error correction,part I: basic concepts and upper bounds”. Communications in Information and Systems. vol.6,no.1, pp 19-36 , 2006.

    [10] N. Cai, R. W. Yeung, “Network error correction,part II: lower bounds”. Communications in Information and Systems. vol.6, no.1, pp 37-54, 2006.

    [11] Z. Zhang, “Linear network error correction codes in packet networks”. IEEE Transactions on Information Theory. vol.54, no.1, pp 209-218,2008.

    [12] R. Kotter, F. R. Kshischang, “Coding for errors and erasures in random network coding”. IEEE Transactions on Information Theory. vol.54, no.8,pp 3579-3591, 2008.

    [13] H. Balli, X. Yan, Z. Zhang, “On randomized linear network codes and their error correction capabilities”. IEEE Transactions on Information Theory. vol.55, no.7, pp 3148-3160, 2009.

    [14] D. Silva, F. Kschischang, R. Kotter, “A rank-metric approach to error control in random network coding”. IEEE Transactions on Information Theory. vol.54, no.9, pp 3951-3967, 2008.

    [15] D. Boneh, D. M. Freeman, “Linearly homomorphic signatures over binary fields and new tools for lattice-based signatures”. Proceedings of Public Key Cryptography (PKC 2011). Springer LNCS 6571, pp 1-16, 2011.

    [16] S. H. Lee, M. Gerla, H. Krawczyk, , K. W. Lee, E.A. Quaglia. “Performance Evaluation of Secure Network Coding using Homomorphic Signature”. International Symposium on Network Coding (NetCod), Beijing, pp 25-27, July, 2011.

    [17] C. Cheng, T. Jiang, “An efficient homomorphic MAC with small key size for authentication in network coding”. IEEE Transactions on Computers. vol.62, no.10, pp 2096-2100, 2013.

    [18] C. Cheng, T. Jiang, Q. Zhang, “TESLA-based homomorphic MAC for authentication in P2P system for live streaming with network coding”.IEEE Journal on Selected Areas in Communications. vol.31, no.9, pp 291-298, 2013.

    [19] C. Cheng, T. Jiang, “A novel homomorphic MAC scheme for authentication in network coding”.IEEE Communications Letters. vol.15, no.11, pp 1228-1230, 2011.

    [20] M. Dai, C. W. Sung, H. Wang, X. Gong, Z. Lu, “A new zigzag-decodable code with efficient repair in wireless distributed storage”, IEEE Transactions on Mobile Computers. vol.16, no.5, pp 1218-1230, 2017.

    [21] S. Lin, D. J. Costello, “Error control coding: fundamentals and applications”. (Pearson Education, Inc. India), pp 51-84, 2004.

    [22] J. Broulim, V. Georgiev, “LDPC error correction code utilization”. The 20th Telecommunications forum TELFOR 2012. Serbia, Belgrade, pp 20-22,Nov, 2012.

    [23] K. Huang, D. G. M. Mitchell, L. Wei, X. Ma and D.J. Costello. “Performance Comparison of LDPC Block and Spatially Coupled Codes Over GF(q)”.IEEE Transactions on Communications. vol.63,no.3, pp 592-604, 2015.

    [24] B. Rong, T. Jiang, X. Li and M. R. Soleymani,“Combine LDPC codes over GF(q) and q-ary modulation for bandwidth efficient transmission”. IEEE Transactions on Broadcasting. vol.54,no.1, pp 78-84, 2008.

    [25] Z. Wan, “Lectures on finite fields and Galois rings”. (World Scientific Publishing Co. Pte. Ltd.New Jersey), pp 49-72, Oct, 2003.

    [26] F. Jiang, E. Psota, L.C. Perez, “Decoding Turbo Codes Based on Their Parity-Check Matrices”.IEEE 39th Southeastern Symposium on System Theory (SSST 2007), Mercer University Macon,Georgia, USA, pp 221-224, 04-06 Mar, 2007.

