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2023-07-31
Albatoosh, Ahmed H., Shuja'a, Mohamed Ibrahim, Al-Nedawe, Basman M..  2022.  Effectiveness Improvement of Offset Pulse Position Modulation System Using Reed-Solomon Codes. 2022 International Congress on Human-Computer Interaction, Optimization and Robotic Applications (HORA). :1—5.
Currently, the pulse position modulation (PPM) schemes are suffering from bandwidth application where the line rate is double that of the initial data rate. Thus, the offset pulse position modulation (OPPM) has been suggested to rectify this concern. Several attempts to improve the OPPM can be found in the open literature. This study focuses on the utilization of Reed Solomon (RS) codes to enhance the forward error correction (FEC) bit error rate, which is not yet explored. The performance of errors of the uncoded OPPM was compared to the one used by RS coded OPPM using the number of photons per pulse, the transmission's efficacy, and bandwidth growth. The results demonstrate that employing FEC coding would increase the system's error performance especially when the RS is operating at its finest settings. Specifically, when operating with a capacity that is equivalent to or even more 0.7, the OPPM with RS code outperforms the uncoded OPPM where the OPPM with MLSD needs only 1.2×103 photons per pulse with an ideal coding rate of about 3/4.
Legrand, Antoine, Macq, Benoît, De Vleeschouwer, Christophe.  2022.  Forward Error Correction Applied to JPEG-XS Codestreams. 2022 IEEE International Conference on Image Processing (ICIP). :3723—3727.
JPEG-XS offers low complexity image compression for applications with constrained but reasonable bit-rate, and low latency. Our paper explores the deployment of JPEG-XS on lossy packet networks. To preserve low latency, Forward Error Correction (FEC) is envisioned as the protection mechanism of interest. Although the JPEG-XS codestream is not scalable in essence, we observe that the loss of a codestream fraction impacts the decoded image quality differently, depending on whether this codestream fraction corresponds to codestream headers, to coefficient significance information, or to low/high frequency data. Hence, we propose a rate-distortion optimal unequal error protection scheme that adapts the redundancy level of Reed-Solomon codes according to the rate of channel losses and the type of information protected by the code. Our experiments demonstrate that, at 5% loss rates, it reduces the Mean Squared Error by up to 92% and 65%, compared to a transmission without and with optimal but equal protection, respectively.
2022-09-16
Cheng, Junyuan, Jiang, Xue-Qin, Bai, Enjian, Wu, Yun, Hai, Han, Pan, Feng, Peng, Yuyang.  2021.  Rate Adaptive Reconciliation Based on Reed-Solomon Codes. 2021 6th International Conference on Communication, Image and Signal Processing (CCISP). :245—249.
Security of physical layer key generation is based on the randomness and reciprocity of wireless fading channel, which has attracted more and more attention in recent years. This paper proposes a rate adaptive key agreement scheme and utilizes the received signal strength (RSS) of the channel between two wireless devices to generate the key. In conventional information reconciliation process, the bit inconsistency rate is usually eliminated by using the filter method, which increases the possibility of exposing the generated key bit string. Building on the strengths of existing secret key extraction approaches, this paper develops a scheme that uses Reed-Solomon (RS) codes, one of forward error correction channel codes, for information reconciliation. Owing to strong error correction performance of RS codes, the proposed scheme can solve the problem of inconsistent key bit string in the process of channel sensing. At the same time, the composition of RS codes can help the scheme realize rate adaptation well due to the construction principle of error correction code, which can freely control the code rate and achieve the reconciliation method of different key bit string length. Through experiments, we find that when the number of inconsistent key bits is not greater than the maximum error correction number of RS codes, it can well meet the purpose of reconciliation.
2022-07-01
Günlü, Onur, Kliewer, Jörg, Schaefer, Rafael F., Sidorenko, Vladimir.  2021.  Doubly-Exponential Identification via Channels: Code Constructions and Bounds. 2021 IEEE International Symposium on Information Theory (ISIT). :1147—1152.
Consider the identification (ID) via channels problem, where a receiver wants to decide whether the transmitted identifier is its identifier, rather than decoding the identifier. This model allows to transmit identifiers whose size scales doubly-exponentially in the blocklength, unlike common transmission (or channel) codes whose size scales exponentially. It suffices to use binary constant-weight codes (CWCs) to achieve the ID capacity. By relating the parameters of a binary CWC to the minimum distance of a code and using higher-order correlation moments, two upper bounds on the binary CWC size are proposed. These bounds are shown to be upper bounds also on the identifier sizes for ID codes constructed by using binary CWCs. We propose two code constructions based on optical orthogonal codes, which are used in optical multiple access schemes, have constant-weight codewords, and satisfy cyclic cross-correlation and autocorrelation constraints. These constructions are modified and concatenated with outer Reed-Solomon codes to propose new binary CWCs optimal for ID. Improvements to the finite-parameter performance of both our and existing code constructions are shown by using outer codes with larger minimum distance vs. blocklength ratios. We also illustrate ID performance regimes for which our ID code constructions perform significantly better than existing constructions.
2022-06-14
Zakharov, E. R., Zakharova, V. O., Vlasov, A. I..  2021.  Methods and Algorithms for Generating a Storage Key Based on Biometric Parameters. 2021 International Russian Automation Conference (RusAutoCon). :137–141.
The theoretical basis made it possible to implement software for automated secure biometric verification and personal identification, which can be used by information security systems (including access control and management systems). The work is devoted to solving an urgent problem - the development of methods and algorithms for generating a key for a storage device based on biometric parameters. Biometric cryptosystems take advantage of biometrics to improve the security of encryption keys. The ability not to store a key that is derived from biometric data is a direct advantage of the method of generating cryptographic keys from biometric data of users over other existing encryption methods.
2022-03-01
Bartz, Hannes, Puchinger, Sven.  2021.  Decoding of Interleaved Linearized Reed-Solomon Codes with Applications to Network Coding. 2021 IEEE International Symposium on Information Theory (ISIT). :160–165.
Recently, Martínez-Peñas and Kschischang (IEEE Trans. Inf. Theory, 2019) showed that lifted linearized Reed-Solomon codes are suitable codes for error control in multishot network coding. We show how to construct and decode lifted interleaved linearized Reed-Solomon codes. Compared to the construction by Martínez-Peñas-Kschischang, interleaving allows to increase the decoding region significantly (especially w.r.t. the number of insertions) and decreases the overhead due to the lifting (i.e., increases the code rate), at the cost of an increased packet size. The proposed decoder is a list decoder that can also be interpreted as a probabilistic unique decoder. Although our best upper bound on the list size is exponential, we present a heuristic argument and simulation results that indicate that the list size is in fact one for most channel realizations up to the maximal decoding radius.
2021-10-12
