Shamir's Threshold Research Articles

A Dual Privacy Preserving Scheme in Continuous Location-Based Services

With the development of wireless communication and positioning technology, location-based services (LBSs) have been gaining tremendous popularity, due to its ability to greatly facilitate the people’s daily lives. Meanwhile, it also entails the risk of location privacy disclosure. To address this issue, general solutions introduce a single trusted anonymizer between the users and the location service provider (LSP). However, a single anonymizer offers limited privacy guarantees and incurs high communication overhead in continuous LBSs. Once the anonymizer is compromised, it may put the user information in jeopardy. In this paper, we propose a dual privacy preserving (DPP) scheme in continuous LBSs to protect the users’ trajectory and query privacy. Our scheme introduces multiple anonymizers between the users and LSP, and combines with Shamir threshold mechanism, dynamic pseudonym mechanism, and ${K}$ -anonymity technology to improve the users’ trajectory and content privacy in continuous LBSs. An anonymizer alone cannot get the users’ trajectory and query contents, and it thus can be semi-trusted. Our scheme can enhance the users’ privacy and effectively solve the single point of failure in single anonymizer structure. At the same time, the query authentication can guarantee the correctness of the query results. The analysis and simulation results demonstrate that the proposed scheme has the ability to protect users’ trajectory and content privacy effectively, and to reduce the computation and communication overhead of the single anonymizer.

Key Escrow with Elliptic Curve Cryptography – Conceptual Framework for Distributed Mobile Networks

In the large scale distributive environment involving mobile network, metadata server and storage applications, the data access and the security measures are of paramount importance. In parallel application processing, data is distributed across multiple servers and storage location. Ensuring confidentiality and availability of the data to the authorised users at the appropriate time involves high level of encryption algorithms, key management schemes and security algorithms. In this paper, key escrow scheme is implemented with the light weighted symmetric algorithm, elliptic curve cryptography in the distributed environment. Key escrow centre is established along with the metadata server and the encryption keys are segmented and shared among the multiple sub agents using Shamir threshold sharing scheme. The implementation of Key Escrow mechanism with Elliptical Curve Cryptography provides wide range of flexibility and confidentiality in the distributed environment. It also eliminates private secret sub key problem and thereby ensuring better security.

A Verifiable Secret Image Sharing Scheme Based on Compressive Sensing

This paper proposes a verifiable secret image sharing scheme based on compressive sensing, secret sharing, and image hashing. In this scheme, Toeplitz matrix generated by two chaotic maps is employed as measurement matrix. With the help of Shamir threshold scheme and image hashing, the receivers can obtain the stored values and the hash value of image. In the verifying stage and restoring stage, there must be at least t legal receivers to get the effective information. By comparing the hash value of the restored image with the hash value of original image, the scheme can effectively prevent the attacker from tampering or forging the shared images. Experimental results show that the proposed scheme has good recovery performance, can effectively reduce space, and is suitable for real-time transmission, storage, and verification.

DaSCE: Data Security for Cloud Environment with Semi-Trusted Third Party

Off-site data storage is an application of cloud that relieves the customers from focusing on data storage system. However, outsourcing data to a third-party administrative control entails serious security concerns. Data leakage may occur due to attacks by other users and machines in the cloud. Wholesale of data by cloud service provider is yet another problem that is faced in the cloud environment. Consequently, high-level of security measures is required. In this paper, we propose data security for cloud environment with semi-trusted third party (DaSCE), a data security system that provides (a) key management (b) access control, and (c) file assured deletion. The DaSCE utilizes Shamir's ( k, n ) threshold scheme to manage the keys, where k out of n shares are required to generate the key. We use multiple key managers, each hosting one share of key. Multiple key managers avoid single point of failure for the cryptographic keys. We (a) implement a working prototype of DaSCE and evaluate its performance based on the time consumed during various operations, (b) formally model and analyze the working of DaSCE using high level petri nets (HLPN), and (c) verify the working of DaSCE using satisfiability modulo theories library (SMT-Lib) and Z3 solver. The results reveal that DaSCE can be effectively used for security of outsourced data by employing key management, access control, and file assured deletion.

A Selective Group Authentication Scheme for IoT-Based Medical Information System.