    [27] S. Benedetto, D. Divsalar, G. Montorsi, F. Pollara,“A soft-input soft-output maximum a posteriori(MAP) module to decode parallel and serial concatenated codes”. TDA Progress Report, pp 42-121, 1995.

    [28] R. G. Gallager, “Low-density parity-check codes”.(MIT Press, Cambridge, Massachusetts), pp 49-54, 1963.

    [29] E. Arikan, “Channel polarization: a method for constructing capacity-achieving codes for symmetric binary-input memoryless channels”. IEEE Transactions on Information Theory. vol.55, no.7,pp 3051-3073, 2009.

    [30] E. Kehdi, B. Li, “Null keys: limiting malicious attacks via null space properties of network coding”. IEEE International Conference on Computer Communications (INFOCOM 2009). Rio de Janeiro, 19-25 Apr, 2009.

    [31] W. Qiao, J. Li, J.Ren. “An efficient error-detection and error-correction (EDEC) scheme for network coding”. IEEE Global Telecommunications Conference (GLOBECOM 2011), Houston, 5-9 Dec,2011.

    [32] A. Couvreur, I. M. Corbella, R. Pellikaan, “A Polynomial Time Attack against Algebraic Geometry Code Based Public Key Cryptosystems”. IEEE International Symposium on Information Theory(ISIT 2014), University of Hawaii, USA, 29 Jun-04 July, 2014.

    [33] A. Shoufan, T. Wink, H. G. Molter, S. A. Huss and E. Kohnert. “A Novel Cryptoprocessor Architecture for the McEliece Public-Key Cryptosystem”.IEEE Transactions on Computers. vol.59, no.11,pp 1533-1546, 2010.

    [34] S. Borade, B. Nakiboglu, L. Zheng, “Some fundamental limits of unequal error protection”.IEEE International Symposium on Information Theory (ISIT 2008) , Toronto, 06-08 July, 2008.

    [35] J. Yue, Z.H. Lin, B. Vucetic, “On Estimation of Protection Parameters for Unequal Error Protection Distributed Fountain Codes in Wireless Relay Networks”. IEEE Wireless Communications and Network Conference (WCNC’ 2014), Istanbul, 06-09 Apr, 2014.