Sun, Yuxin, Zhang, Yingzhou, Zhu, Linlin.  2020.  An Anti-Collusion Fingerprinting based on CFF Code and RS Code. 2020 International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery (CyberC). :56–63.
Data security is becoming more and more important in data exchange. Once the data is leaked, it will pose a great threat to the privacy and property security of users. Copyright authentication and data provenance have become an important requirement of the information security defense mechanism. In order to solve the collusion leakage of the data distributed by organization and the low efficiency of tracking the leak provenance after the data is destroyed, this paper proposes a concatenated-group digital fingerprint coding based on CFF code and Reed-solomon (RS) that can resist collusion attacks and corresponding detection algorithm. The experiments based on an asymmetric anti-collusion fingerprint protocol show that the proposed method has better performance to resist collusion attacks than similar non-grouped fingerprint coding and effectively reduces the percentage of misjudgment, which verifies the availability of the algorithm and enriches the means of organization data security audit.
2021-08-31
Freitas, Lucas F., Nogueira, Adalberto R., Melgar, Max E. Vizcarra.  2020.  Visual Authentication Scheme Based on Reversible Degradation and QR Code. 2020 Fourth World Conference on Smart Trends in Systems, Security and Sustainability (WorldS4). :58—63.
Two-Dimensional barcodes are used as data authentication storage tool on several cryptographic architectures. This article describes a novel meaningful image authentication method for data validation using the Meaningless Reversible Degradation concept and QR Codes. The system architecture use the Meaningless Reversible Degradation algorithm, systematic Reed-Solomon error correction codes, meaningful images, and QR Codes. The encoded images are the secret key for visual validation. The proposed work encodes any secret image file up to 3.892 Bytes and is decoded using data stored in a QR Code and a digital file retrieved through a wireless connection on a mobile device. The QR Code carries partially distorted and stream ciphered bits. The QR Code version is defined in conformity with the secret image file size. Once the QR Code data is decoded, the authenticating party retrieves a previous created Reed-Solomon redundancy file to correct the QR Code stored data. Finally, the secret image is decoded for user visual identification. A regular QR Code reader cannot decode any meaningful information when the QR Code is scanned. The presented cryptosystem improves the redundancy download file size up to 50% compared to a plaintext image transmission.
2021-03-22
Jeong, S., Kang, S., Yang, J.-S..  2020.  PAIR: Pin-aligned In-DRAM ECC architecture using expandability of Reed-Solomon code. 2020 57th ACM/IEEE Design Automation Conference (DAC). :1–6.
The computation speed of computer systems is getting faster and the memory has been enhanced in performance and density through process scaling. However, due to the process scaling, DRAMs are recently suffering from numerous inherent faults. DRAM vendors suggest In-DRAM Error Correcting Code (IECC) to cope with the unreliable operation. However, the conventional IECC schemes have concerns about miscorrection and performance degradation. This paper proposes a pin-aligned In-DRAM ECC architecture using the expandability of a Reed-Solomon code (PAIR), that aligns ECC codewords with DQ pin lines (data passage of DRAM). PAIR is specialized in managing widely distributed inherent faults without the performance degradation, and its correction capability is sufficient to correct burst errors as well. The experimental results analyzed with the latest DRAM model show that the proposed architecture achieves up to 106 times higher reliability than XED with 14% performance improvement, and 10 times higher reliability than DUO with a similar performance, on average.
2021-01-18
Bentahar, A., Meraoumia, A., Bendjenna, H., Chitroub, S., Zeroual, A..  2020.  Fuzzy Extractor-Based Key Agreement for Internet of Things. 020 1st International Conference on Communications, Control Systems and Signal Processing (CCSSP). :25–29.
The emergence of the Internet of Things with its constraints obliges researchers in this field to find light and accurate solutions to secure the data exchange. This document presents secure authentication using biometrics coupled with an effective key agreement scheme to save time and energy. In our scheme, the agreed key is used to encrypt transmission data between different IoT actors. While the fuzzy extractor based on the fuzzy vault principle, is used as authentication and as key agreement scheme. Besides, our system incorporates the Reed Solomon and Hamming codes to give some tolerance to errors. The experimental results have been discussed according to several recognition rates and computation times. Indeed, the recognition rate results have been compared to other works to validate our system. Also, we clarify how our system resists to specific transmission attacks without affecting lightness and accuracy.
2020-11-02
Kralevska, Katina, Gligoroski, Danilo, Jensen, Rune E., Øverby, Harald.  2018.  HashTag Erasure Codes: From Theory to Practice. IEEE Transactions on Big Data. 4:516—529.
Minimum-Storage Regenerating (MSR) codes have emerged as a viable alternative to Reed-Solomon (RS) codes as they minimize the repair bandwidth while they are still optimal in terms of reliability and storage overhead. Although several MSR constructions exist, so far they have not been practically implemented mainly due to the big number of I/O operations. In this paper, we analyze high-rate MDS codes that are simultaneously optimized in terms of storage, reliability, I/O operations, and repair-bandwidth for single and multiple failures of the systematic nodes. The codes were recently introduced in [1] without any specific name. Due to the resemblance between the hashtag sign \# and the procedure of the code construction, we call them in this paper HashTag Erasure Codes (HTECs). HTECs provide the lowest data-read and data-transfer, and thus the lowest repair time for an arbitrary sub-packetization level α, where α ≤ r⌈k/r⌉, among all existing MDS codes for distributed storage including MSR codes. The repair process is linear and highly parallel. Additionally, we show that HTECs are the first high-rate MDS codes that reduce the repair bandwidth for more than one failure. Practical implementations of HTECs in Hadoop release 3.0.0-alpha2 demonstrate their great potentials.
2020-09-08
Wang, Yufan, Peng, Linning, Fu, Hua, Li, Guyue, Hu, Aiqun.  2019.  Performance Analysis of Concatenated Error Correction Code in Secret Key Generation System. 2019 IEEE 19th International Conference on Communication Technology (ICCT). :270–275.
Secret key generation from wireless channel is an emerging technique of physical layer security. At present, most of the secret key generation schemes use information reconciliation to obtain symmetric keys. This paper introduces a non-interactive information reconciliation scheme based on channel coding and stream encryption, and considering the error correction capability, we design a concatenated code of BCH and RS codes as channel coding. The performance of concatenated error correction code has been analyzed in this scheme. Then, we compare the concatenated code with first-level error correction code in different test environments. Extensive numerical simulations and experiments demonstrate that the decoding performance of this second-level concatenated code is better than the first-level error correction code, and it can also effectively eliminate third-party eavesdropping.
2020-06-19
Michel, François, De Coninck, Quentin, Bonaventure, Olivier.  2019.  QUIC-FEC: Bringing the benefits of Forward Erasure Correction to QUIC. 2019 IFIP Networking Conference (IFIP Networking). :1—9.