The technology of IoT combined with medical systems is expected to support advanced medical services. However, unsolved security problems, such as misuse of medical devices, illegal access to the medical server and so on, make IoT-based medical systems not be applied widely. In addition, users have a high burden of computation to access Things for the explosive growth of IoT devices. Because medical information is critical and important, but users have a restricted computing power, IoT-based medical systems are required to provide secure and efficient authentication for users. In this paper, we propose a selective group authentication scheme using Shamir's threshold technique. The property of selectivity gives the right of choice to users to form a group which consists of things users select and access. And users can get an access authority for those Things at a time. Thus, our scheme provides an efficient user authentication for multiple Things and conditional access authority for safe IoT-based medical information system. To the best of our knowledge, our proposed scheme is the first in which selectivity is combined with group authentication in IoT environments.

SETUP in secret sharing schemes using random values

AbstractSecret sharing schemes divide a secret among multiple participants so that only authorized subsets of parties can reconstruct it. We show that secretly embedded trapdoor with universal protection attack can be embedded in secret sharing schemes that employ enough randomness to give the attacker an overwhelming advantage to access the secret. In case of ideal schemes, a coalition of a few participants (within at least one is the attacker) can succeed the attack, while in case of non‐ideal schemes, the attacker's knowledge can be enough to reveal the secret. We exemplify the attack against Shamir's threshold scheme, which is the most well known and used secret sharing scheme. Finally, we consider some prevention techniques against the proposed attack. Copyright © 2017 John Wiley & Sons, Ltd.

Secure and Efficient Secret Sharing Scheme with General Access Structures Based on Elliptic Curve and Pairing

Secret sharing techniques allow a secret to be shared among n participants in such a way that a specified subset of participant can reconstruct the secret by combining their shares. Secret sharing techniques are now the building blocks of several security protocols. Shamir's (t, n) threshold secret sharing scheme is one in which t or more participant can join together to retrieve the secret from the set of n participants. Traditional single secret sharing schemes are modified and generalized to share multiple secrets. Use of Elliptic Curve and Pairing in secret sharing is gaining more importance. The use of Elliptic Curve helps to improve the security and also the computational complexity is reduced. In this paper we propose a secret sharing scheme with a monotone generalized access structure. The scheme makes use of Shamir's scheme and Elliptic Curve pairing. The shares are chosen by the participant itself. So the consistency of the shares are ensured in this scheme. The participant shares remain secret during the reconstruction phase and this provides multi use facility where the same share can be used for the reconstruction of multiple secret. The shared secret, access structure or the participant set can be modified without updating the secret shadow of the participant. This provides dynamism and adds more flexibility to the scheme. The combiner can also verify the shares submitted by the participants during the reconstruction phase in order to identify the cheaters. The cheating detection and cheater identification is done by using bilinear pairing. This proposed scheme is simple and easy to implement compared with other generalized multi secret sharing scheme with extended capabilities using pairing.

Encryption On Grayscale Image For Digital Image Confidentiality Using Shamir Secret Sharing Scheme

The use of high-frequency internet in the process of exchanging information and digital transaction is often accompanied by transmitting digital image in the form of raster images. Secret sharing schemes are multiparty protocols that related to the key establishment which provides protection against any threats of losing cryptography key. The greater the key duplication, the higher the risk of losing the key and vice versa. In this study, Secret Sharing Method was used by employing Shamir Threshold Scheme Algorithm on grayscale digital image with the size of 256×256 pixel obtaining 128×128 pixels of shared image with threshold values (4, 8). The result number of shared images were 8 parts and the recovery process can be carried out by at least using 4 shares of the 8 parts. The result of encryption on grayscale image is capable of producing vague shared image (i.e., no perceptible information), therefore a message in the form of digital image can be kept confidential and secure.

Fair secret reconstruction in (t, n) secret sharing

In Shamir's (t, n) threshold secret sharing scheme, one secret s is divided into n shares by a dealer and all shares are shared among n shareholders, such that knowing t or more than t shares can reconstruct this secret; but knowing fewer than t shares cannot reveal any information about the secret s. The secret reconstruction phase in Shamir's (t, n) threshold secret sharing is very simple and unconditionally secure. In 2014, Harn has shown that Shamir's secret reconstruction phase cannot prevent an outside attacker from knowing the secret if more than t participants work together in the secret reconstruction phase. Harn's paper also has proposed a reconstruction scheme which can prevent the outside adversary from knowing the secret. However, in Shamir's secret reconstruction, when shares are released asynchronously, a dishonest shareholder (an inside adversary) can always release a fake share last so the dishonest shareholder can exclusively retrieve the secret; but other honest shareholders retrieve a fake secret. In this paper, we design a secret reconstruction scheme against both inside and outside adversaries. This scheme can also be called an asynchronously rational secret sharing scheme. Unlike other rational secret sharing schemes, our scheme does not need any interactive dealer, complicate cryptographic primitives, or any assumption on the number of honest shareholders.