    亚洲一区中文字幕在线| 国产av又大| 99精品欧美一区二区三区四区| 精品国产超薄肉色丝袜足j| 亚洲av片天天在线观看| 正在播放国产对白刺激| 法律面前人人平等表现在哪些方面| x7x7x7水蜜桃| 欧美3d第一页| 日韩有码中文字幕| 久久香蕉激情| 国产成人影院久久av| 免费搜索国产男女视频| 夜夜爽天天搞| 精品久久久久久久末码| 毛片女人毛片| 18美女黄网站色大片免费观看| 老鸭窝网址在线观看| cao死你这个sao货| 日本a在线网址| 亚洲一码二码三码区别大吗| 久久久久久久精品吃奶| 色精品久久人妻99蜜桃| 国产亚洲av嫩草精品影院| 成年人黄色毛片网站| 无人区码免费观看不卡| 狂野欧美激情性xxxx| 亚洲av电影不卡..在线观看| 国产久久久一区二区三区| 欧美国产日韩亚洲一区| 国内久久婷婷六月综合欲色啪| 国产av一区在线观看免费| 久久国产精品人妻蜜桃| 免费一级毛片在线播放高清视频| 黑人操中国人逼视频| 中文字幕高清在线视频| 亚洲av成人一区二区三| 特级一级黄色大片| 国内精品一区二区在线观看| 国产精品一区二区三区四区免费观看 | 99久久久亚洲精品蜜臀av| 女警被强在线播放| 国产精品美女特级片免费视频播放器 | www.自偷自拍.com| 12—13女人毛片做爰片一| 18禁观看日本| 久久欧美精品欧美久久欧美| av天堂在线播放| 99国产极品粉嫩在线观看| 欧美日本亚洲视频在线播放| 久久国产乱子伦精品免费另类| 丁香欧美五月| 国产av一区二区精品久久| 国产主播在线观看一区二区| www.www免费av| 一进一出好大好爽视频| 国产亚洲精品一区二区www| 国内精品一区二区在线观看| 亚洲avbb在线观看| 91麻豆av在线| 精品日产1卡2卡| 伦理电影免费视频| 夜夜躁狠狠躁天天躁| 精品久久久久久久人妻蜜臀av| 久久精品国产综合久久久| 欧美乱色亚洲激情| 亚洲最大成人中文| 国产精品99久久99久久久不卡| 亚洲欧美日韩东京热| 国产精品乱码一区二三区的特点| 白带黄色成豆腐渣| 777久久人妻少妇嫩草av网站| 99国产精品一区二区三区| 国产精品1区2区在线观看.| 免费一级毛片在线播放高清视频| 别揉我奶头~嗯~啊~动态视频| 中国美女看黄片| 最近在线观看免费完整版| 久久久久久大精品| 欧美日韩中文字幕国产精品一区二区三区| 午夜影院日韩av| 亚洲自拍偷在线| 国产不卡一卡二| 欧美午夜高清在线| 黄色视频不卡| 岛国在线免费视频观看| 在线观看免费日韩欧美大片| 别揉我奶头~嗯~啊~动态视频| 美女 人体艺术 gogo| 欧美极品一区二区三区四区| 男女那种视频在线观看| 看片在线看免费视频| 日韩欧美在线乱码| 欧美激情久久久久久爽电影| 中文亚洲av片在线观看爽| 男人舔女人的私密视频| 国产亚洲精品第一综合不卡| 日韩精品免费视频一区二区三区| 99精品欧美一区二区三区四区| 久久久久久大精品| 亚洲一码二码三码区别大吗| 毛片女人毛片| 成人国语在线视频| 成人18禁在线播放| 91老司机精品| 欧美日韩国产亚洲二区| 一级黄色大片毛片| 久久久久久九九精品二区国产 | 夜夜爽天天搞| 99在线视频只有这里精品首页| 国产日本99.