Originally implemented by Google, QUIC gathers a growing interest by providing, on top of UDP, the same service as the classical TCP/TLS/HTTP/2 stack. The IETF will finalise the QUIC specification in 2019. A key feature of QUIC is that almost all its packets, including most of its headers, are fully encrypted. This prevents eavesdropping and interferences caused by middleboxes. Thanks to this feature and its clean design, QUIC is easier to extend than TCP. In this paper, we revisit the reliable transmission mechanisms that are included in QUIC. More specifically, we design, implement and evaluate Forward Erasure Correction (FEC) extensions to QUIC. These extensions are mainly intended for high-delays and lossy communications such as In-Flight Communications. Our design includes a generic FEC frame and our implementation supports the XOR, Reed-Solomon and Convolutional RLC error-correcting codes. We also conservatively avoid hindering the loss-based congestion signal by distinguishing the packets that have been received from the packets that have been recovered by the FEC. We evaluate its performance by applying an experimental design covering a wide range of delay and packet loss conditions with reproducible experiments. These confirm that our modular design allows the protocol to adapt to the network conditions. For long data transfers or when the loss rate and delay are small, the FEC overhead negatively impacts the download completion time. However, with high packet loss rates and long delays or smaller files, FEC allows drastically reducing the download completion time by avoiding costly retransmission timeouts. These results show that there is a need to use FEC adaptively to the network conditions.

