THE ATTACKERS POWER BOUNDARIES FOR TRACEABILITY OF ALGEBRAIC GEOMETRIC CODES ON SPECIAL CURVES

2021 ◽  
pp. 55-74
Author(s):  
V. M. Deundyak ◽  
◽  
D. V. Zagumennov ◽  
◽  
Keyword(s):  
Distributed Storage ◽  
Single Point ◽  
Data Distribution ◽  
Error Correcting Codes ◽  
Equivalence Classes ◽  
Broadcast Encryption ◽  
Network Data ◽  
Distributed Data ◽  
Algebraic Geometric Codes ◽  
Geometric Codes

Broadcast encryption is a data distribution protocol which can prevent malefactor parties from unauthorized accessing or copying the distributed data. It is widely used in distributed storage and network data protection schemes. To block the socalled coalition attacks on the protocol, classes of error-correcting codes with special properties are used, namely c-FP and c-TA properties. We study the problem of evaluating the lower and the upper boundaries on coalition power, within which the algebraic geometry codes possess these properties. Earlier, these boundaries were calculated for single-point algebraic-geometric codes on curves of the general form. Now, we clarified these boundaries for single-point codes on curves of a special form; in particular, for codes on curves on which there are many equivalence classes after factorization by equality of the corresponding points coordinates relation.

scholarly journals On the Properties of Algebraic Geometric Codes as Copy Protection Codes

2020 ◽  
Vol 27 (1) ◽  
pp. 22-38
Author(s):  
Vladimir M. Deundyak ◽  
Denis V. Zagumennov
Keyword(s):  
Lower Bound ◽  
Error Correcting Code ◽  
Error Correcting Codes ◽  
Broadcast Encryption ◽  
Distributed Data ◽  
Algebraic Geometric Codes ◽  
Authorized User ◽  
Infinite Point ◽  
Encryption Schemes ◽  
Geometric Codes

Traceability schemes which are applied to the broadcast encryption can prevent unauthorized parties from accessing the distributed data. In a traceability scheme a distributor broadcasts the encrypted data and gives each authorized user unique key and identifying word from selected error-correcting code for decrypting. The following attack is possible in these schemes: groups of c malicious users are joining into coalitions and gaining illegal access to the data by combining their keys and identifying codewords to obtain pirate key and codeword. To prevent this attacks, classes of error-correcting codes with special c-FP and c-TA properties are used. In particular, c -FP codes are codes that make direct compromise of scrupulous users impossible and c -TA codes are codes that make it possible to identify one of the a‹ackers. We are considering the problem of evaluating the lower and the upper boundaries on c, within which the L-construction algebraic geometric codes have the corresponding properties. In the case of codes on an arbitrary curve the lower bound for the c-TA property was obtained earlier; in this paper, the lower bound for the c-FP property was constructed. In the case of curves with one infinite point, the upper bounds for the value of c are obtained for both c-FP and c-TA properties. During our work, we have proved an auxiliary lemma and the proof contains an explicit way to build a coalition and a pirate identifying vector. Methods and principles presented in the lemma can be important for analyzing broadcast encryption schemes robustness. Also, the c-FP and c-TA boundaries monotonicity by subcodes are proved.

scholarly journals Research on Distributed Data Sharing System based on Internet of Things and Blockchain

2021 ◽  
Vol 9 (3) ◽  
pp. 239-254
Author(s):  
Enchang Sun ◽  
Kang Meng ◽  
Ruizhe Yang ◽  
Yanhua Zhang ◽  
Meng Li
Keyword(s):  
Internet Of Things ◽  
Data Sharing ◽  
Data Storage ◽  
Network Architecture ◽  
Data Privacy ◽  
Distributed Storage ◽  
Global Network ◽  
Local Network ◽  
Network Data ◽  
Distributed Data

Abstract Aiming at the problems of the traditional centralized data sharing platform, such as poor data privacy protection ability, insufficient scalability of the system and poor interaction ability, this paper proposes a distributed data sharing system architecture based on the Internet of Things and blockchain technology. In this system, the distributed consensus mechanism of blockchain and the distributed storage technology are employed to manage the access and storage of Internet of Things data in a secure manner. Up to the physical topology of the network, a hierarchical blockchain network architecture is proposed for local network data storage and global network data sharing, which reduces networking complexity and improves the scalability of the system. In addition, smart contract and distributed machine learning are adopted to design automatic processing functions for different types of data (public or private) and supervise the data sharing process, improving both the security and interactive ability of the system.

scholarly journals Semantically Secure Symmetric Encryption with Error Correction for Distributed Storage

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Juha Partala
Keyword(s):  
Error Correction ◽  
Network Coding ◽  
Linear Combination ◽  
Distributed Storage ◽  
Homomorphic Encryption ◽  
Error Correcting Codes ◽  
Symmetric Encryption ◽  
Goppa Codes ◽  
Linear Network ◽  
Linear Network Coding

A distributed storage system (DSS) is a fundamental building block in many distributed applications. It applies linear network coding to achieve an optimal tradeoff between storage and repair bandwidth when node failures occur. Additively homomorphic encryption is compatible with linear network coding. The homomorphic property ensures that a linear combination of ciphertext messages decrypts to the same linear combination of the corresponding plaintext messages. In this paper, we construct a linearly homomorphic symmetric encryption scheme that is designed for a DSS. Our proposal provides simultaneous encryption and error correction by applying linear error correcting codes. We show its IND-CPA security for a limited number of messages based on binary Goppa codes and the following assumption: when dividing a scrambled generator matrix G^ into two parts G1^ and G2^, it is infeasible to distinguish G2^ from random and to find a statistical connection between G1^ and G2^. Our infeasibility assumptions are closely related to those underlying the McEliece public key cryptosystem but are considerably weaker. We believe that the proposed problem has independent cryptographic interest.

scholarly journals An Architecture for Distributed Electronic Documents Storage in Decentralized Blockchain B2B Applications

Computers ◽  
2021 ◽  
Vol 10 (11) ◽  
pp. 142
Author(s):  
Obadah Hammoud ◽  
Ivan Tarkhanov ◽  
Artyom Kosmarski
Keyword(s):  
Distributed Systems ◽  
Data Storage ◽  
Distributed Storage ◽  
Distributed Data ◽  
Erasure Coding ◽  
Distributed Data Storage ◽  
Electronic Documents ◽  
File Storage ◽  
Load Balancer ◽  
The Cost

This paper investigates the problem of distributed storage of electronic documents (both metadata and files) in decentralized blockchain-based b2b systems (DApps). The need to reduce the cost of implementing such systems and the insufficient elaboration of the issue of storing big data in DLT are considered. An approach for building such systems is proposed, which allows optimizing the size of the required storage (by using Erasure coding) and simultaneously providing secure data storage in geographically distributed systems of a company, or within a consortium of companies. The novelty of this solution is that we are the first who combine enterprise DLT with distributed file storage, in which the availability of files is controlled. The results of our experiment demonstrate that the speed of the described DApp is comparable to known b2c torrent projects, and subsequently justify the choice of Hyperledger Fabric and Ethereum Enterprise for its use. Obtained test results show that public blockchain networks are not suitable for creating such a b2b system. The proposed system solves the main challenges of distributed data storage by grouping data into clusters and managing them with a load balancer, while preventing data tempering using a blockchain network. The considered DApps storage methodology easily scales horizontally in terms of distributed file storage and can be deployed on cloud computing technologies, while minimizing the required storage space. We compare this approach with known methods of file storage in distributed systems, including central storage, torrents, IPFS, and Storj. The reliability of this approach is calculated and the result is compared to traditional solutions based on full backup.

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