免费观看| 亚洲人与动物交配视频| 亚洲第一欧美日韩一区二区三区| 日韩欧美在线二视频| 观看免费一级毛片| 久久精品国产综合久久久| 国语自产精品视频在线第100页| 人妻夜夜爽99麻豆av| 亚洲欧美日韩无卡精品| 精品国产美女av久久久久小说| 十八禁网站免费在线| 亚洲九九香蕉| 久久天躁狠狠躁夜夜2o2o| 女警被强在线播放| 欧洲精品卡2卡3卡4卡5卡区| 成人一区二区视频在线观看| 欧美日本视频| 又黄又爽又免费观看的视频| 日韩中文字幕欧美一区二区| 国产成人系列免费观看| 男女做爰动态图高潮gif福利片| 国产三级黄色录像| 性色av乱码一区二区三区2| 十八禁人妻一区二区| 亚洲成a人片在线一区二区| 久久伊人香网站| 成熟少妇高潮喷水视频| 国产av麻豆久久久久久久| 国产精品亚洲美女久久久| 亚洲国产高清在线一区二区三| 国产野战对白在线观看| www.999成人在线观看| 国产黄色小视频在线观看| 一边摸一边抽搐一进一小说| 亚洲成av人片免费观看| 老司机福利观看| 欧美最黄视频在线播放免费| 老司机深夜福利视频在线观看| 精品国产超薄肉色丝袜足j| 亚洲乱码一区二区免费版| 长腿黑丝高跟| 69av精品久久久久久| 久久午夜亚洲精品久久| 国产成人啪精品午夜网站| 一级毛片女人18水好多| 搞女人的毛片| 日本黄大片高清| 久久精品人妻少妇| 他把我摸到了高潮在线观看| 久久精品影院6| 51午夜福利影视在线观看| 黄片大片在线免费观看| 国产69精品久久久久777片 | 午夜福利成人在线免费观看| 午夜精品一区二区三区免费看| 免费一级毛片在线播放高清视频| 成人高潮视频无遮挡免费网站| 久久婷婷成人综合色麻豆| 此物有八面人人有两片| 精品乱码久久久久久99久播| 51午夜福利影视在线观看| 国产麻豆成人av免费视频| 日本三级黄在线观看| 亚洲av片天天在线观看| 国产精品98久久久久久宅男小说| 身体一侧抽搐| 一级a爱片免费观看的视频| 午夜免费观看网址| 日本a在线网址| 亚洲成人久久爱视频| 精品第一国产精品| 中文字幕高清在线视频| 亚洲欧美日韩高清在线视频| 最近最新中文字幕大全电影3| www日本在线高清视频| 伊人久久大香线蕉亚洲五| 老汉色av国产亚洲站长工具| 久久天躁狠狠躁夜夜2o2o| 成人国语在线视频| 天堂av国产一区二区熟女人妻 | 99re在线观看精品视频| 视频区欧美日本亚洲| 欧美成狂野欧美在线观看| svipshipincom国产片| 香蕉久久夜色| 男人舔女人的私密视频| 岛国视频午夜一区免费看| 日本 欧美在线| 久久久久久亚洲精品国产蜜桃av| 99久久99久久久精品蜜桃| 99久久久亚洲精品蜜臀av| www.999成人在线观看| 最近最新免费中文字幕在线| 国产v大片淫在线免费观看| 国产亚洲精品综合一区在线观看 | 国产熟女午夜一区二区三区| 高清在线国产一区| 亚洲av五月六月丁香网| 国产男靠女视频免费网站| 久久久久久国产a免费观看| 欧美乱妇无乱码| 国产又黄又爽又无遮挡在线| 欧美绝顶高潮抽搐喷水| 国产三级中文精品| 久久久水蜜桃国产精品网| 欧美成人一区二区免费高清观看 | 婷婷丁香在线五月| 中文字幕高清在线视频| 欧美一区二区精品小视频在线| 丰满人妻一区二区三区视频av | 九色国产91popny在线| 亚洲va日本ⅴa欧美va伊人久久| 国产av在哪里看| 亚洲国产欧美人成| 男插女下体视频免费在线播放| 精品午夜福利视频在线观看一区| 亚洲av成人一区二区三| 国产一级毛片七仙女欲春2| 两个人免费观看高清视频| 叶爱在线成人免费视频播放| xxxwww97欧美| 亚洲在线自拍视频| 日本成人三级电影网站| 国产精品久久久av美女十八| 91成年电影在线观看| 99在线视频只有这里精品首页| 亚洲国产中文字幕在线视频| 亚洲欧美日韩东京热| 免费看a级黄色片| 欧美日韩中文字幕国产精品一区二区三区| 精品欧美国产一区二区三| 