2020-04-06
Martínez-Peñas, Umberto, Kschischang, Frank R..  2018.  Reliable and Secure Multishot Network Coding using Linearized Reed-Solomon Codes. 2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton). :702–709.
Multishot network coding is considered in a worst-case adversarial setting in which an omniscient adversary with unbounded computational resources may inject erroneous packets in up to t links, erase up to ρ packets, and wire-tap up to μ links, all throughout ℓ shots of a (random) linearly-coded network. Assuming no knowledge of the underlying linear network code (in particular, the network topology and underlying linear code may change with time), a coding scheme achieving zero-error communication and perfect secrecy is obtained based on linearized Reed-Solomon codes. The scheme achieves the maximum possible secret message size of ℓn'-2t-ρ-μ packets, where n' is the number of outgoing links at the source, for any packet length m ≥ n' (largest possible range), with only the restriction that ℓ\textbackslashtextless;q (size of the base field). By lifting this construction, coding schemes for non-coherent communication are obtained with information rates close to optimal for practical instances. A Welch-Berlekamp sum-rank decoding algorithm for linearized Reed-Solomon codes is provided, having quadratic complexity in the total length n = ℓn', and which can be adapted to handle not only errors, but also erasures, wire-tap observations and non-coherent communication.
2020-01-21
Zhou, Yiwen, Shen, Qili, Dong, Mianxiong, Ota, Kaoru, Wu, Jun.  2019.  Chaos-Based Delay-Constrained Green Security Communications for Fog-Enabled Information-Centric Multimedia Network. 2019 IEEE 89th Vehicular Technology Conference (VTC2019-Spring). :1–6.
The Information-Centric Network possessing the content-centric features, is the innovative architecture of the next generation of network. Collaborating with fog computing characterized by its strong edge power, ICN will become the development trend of the future network. The emergence of Information-Centric Multimedia Network (ICMN) can meet the increasing demand for transmission of multimedia streams in the current Internet environment. The data transmission has become more delay-constrained and convenient because of the distributed storage, the separation between the location of information and terminals, and the strong cacheability of each node in ICN. However, at the same time, the security of the multimedia streams in the delivery process still requires further protection against wiretapping, interception or attacking. In this paper, we propose the delay-constrained green security communications for ICMN based on chaotic encryption and fog computing so as to transmit multimedia streams in a more secure and time-saving way. We adapt a chaotic cryptographic method to ICMN, implementing the encryption and decryption of multimedia streams. Meanwhile, the network edge capability to process the encryption and decryption is enhanced. Thanks to the fog computing, the strengthened transmission speed of the multimedia streams can fulfill the need for short latency. The work in the paper is of great significance to improve the green security communications of multimedia streams in ICMN.
2019-11-25
Kışlal, Ahmet Oguz, Pusane, Ali Emre, Tuğcu, Tuna.  2018.  A comparative analysis of channel coding for molecular communication. 2018 26th Signal Processing and Communications Applications Conference (SIU). :1–4.
Networks established among nanomachines, also called nanonetworks, are crucial since, a single nanomachine most likely cannot handle task by itself. At the nano scale, electromagnetic waves lose their effectiveness. Molecular communication via diffusion (MCvD) is a new concept that aims to solve this problem. Information is carried out by either the type of molecules, or their concentration. The robustness of this communication method, as in the example of classical communication, is very important. Channel coding is the component that make communication less erroneous. If the desired error performance is high, channel coding is mandatory. In this paper, the performance of Bose-Chaudhuri-Hocquenghem (BCH) and Reed-Solomon (RS) codes for MCvD are evaluated by simulation and results are analyzed.
Benamira, Elias, Merazka, Fatiha, Kurt, Gunes Karabulut.  2018.  Joint Channel Coding and Cooperative Network Coding on PSK Constellations in Wireless Networks. 2018 International Conference on Smart Communications in Network Technologies (SaCoNeT). :132–137.
In this paper, we consider the application of Reed-Solomon (RS) channel coding for joint error correction and cooperative network coding on non-binary phase shift keying (PSK) modulated signals. The relay first decodes the RS channel coded messages received each in a time slot from all sources before applying network coding (NC) by the use of bit-level exclusive OR (XOR) operation. The network coded resulting message is then channel encoded before its transmission to the next relay or to the destination according to the network configuration. This scenario shows superior performance in comparison with the case where the relay does not perform channel coding/decoding. For different orders of PSK modulation and different wireless configurations, simulation results demonstrate the improvements resulting from the use of RS channel codes in terms of symbol error rate (SER) versus signal-to-noise ratio (SNR).
2019-04-29
Kar, Diptendu Mohan, Ray, Indrajit, Gallegos, Jenna, Peccoud, Jean.  2018.  Digital Signatures to Ensure the Authenticity and Integrity of Synthetic DNA Molecules. Proceedings of the New Security Paradigms Workshop. :110–122.

