Shamir's Secret Sharing Research Articles

Security, QoS and energy aware optimization of cloud-edge data centers using game theory and homomorphic encryption: Modeling and formal verification

Privacy and efficient data processing are crucial research areas in the field of outsourcing computing. Thus, the contribution of the paper is twofold. First of all, we develop a secure offloading technique that can process data while preserving privacy. Although RSA and Paillier cryptosystems are highly beneficial for mathematical operations on basic encrypted data due to their homomorphic properties, images are processed using permutation-ordered binary (POB) and Shamir's secret sharing (SSS). Second, a non-cooperative game theory model was formulated to examine the interactions between service providers, characterizing each edge as an M/M/1 system with an infinite queue. Through formal verification using rigorous mathematical reasoning, the suggested strategies for task offloading and resource allocation are shown to be effective in terms of security, quality of service (QoS), and energy consumption. The best-response dynamics approach is used to calculate the final strategy for each participant and assess how fairly resources are allocated. Finally, the potential of our approach is demonstrated numerically, revealing a faster convergence towards attaining Nash equilibrium in a duopoly cloud-edge data center market, granted that the necessary and sufficient conditions are met.

Achieving Secure and Reliable UAV Authentication: A Shamir's Secret Sharing Based Approach

Achieving Secure and Reliable UAV Authentication: A Shamir's Secret Sharing Based Approach

Lightweight Group Authentication Scheme Leveraging Shamir's Secret Sharing and PUFs

Lightweight Group Authentication Scheme Leveraging Shamir's Secret Sharing and PUFs

An Energy-Efficient improved Grey Wolf Optimization Algorithm-Based Cluster Head and Shamir Secrets Sharing-Based WSNs with Secure Data Transfer

Introduction: Due to its self-configurability, ease of maintenance, and scalability capabilities, WSNs (Wireless Sensor Networks) have intrigued plenty of interest in a variety of fields. To move data within the network, WSNs are set up with more nodes. The security of SNs (sensing nodes), which are vulnerable to malevolent attackers since they are network nodes, is a crucial element of an IoT (Internet of Things)-based WSN. This study's primary objective is to provide safe routing and mutual authentication with IoT-based WSNs. Methods: The basic GWO algorithm's imbalances between explorations and mining, lack of population heterogeneity, and early convergences are all issues that this paper addresses by selecting energy-efficient CHs (cluster Heads) using EECIGWO algorithm, an upgraded version of the GWO, is used. Mean distances within clusters, well-spaced residual energies, and equilibrium of CHs are all factors that influence the choices of CHs. The average intra-cluster distances, sink distances, residual energies, and CHs balances are some of the criteria used to choose CHs. Results and Discussion: The proposed EECHIGWO-based clustering protocol's average throughput, dead node counts, energy consumption, and operation round counts have all been evaluated. Additionally, mutual authentication between the nodes is provided through SSS (Shamir Secret Sharing) mechanism. PDR (Packet Delivery Ratio) analysis is used to assess how well the EECHIGWO-IOT-WSNs are performing. Conclusion: The suggested proposed approach is assessed against existing methods like HHH-SS (Hybrid Harris Hawk and Salp Swarm), ESR (Energy-efficient and Secure Routing) protocol, and LWTS (Light Weight Trust Sensing) approaches in terms of AEED (Average End-to-End Delay), network overheads, and PLR (Packet Loss Ratio).

Blockchain-Based Efficiently Privacy-Preserving Federated Learning Framework Using Shamir Secret Sharing

Blockchain-Based Efficiently Privacy-Preserving Federated Learning Framework Using Shamir Secret Sharing

Secure One-time Password Generation using Shamir's Secret Sharing

- The process of authenticating users is critical for ensuring security. Static passwords are a popular and traditional authentication method due to their simplicity, but they are vulnerable to attacks such as password leakage, replay, guessing, eavesdropping, phishing, and spoofing, among others. One-time passwords (OTP) were introduced to address these limitations, but research has found that they are not immune to middle man attacks. To enhance the security of OTP, a new technique called Visual Cryptography Schema is proposed in this paper. In this method, we use Shamir’s Secret Sharing theory in which the main OTP is parted into three shares. Out of these shares, one is sent to the user and the other two shares are stored in different locations in the server. To retrieve