亚洲avbb在线观看| 国产成+人综合+亚洲专区| 午夜福利18| 九九热线精品视视频播放| 亚洲人与动物交配视频| 99热这里只有是精品50| 亚洲一区二区三区色噜噜| 天堂动漫精品| 一个人免费在线观看的高清视频| 欧美乱妇无乱码| 欧美一级a爱片免费观看看 | 欧美成人一区二区免费高清观看 | 国内久久婷婷六月综合欲色啪| 午夜激情av网站| 亚洲成人中文字幕在线播放| 一夜夜www| 久久久久久亚洲精品国产蜜桃av| 亚洲av成人一区二区三| 99国产极品粉嫩在线观看| 亚洲无线在线观看| 国产成人av教育| 在线国产一区二区在线| 国内少妇人妻偷人精品xxx网站 | 麻豆国产97在线/欧美 | 精品国内亚洲2022精品成人| 老汉色∧v一级毛片| 在线免费观看的www视频| 男人的好看免费观看在线视频 | 国产精品一及| 丝袜人妻中文字幕| 男女那种视频在线观看| 妹子高潮喷水视频| 波多野结衣高清作品| 在线观看免费日韩欧美大片| 日本一本二区三区精品| 日本黄大片高清| 久久香蕉国产精品| 国产精品美女特级片免费视频播放器 | 久久精品91无色码中文字幕| 午夜成年电影在线免费观看| 成人国产综合亚洲| 免费电影在线观看免费观看| 成年人黄色毛片网站| 一级毛片精品| 99国产极品粉嫩在线观看| 极品教师在线免费播放| 99热6这里只有精品| 超碰成人久久| 国产一区二区在线观看日韩 | 夜夜躁狠狠躁天天躁| 日本成人三级电影网站| 国产私拍福利视频在线观看| 国产亚洲av嫩草精品影院| 成人欧美大片| 成人三级黄色视频| 久久久水蜜桃国产精品网| 久久午夜亚洲精品久久| 久久精品国产99精品国产亚洲性色| 日本熟妇午夜| 国产真人三级小视频在线观看| 搡老妇女老女人老熟妇| 丝袜人妻中文字幕| 亚洲国产中文字幕在线视频| 真人做人爱边吃奶动态| 亚洲中文字幕一区二区三区有码在线看 | 欧美三级亚洲精品| 美女高潮喷水抽搐中文字幕| 最近在线观看免费完整版| 麻豆一二三区av精品| 亚洲欧美日韩无卡精品| 亚洲国产精品成人综合色| 一本精品99久久精品77| 身体一侧抽搐| 国产精品爽爽va在线观看网站| 两人在一起打扑克的视频| 在线十欧美十亚洲十日本专区| 亚洲国产精品sss在线观看| 人成视频在线观看免费观看| 欧美国产日韩亚洲一区| 少妇粗大呻吟视频| 久久人妻福利社区极品人妻图片| 精品日产1卡2卡| 一边摸一边做爽爽视频免费| 国产精品一区二区三区四区久久| 后天国语完整版免费观看| 久久精品国产综合久久久| 国内揄拍国产精品人妻在线| 十八禁人妻一区二区| 99国产精品99久久久久| 日韩欧美精品v在线| 国产精品 国内视频| 级片在线观看| 伊人久久大香线蕉亚洲五| 香蕉丝袜av| 制服人妻中文乱码| 午夜视频精品福利| 亚洲九九香蕉| 级片在线观看| 每晚都被弄得嗷嗷叫到高潮| 精品国产乱码久久久久久男人| 一卡2卡三卡四卡精品乱码亚洲| 亚洲精品在线美女| 欧美日韩中文字幕国产精品一区二区三区| www国产在线视频色| 成人特级黄色片久久久久久久| 亚洲狠狠婷婷综合久久图片| 特大巨黑吊av在线直播| 欧美激情久久久久久爽电影| 舔av片在线| 国产又黄又爽又无遮挡在线| 我的老师免费观看完整版| 国产精品av久久久久免费| 日本在线视频免费播放| 老熟妇仑乱视频hdxx| 国产亚洲精品久久久久5区| 日韩欧美国产在线观看| 日韩精品青青久久久久久| 亚洲国产精品成人综合色| 高潮久久久久久久久久久不卡| 国产av在哪里看| 久久久久国内视频| 窝窝影院91人妻| av在线播放免费不卡| 午夜精品久久久久久毛片777| 