DNA synthesis has become increasingly common, and many synthetic DNA molecules are licensed intellectual property (IP). DNA samples are shared between academic labs, ordered from DNA synthesis companies and manipulated for a variety of different purposes, mostly to study their properties and improve upon them. However, it is not uncommon for a sample to change hands many times with very little accompanying information and no proof of origin. This poses significant challenges to the original inventor of a DNA molecule, trying to protect her IP rights. More importantly, following the anthrax attacks of 2001, there is an increased urgency to employ microbial forensic technologies to trace and track agent inventories. However, attribution of physical samples is next to impossible with existing technologies. In this paper, we describe our efforts to solve this problem by embedding digital signatures in DNA molecules synthesized in the laboratory. We encounter several challenges that we do not face in the digital world. These challenges arise primarily from the fact that changes to a physical DNA molecule can affect its properties, random mutations can accumulate in DNA samples over time, DNA sequencers can sequence (read) DNA erroneously and DNA sequencing is still relatively expensive (which means that laboratories would prefer not to read and re-read their DNA samples to get error-free sequences). We address these challenges and present a digital signature technology that can be applied to synthetic DNA molecules in living cells.

2018-02-02
Bu, L., Nguyen, H. D., Kinsy, M. A..  2017.  RASSS: A perfidy-aware protocol for designing trustworthy distributed systems. 2017 IEEE International Symposium on Defect and Fault Tolerance in VLSI and Nanotechnology Systems (DFT). :1–6.