Consensus-based mutual authentication scheme for Industrial IoT

Authentication of new joining nodes in IoT networks is a critical element for maintaining its security. It ensures the legitimacy of the network to the joining node, and the authorization of this new node to the network coordinator. Most of the mutual authentication schemes in IoT rely on a pre-shared key (PSK) between the network coordinator and the joining node. The process of sharing this PSK is however usually not defined in the standards. Moreover, in large scale and dynamic networks, like Industrial IoT (IIoT), configuring each device with a distinct key before the joining phase is impractical.To address these challenges, we propose in this paper an autonomous mutual authentication and key establishment protocol for IIoT. In our solution, the network coordinator authenticates first the new joining node using its certificate. Second, the network coordinator is authenticated by the joining node through a novel and lightweight consensus. This is based on Shamir Secret Sharing and achieved among multiple nodes already part of the network. Once this mutual authentication is accomplished, a key is established between the network coordinator and the joining node over a public channel.We integrated our solution with the joining phase of 6TiSCH framework to evaluate its performance on a real industrial protocol. In term of security, the evaluation results proved the robustness of our solution with a high success rate of authentication, even when up to one third of the nodes in the network are malicious. Furthermore, the evaluation results proved its efficiency in term of communication, latency and energy consumption, even when implemented on constrained devices and across various network topologies.

Decentralized privacy-preserving truth discovery for crowd sensing

Truth discovery is an efficient technique for tackling data conflict problems in crowd sensing for distributed data collection. As the sensory data to be collected may include sensitive information about users, privacy-preserving truth discovery has attracted significant attention in recent years. Most existing studies apply a centralized architecture based on a cryptographic system, which may be vulnerable to single-point attacks and also has a very high computational cost. In this paper, we propose DPriTD, a decentralized privacy-preserving framework for truth discovery in crowd sensing. The proposed approach leverages the additively homomorphic property of Shamir's Secret Sharing scheme to protect user's privacy. DPriTD provides a strict privacy guarantee for crowd sensing applications. Because each sensitive data point, considered to be a secret, is split into a batch of shares, and the secret cannot be recovered unless a sufficient number of shares are aggregated, DPriTD achieves effective truth discovery while protecting sensitive data from collusion attacks. Furthermore, DPriTD is independent of a centralized server and can perform reliably when not all participants are online in real time. It thus enhances the robustness of a crowd sensing system. Extensive experiments conducted on real-world datasets demonstrate the high performance of our method compared with existing mechanisms.

Implementation of Shamir’s Secret Sharing Scheme in Cloud Computing

With the increase in the use of cloud systems, security on cloud systems has become one of the most important items that underlined. Due to the nature of the cloud systems, it is difficult to manage multi-user systems and access control devices, resulting in some security vulnerabilities. In this paper we studied on Cloud Computing with Shamir’s Secret Sharing Scheme with Advanced Encryption Standard (AES) algorithm for encryption and decryption process. For encryption and decryption process AES in Cryptool 1.4.41 has been used. For implementing Shamir Secret Sharing Scheme, Python language has been chosen and Spyder 3.8 has been chosen for environment. As a result, we successfully demonstrate the Shamir’s Scheme implementation with file operations.

A Modified Shamir Secret Sharing Scheme With Efficient Encoding

The Shamir secret sharing (SSS) scheme requires a Maximum Distance Separable (MDS) code, and in its most common implementation, a Reed-Solomon (RS) code is used. In this letter, we observe that the encoding procedure can be made simpler and faster by dropping the MDS condition and specifying the possible symbols that can be shared. In particular, the process can be made even faster by using array codes based on exclusive-or (XOR) operations instead of RS codes.

Centralized Threshold Key Generation Protocol Based on Shamir Secret Sharing and HMAC Authentication.