欧美精品啪啪一区二区三区| 欧美黄色片欧美黄色片| 欧美丝袜亚洲另类 | 亚洲成人久久爱视频| 少妇熟女aⅴ在线视频| 亚洲男人天堂网一区| 日韩有码中文字幕| 天天一区二区日本电影三级| 免费在线观看完整版高清| 国产又色又爽无遮挡免费看| 日韩大码丰满熟妇| 黑人欧美特级aaaaaa片| 又粗又爽又猛毛片免费看| 免费人成视频x8x8入口观看| 国产精品野战在线观看| 日韩 欧美 亚洲 中文字幕| 十八禁人妻一区二区| 色综合婷婷激情| 两个人免费观看高清视频| 无人区码免费观看不卡| 亚洲最大成人中文| 免费在线观看完整版高清| 欧美3d第一页| 亚洲精品在线美女| 在线观看美女被高潮喷水网站 | 亚洲成a人片在线一区二区| 亚洲成人免费电影在线观看| 国产精品自产拍在线观看55亚洲| 丰满人妻熟妇乱又伦精品不卡| 午夜福利高清视频| 两个人视频免费观看高清| 日本一本二区三区精品| 亚洲自拍偷在线| 亚洲欧美日韩高清专用| 日本熟妇午夜| 亚洲国产欧洲综合997久久,| 免费看日本二区| 欧美日韩黄片免| 日本免费a在线| 国产在线精品亚洲第一网站| 大型黄色视频在线免费观看| 免费看美女性在线毛片视频| 九色国产91popny在线| 精品久久久久久,| 后天国语完整版免费观看| 老熟妇乱子伦视频在线观看| 黄色视频不卡| 欧美中文综合在线视频| 波多野结衣高清无吗| 久久久久久久精品吃奶| 麻豆一二三区av精品| 国产精品久久久人人做人人爽| xxxwww97欧美| 老汉色∧v一级毛片| 啪啪无遮挡十八禁网站| 两个人看的免费小视频| 亚洲精品一区av在线观看| 91国产中文字幕| 免费在线观看视频国产中文字幕亚洲| 在线永久观看黄色视频| 在线观看日韩欧美| 99久久国产精品久久久| 亚洲最大成人中文| 免费高清视频大片| www国产在线视频色| 午夜视频精品福利| 中国美女看黄片| 搞女人的毛片| 天堂动漫精品| 一卡2卡三卡四卡精品乱码亚洲| 成人国产一区最新在线观看| 日韩高清综合在线| 在线十欧美十亚洲十日本专区| videosex国产| 一本精品99久久精品77| 成人三级黄色视频| 好男人在线观看高清免费视频| 欧美不卡视频在线免费观看 | 国产成人av激情在线播放| 亚洲欧美日韩无卡精品| av福利片在线| 三级男女做爰猛烈吃奶摸视频| 久久中文字幕人妻熟女| 精品久久久久久久久久免费视频| 丁香欧美五月| 18禁黄网站禁片午夜丰满| 女同久久另类99精品国产91| 51午夜福利影视在线观看| 久久 成人 亚洲| 一进一出好大好爽视频| 国产v大片淫在线免费观看| 男人舔女人的私密视频| 国产成人影院久久av| 在线十欧美十亚洲十日本专区| 国产精品野战在线观看| 波多野结衣高清作品| 国产激情久久老熟女| 欧美又色又爽又黄视频| 欧美色视频一区免费| 国产黄片美女视频| 亚洲性夜色夜夜综合| 亚洲欧美日韩高清在线视频| 国产精品一及| 欧美中文综合在线视频| 天天躁狠狠躁夜夜躁狠狠躁| 欧美日韩福利视频一区二区| 久久国产精品影院| 啪啪无遮挡十八禁网站| 一本综合久久免费| 久久久久久大精品| 国产探花在线观看一区二区| 精品国产美女av久久久久小说| 成年女人毛片免费观看观看9| 日本免费一区二区三区高清不卡| www.www免费av| 国产精品国产高清国产av| 丝袜美腿诱惑在线| 日日夜夜操网爽| 一进一出好大好爽视频| 亚洲男人的天堂狠狠| 国产成人系列免费观看| 久久久久性生活片| 精品电影一区二区在线| 午夜免费激情av| 小说图片视频综合网站| 人成视频在线观看免费观看| 