Robust Adaptive Secure Secret Sharing (RASSS) is a protocol for reconstructing secrets and information in distributed computing systems even in the presence of a large number of untrusted participants. Since the original Shamir's Secret Sharing scheme, there have been efforts to secure the technique against dishonest shareholders. Early on, researchers determined that the Reed-Solomon encoding property of the Shamir's share distribution equation and its decoding algorithm could tolerate cheaters up to one third of the total shareholders. However, if the number of cheaters grows beyond the error correcting capability (distance) of the Reed-Solomon codes, the reconstruction of the secret is hindered. Untrusted participants or cheaters could hide in the decoding procedure, or even frame up the honest parties. In this paper, we solve this challenge and propose a secure protocol that is no longer constrained by the limitations of the Reed-Solomon codes. As long as there are a minimum number of honest shareholders, the RASSS protocol is able to identify the cheaters and retrieve the correct secret or information in a distributed system with a probability close to 1 with less than 60% of hardware overhead. Furthermore, the adaptive nature of the protocol enables considerable hardware and timing resource savings and makes RASSS highly practical.

Huang, W., Bruck, J..  2016.  Secure RAID schemes for distributed storage. 2016 IEEE International Symposium on Information Theory (ISIT). :1401–1405.

We propose secure RAID, i.e., low-complexity schemes to store information in a distributed manner that is resilient to node failures and resistant to node eavesdropping. We generalize the concept of systematic encoding to secure RAID and show that systematic schemes have significant advantages in the efficiencies of encoding, decoding and random access. For the practical high rate regime, we construct three XOR-based systematic secure RAID schemes with optimal encoding and decoding complexities, from the EVENODD codes and B codes, which are array codes widely used in the RAID architecture. These schemes optimally tolerate two node failures and two eavesdropping nodes. For more general parameters, we construct efficient systematic secure RAID schemes from Reed-Solomon codes. Our results suggest that building “keyless”, information-theoretic security into the RAID architecture is practical.

2018-01-23
Chandran, V., Sekhar, A..  2017.  A secure and reliable channel error correction technique for picode. 2017 IEEE International Conference on Electrical, Instrumentation and Communication Engineering (ICEICE). :1–4.

With the advent of QR readers and mobile phones the use of graphical codes like QR codes and data matrix code has become very popular. Despite the noise like appearance, it has the advantage of high data capacity, damage resistance and fast decoding robustness. The proposed system embeds the image chosen by the user to develop visually appealing QR codes with improved decoding robustness using BCH algorithm. The QR information bits are encoded into luminance value of the input image. The developed Picode can inspire perceptivity in multimedia applications and can ensure data security for instances like online payments. The system is implemented on Matlab and ARM cortex A8.

2017-11-27
Gorbenko, Y., Svatovskiy, I., Shevtsov, O..  2016.  Post-quantum message authentication cryptography based on error-correcting codes. 2016 Third International Scientific-Practical Conference Problems of Infocommunications Science and Technology (PIC S T). :51–54.

In this paper we analyse possibilities of application of post-quantum code based signature schemes for message authentication purposes. An error-correcting code based digital signature algorithm is presented. There also shown results of computer simulation for this algorithm in case of Reed-Solomon codes and the estimated efficiency of its software implementation. We consider perspectives of error-correcting codes for message authentication and outline further research directions.

2017-08-22
Luo, Ge, Gao, Ying, Zheng, Changchun.  2016.  Strongly Secure Network Coding via Reed-Solomon Codes. Proceedings of the Fifth International Conference on Network, Communication and Computing. :110–114.

To consider construction of strongly secure network coding scheme without universality, this paper focuses on properties of MDS(maximum distance separable) codes, especially, Reed-Solomon codes. Our scheme applies Reed-Solomon codes in coset coding scheme to achieve the security based on the classical underlying network coding. Comparing with the existing scheme, MRD(maximum rank distance) code and a necessary condition based on MRD are not required in the scheme. Furthermore, considering the conditions between the code for security and the underlying network code, the scheme could be applied for more situations on fields.

2015-05-01
Koga, H., Honjo, S..  2014.  A secret sharing scheme based on a systematic Reed-Solomon code and analysis of its security for a general class of sources. Information Theory (ISIT), 2014 IEEE International Symposium on. :1351-1355.

In this paper we investigate a secret sharing scheme based on a shortened systematic Reed-Solomon code. In the scheme L secrets S1, S2, ..., SLand n shares X1, X2, ..., Xn satisfy certain n - k + L linear equations. Security of such a ramp secret sharing scheme is analyzed in detail. We prove that this scheme realizes a (k; n)-threshold scheme for the case of L = 1 and a ramp (k, L, n)-threshold scheme for the case of 2 ≤ L ≤ k - 1 under a certain assumption on S1, S2, ..., SL.