Many group key management protocols have been proposed to manage key generation and distribution of vehicular communication. However, most of them suffer from high communication and computation costs due to the complex elliptic curve and bilinear pairing cryptography. Many shared secret protocols have been proposed using polynomial evaluation and interpolation to solve the previous complexity issues. This paper proposes an efficient centralized threshold shared secret protocol based on the Shamir secret sharing technique and supporting key authentication using Hashed Message Authentication Code Protocol (HMAC). The proposed protocol allows the group manager to generate a master secret key for a group of vehicles and split this key into secret shares; each share is distributed securely to every group member. -of- vehicles must recombine their secret shares and recover the original secret key. The acceptance of the recovered key is based on the correctness of the received HMAC signature to verify the group manager’s identity and ensure the key confidentiality. The proposed protocol is unconditionally secure and unbreakable using infinite computing power as , or more than secret shares are required to reconstruct the key. In contrast, attackers with secret shares cannot leak any information about the original secret key. Moreover, the proposed protocol reduces the computation cost due to using polynomial evaluation to generate the secret key and interpolation to recover the secret key, which is very simple and lightweight compared with the discrete logarithm computation cost in previous protocols. In addition, utilizing a trusted group manager that broadcasts some public information is important for the registered vehicles to reconstruct the key and eliminate secure channels between vehicles. The proposed protocol reduces the communication cost in terms of transmitted messages between vehicles from messages in previous shared secret protocols to zero messages. Moreover, it reduces the received messages at vehicles from to two messages. At the same time, it allows vehicles to store only a single secret share compared with other shared secret protocols that require storage of secret shares. The proposed protocol security level outperforms the other shared secret protocols security, as it supports key authentication and confidentiality using HMAC that prevents attackers from compromising or faking the key.

Rethinking the adversary and operational characteristics of deniable storage

Aim: With the widespread adoption of disk encryption technologies, it has become common for adversaries to employ coercive tactics to force users to surrender encryption keys. For some users, this creates a need for hidden volumes that provide plausible deniability, the ability to deny the existence of sensitive information. Previous deniable storage solutions only offer pieces of an implementable solution that do not take into account more advanced adversaries, such as intelligence agencies, and operational concerns. Specifically, they do not address an adversary that is familiar with the design characteristics of any deniable system. Methods: We evaluated existing threat models and deniable storage system designs to produce a new, stronger threat model and identified design characteristics necessary in a plausibly deniable storage system. To better explore the implications of this stronger adversary, we developed Artifice, the first tunable, operationally secure, self repairing, and fully deniable storage system. Results: With Artifice, hidden data blocks are split with an information dispersal algorithm such as Shamir Secret Sharing to produce a set of obfuscated carrier blocks that are indistinguishable from other pseudorandom blocks on the disk. The blocks are then stored in unallocated space of an existing file system. The erasure correcting capabilities of an information dispersal algorithm allow Artifice to self repair damage caused by writes to the public file system. Unlike preceding systems, Artifice addresses problems regarding flash storage devices and multiple snapshot attacks through simple block allocation schemes and operational security measures. To hide the user’s ability to run a deniable system and prevent information leakage, a user accesses Artifice through a separate OS stored on an external Linux live disk. Conclusion: In this paper, we present a stronger adversary model and show that our proposed design addresses the primary weaknesses of existing approaches to deniable storage under this stronger assumed adversary.

A Hybrid Optimization Algorithm and Shamir Secret Sharing Based Secure Data Transmission for IoT based WSN

A Hybrid Optimization Algorithm and Shamir Secret Sharing Based Secure Data Transmission for IoT based WSN

Collusion resistant secret sharing scheme for secure data storage and processing over cloud

Shamir secret sharing (SSS) is considered as a promising method for outsourcing the data securely due to its ability to support privacy preserving data processing while ensuring data availability. Major drawbacks of original SSS scheme are its susceptibility to collusion attack and high storage overhead. Hence in this paper, we first propose a modified SSS scheme (MSSS) which can resist collusion attack and provide adequate security even with two shares. However, the storage overhead of this scheme is high when it is extended to ensure data availability and integrity in cloud storage systems. Therefore, a modified ramp secret sharing (MRSS) with reduced storage overhead compared to MSSS scheme is also proposed in this paper. The proposed schemes can be employed for any privacy preserving data processing application which involve linear operations on the data. In this paper, in order to demonstrate the capability of proposed schemes to support privacy preserving data processing, Haar discrete wavelet transform (DWT) computation on medical images is considered as an example as DWT is widely used in feature extraction for disease diagnosis from pathological images. We present an algorithm for computing Haar DWT from medical image shares. The security of the proposed scheme is evaluated through mathematical cryptanalysis and resistance against various statistical attacks. The performance analysis shows that shared domain DWT offers same accuracy levels as that of plaintext domain.