国产成+人综合+亚洲专区| 九九热线精品视视频播放| 精品国产乱子伦一区二区三区| 国产一区二区在线观看日韩 | 欧美乱色亚洲激情| 国产三级黄色录像| 人妻丰满熟妇av一区二区三区| 久久天堂一区二区三区四区| 精品久久久久久成人av| 巨乳人妻的诱惑在线观看| 成年免费大片在线观看| 国产精品久久久久久亚洲av鲁大| 久99久视频精品免费| 亚洲精品中文字幕在线视频| 禁无遮挡网站| 变态另类成人亚洲欧美熟女| 欧美zozozo另类| 欧美性长视频在线观看| 亚洲精品中文字幕一二三四区| 搞女人的毛片| 波多野结衣高清无吗| 女警被强在线播放| 一区二区三区高清视频在线| 欧美色视频一区免费| 日本黄大片高清| 1024手机看黄色片| 国产一区二区三区视频了| 日本一二三区视频观看| 国产精品亚洲一级av第二区| 母亲3免费完整高清在线观看| 国产免费男女视频| 亚洲九九香蕉| 99久久99久久久精品蜜桃| a级毛片a级免费在线| 天堂av国产一区二区熟女人妻 | 亚洲成av人片免费观看| 午夜两性在线视频| 免费看十八禁软件| 精品少妇一区二区三区视频日本电影| 亚洲精品久久国产高清桃花| 在线a可以看的网站| 久久久久九九精品影院| 日韩中文字幕欧美一区二区| 99riav亚洲国产免费| 亚洲成人免费电影在线观看| 一本一本综合久久| 两个人的视频大全免费| 别揉我奶头~嗯~啊~动态视频| 一区二区三区高清视频在线| 欧美日韩福利视频一区二区| 久久欧美精品欧美久久欧美| 国产日本99.免费观看| 人人妻人人澡欧美一区二区| 亚洲成a人片在线一区二区| 国产男靠女视频免费网站| 成年免费大片在线观看| 欧美日本亚洲视频在线播放| 久久久国产成人精品二区| 啦啦啦免费观看视频1| 欧美另类亚洲清纯唯美| 国内揄拍国产精品人妻在线| 法律面前人人平等表现在哪些方面| 日韩 欧美 亚洲 中文字幕| √禁漫天堂资源中文www| 他把我摸到了高潮在线观看| xxx96com| 五月玫瑰六月丁香| 日日爽夜夜爽网站| 欧美性猛交黑人性爽| 好看av亚洲va欧美ⅴa在| 精品国产乱码久久久久久男人| 亚洲最大成人中文| 母亲3免费完整高清在线观看| xxxwww97欧美| 身体一侧抽搐| 亚洲精品在线观看二区| 亚洲av熟女| 亚洲av五月六月丁香网| 亚洲精华国产精华精| 国产免费男女视频| 听说在线观看完整版免费高清| 亚洲专区字幕在线| 欧美成人一区二区免费高清观看 | 久久精品亚洲精品国产色婷小说| 久久亚洲真实| 动漫黄色视频在线观看| 美女 人体艺术 gogo| 亚洲国产看品久久| 久久午夜综合久久蜜桃| 视频区欧美日本亚洲| 亚洲国产精品合色在线| 毛片女人毛片| 亚洲真实伦在线观看| 午夜成年电影在线免费观看| 99热只有精品国产| 国产又黄又爽又无遮挡在线| 亚洲熟妇中文字幕五十中出| 亚洲中文日韩欧美视频| 日韩欧美免费精品| 欧美日韩一级在线毛片| 成年版毛片免费区| 久久精品成人免费网站| 一区二区三区激情视频| 成人av在线播放网站| 午夜福利在线在线| 精品久久蜜臀av无| 免费av毛片视频| 中文字幕久久专区| 国产精品自产拍在线观看55亚洲| 国产成+人综合+亚洲专区| 亚洲国产精品成人综合色| 全区人妻精品视频| 亚洲成人久久爱视频| 最好的美女福利视频网| 国产亚洲欧美98| 国产真人三级小视频在线观看| 伦理电影免费视频| 麻豆国产97在线/欧美 | 亚洲精品在线美女| 国产麻豆成人av免费视频| 一级a爱片免费观看的视频| 国产av一区在线观看免费| 亚洲精品美女久久久久99蜜臀| netflix在线观看网站|