A Privacy-Preserving Reinforcement Learning Algorithm for Multi-Domain Virtual Network Embedding

The problem of optimally deploying a virtual network onto a substrate physical network is referred to as Virtual Network Embedding (VNE). In general, this embedding is requested by a customer to an Internet Service Provider (ISP), which performs the VNE over its physical telecom network. In several situations, the physical substrate infrastructure is composed of multiple independent ISPs. In this scenario, ISPs are concerned about exposing to a third-party entity (e.g., the customer) sensitive infrastructural details that are needed to perform an effective embedding. Following a common privacy-preserving approach, known as Limited Information Disclosure (LID), the embedding may be performed by the customer based on a limited and abstracted view of the multi-domain infrastructure that ISPs accept to expose. With this approach, embedding is sub-optimal (e.g., embedding cost is not minimized) in comparison with the case where all information is available, i.e., Full Information Disclosure (FID). In this work, we propose a Reinforcement-Learning-based algorithm able to process data that the customer and ISPs cipher under the Shamir Secret Sharing (SSS) scheme. This approach guarantees total privacy to both the customer and the ISPs (e.g., details about a virtual function are only revealed to the ISP in charge of hosting it) and achieves comparable embedding cost of an existing FID heuristic, as observed from extensive simulations. The main drawback of our algorithm is the high overhead of data that ISPs and the customer need to exchange with each other to execute it. Hence, we also explore the trade-off between embedding cost and data overhead resulting from the reduction of operations done by the RL. In general, intermediate embedding costs between the FID and LID heuristics can be obtained at a significant reduction of data overhead, while not sacrificing any privacy guarantees.

Attribute-Based Authenticated Group Key Transfer Protocol without Pairing

Group key establishment protocol is the primary requirement of several group-ware applications, like secure conferences, pay per view, collaborative work space that needs to establish a secure session among a group of participants. However, some of the applications often need to establish a secure session among the participants without knowing their actual identities. In such cases, the legitimacy of participants is decided based up on a descriptive set of attributes usually called as access structure. The participants should have sufficient set of attributes to satisfy the access structure, which are to consider as authenticated and eligible for the group conversation. This paper introducing an attribute based authenticated group key transfer protocol without using bilinear pairing. Group key management based on attributes gives fine-grained access control over the group of members that are authenticated by the set of attributes. The proposed protocol uses, Shamir Secret Sharing and elliptic curve arithmetic instead of bilinear pairing computations. The members are authenticated based on the access structure defined by the session initiator. The group key is securely transferred to only those participants, who are authenticated by their attributes. The authentication process of proposed protocol is information theoretically secure, while the key confidentiality relies on the intractability of Elliptic Curve Discrete Logarithm Problem.

Cryptic Commonalities

Based on ongoing interdisciplinary research about advances in a cryptographic technique called Secure Multiparty Computation (MPC), this article explores how research commonalities are carved out among mathematicians, engineers and anthropologists. STS scholars and anthropologists are increasingly engaged in research about and with data scientists and engineers, particularly as this relates to discrimination, surveillance and rights. Cryptography - a sub-genre of mathematics and often-invisible infrastructure enabling secure digital communication has received less attention. The article argues that the ubiquity of digital computing in our lives necessitates the creation of socio-mathematical vocabularies. Such vocabularies have the potential to lead to new situated data security practices based on local perceptions of rights and protection. STS scholars and anthropologists are uniquely situated to do this work. The article follows three anthropologists in their endeavors to find “cryptic commonalities” by “tacking back and forth” (Cf. Helmreich 2009) between mathematicians’, engineers’ and their own scientific vocabularies. Despite these attempts, however, the parties often “talk past each other”. Instead of shying away from the awkwardness that such moments produce, the authors embrace “epistemic disconcertment” (Cf. Verran 2013a), carving out a space in which they can communicate productively with each other. This space does not turn mathematicians into anthropologists or STS scholars into engineers, but it does make space for a shared scientific “pidgin” that enables collaboration (Cf. Galison 2010). With this pidgin, the authors walk the reader through the logics of MPC, and specifically, a cryptographic technique called “Shamir Secret Sharing” (Shamir 1979). In doing so, we join emerging voices in the crypto-community in an effort to develop cryptographic techniques for social good. This requires not just an understanding of the math, but also the social worlds impacted by these techniques.

A Multi-server ORAM Framework with Constant Client Bandwidth Blowup

Oblivious Random Access Machine (ORAM) allows a client to hide the access pattern when accessing sensitive data on a remote server. It is known that there exists a logarithmic communication lower bound on any passive ORAM construction, where the server only acts as the storage service. This overhead, however, was shown costly for some applications. Several active ORAM schemes with server computation have been proposed to overcome this limitation. However, they mostly rely on costly homomorphic encryptions, whose performance is worse than passive ORAM. In this article, we propose S 3 ORAM, a new multi-server ORAM framework, which features O (1) client bandwidth blowup and low client storage without relying on costly cryptographic primitives. Our key idea is to harness Shamir Secret Sharing and a multi-party multiplication protocol on applicable binary tree-ORAM paradigms. This strategy allows the client to instruct the server(s) to perform secure and efficient computation on his/her behalf with a low intervention thereby, achieving a constant client bandwidth blowup and low server computational overhead. Our framework can also work atop a general k -ary tree ORAM structure ( k ≥ 2). We fully implemented our framework, and strictly evaluated its performance on a commodity cloud platform (Amazon EC2). Our comprehensive experiments confirmed the efficiency of S 3 ORAM framework, where it is approximately 10× faster than the most efficient passive ORAM (i.e., Path-ORAM) for a moderate network bandwidth while being three orders of magnitude faster than active ORAM with O (1) bandwidth blowup (i.e., Onion-ORAM). We have open-sourced the implementation of our framework for public testing and adaptation.

Stateless Cloud Auditing Scheme for Non-Manager Dynamic Group Data With Privacy Preservation

As one of the core services of cloud computing, cloud storage could satisfy various storage and management requirements caused by the growth of data. Considering the complexity and uncontrollability of the cloud storage environment, many cloud auditing schemes were presented to assure the integrity of data in the cloud. However, most existing schemes have security risks, such as identity privacy and data privacy disclosure, authority abuse of group managers and collusion attacks during user revocation. To solve these problems, we propose a stateless cloud auditing scheme for non-manager dynamic group data with privacy preservation. The proposed scheme not only realizes user identity privacy preservation but also preserves data privacy security with the random masking technique. Unlike other solutions, our scheme allows $t$ group users to trace the user’s identity cooperatively without group managers, which eliminates authority abuse of group managers and provides non-frameability. Meanwhile, utilizing the concept of Shamir Secret Sharing, our scheme divides the re-signing process into several parts to resist collusion attacks during user revocation. By the designed binary tree, group users could trace dynamic data changes and recover the latest data when existing data are damaged. Besides, both users and the third-party auditor (TPA) are stateless in our scheme; that is, they no need to maintain data index information during cloud auditing. Our scheme also achieves mutual supervision between users and cloud service providers (CSPs), which ensures data are non-repudiation on both parties. Furthermore, we construct an efficient incentive for data visitors by using the blockchain technology and design a secure data sharing model to guarantee that data owners control their data ownership. Certificateless cryptography assures that the proposed scheme avoids certificate management and key escrow problems. Finally, security analysis and performance evaluation show that our scheme is secure and efficient.

A Secure Data Sharing Platform Using Blockchain and Interplanetary File System

In a research community, data sharing is an essential step to gain maximum knowledge from the prior work. Existing data sharing platforms depend on trusted third party (TTP). Due to the involvement of TTP, such systems lack trust, transparency, security, and immutability. To overcome these issues, this paper proposed a blockchain-based secure data sharing platform by leveraging the benefits of interplanetary file system (IPFS). A meta data is uploaded to IPFS server by owner and then divided into n secret shares. The proposed scheme achieves security and access control by executing the access roles written in smart contract by owner. Users are first authenticated through RSA signatures and then submit the requested amount as a price of digital content. After the successful delivery of data, the user is encouraged to register the reviews about data. These reviews are validated through Watson analyzer to filter out the fake reviews. The customers registering valid reviews are given incentives. In this way, maximum reviews are submitted against every file. In this scenario, decentralized storage, Ethereum blockchain, encryption, and incentive mechanism are combined. To implement the proposed scenario, smart contracts are written in solidity and deployed on local Ethereum test network. The proposed scheme achieves transparency, security, access control, authenticity of owner, and quality of data. In simulation results, an analysis is performed on gas consumption and actual cost required in terms of USD, so that a good price estimate can be done while deploying the implemented scenario in real set-up. Moreover, computational time for different encryption schemes are plotted to represent the performance of implemented scheme, which is shamir secret sharing (SSS). Results show that SSS shows the least computational time as compared to advanced encryption standard (AES) 128 and 256.