Implementations of a Hash Function Based Secret Sharing Scheme

Secret sharing scheme creates an effective method to safeguard a secret by dividing it among several participants. By using cryptographic hash functions and the herding hashes technique, Chum and Zhang proposed a simple and efficient secret sharing scheme. In this article, we implement such scheme by several examples, namely, a general (t, n) threshold scheme, a one-weighted (t, n) threshold scheme, a multisecret scheme, a verifiable (t, n) threshold scheme, and a proactive scheme. We conduct a performance comparison study and find that the hash-based threshold scheme setup is two times, and secret recovery is six times faster than Shamir threshold scheme.

A Secret Sharing Scheme Based on AES

In order to solve the key setting difficulty and the key security problem in the file encryption, key distributed storage technology may be a proper choice to help improve the safety of the key. In the paper, a novel secret sharing scheme is proposed by AES encryption algorithm for file confidentiality, dynamic key generation mechanism to generate keys, multisecret-sharing ideas on key pre-treatment, using Shamir threshold scheme for secret dispersed storage. Finally, a few tests are carried out and the test results suggest that the efficiency of the whole scheme is good.

An ID-based signcryption scheme with compartmented secret sharing for unsigncryption

In this paper the ID-based signcryption scheme of Li, Xin, and Hu is extended to a compartmented scheme. If an organization is partitioned into different compartments, this scheme allows any member of a specific compartment to participate in the unsigncryption; moreover, each member of a compartment has information unique to that individual. This construction is the first (to the authors' knowledge) to combine identity-based encryption, Shamir's threshold scheme, and signcryption into an implementable compartmented sharing scheme.

极小特权数组上的理想多秘密共享方案

How to construct an ideal multi-secret sharing scheme for general access structures is difficult. In this paper, we solve a public problem proposed by Spiez et al. recently [Finite fields and their application, 2011, 17: 329-342], namely to design an algorithm of privileged coalitions of any length if such coalitions exist. Furthermore, in terms of privileged coalitions, we show that most of the existing multi-secret sharing schemes based on Shamir threshold secret sharing are not perfect by analyzing Yang et al.s scheme and Pang et al.s scheme. Finally, based on the algorithm mentioned above, we devise an ideal multi-secret sharing scheme for families of access structures, which possesses more vivid qualified sets than that of the threshold scheme.

An efficient forward-secure group certificate digital signature scheme to enhance EMR authentication process

The frequently used digital signature algorithms, such as RSA and the Digital Signature Algorithm (DSA), lack forward-secure function. The result is that, when private keys are renewed, trustworthiness is lost. In other words, electronic medical records (EMRs) signed by revoked private keys are no longer trusted. This significant security threat stands in the way of EMR adoption. This paper proposes an efficient forward-secure group certificate digital signature scheme that is based on Shamir's (t,n) threshold scheme and Schnorr's digital signature scheme to ensure trustworthiness is maintained when private keys are renewed and to increase the efficiency of EMRs' authentication processes in terms of number of certificates, number of keys, forward-secure ability and searching time.

Shamir's Threshold Scheme to Ensure Security in Cloud Computing Services

Cloud computing system preserves the security and privacy of a user's data by replicating data among several clouds and by using the secret sharing approach. It uses the database management system DBMS (data source) to manage and control the operations between the clients and them ulti-clouds inside a cloud service provider [1]. Generally speaking, The Shamir's threshold scheme is suitable for the shares in the cloud computing. The Shamir's threshold scheme as a secret sharing scheme will attract more attention in the cloud computing in future.

Verifiable multi-secret sharing scheme based on linear one-way function

Based on Shamir's threshold secret sharing scheme,the security of the linear one-way function and the difficulty of the discrete logarithm problem,a verifiable multi-secret sharing scheme was proposed.In this scheme,each participant needed just one secret share to share a set of secrets.Before recovering the secrets,participants could verify the correctness of the shadow shares provided by other participants.After recovering all of the secrets,the secret shares of the participants were still kept confidential and the secret shares could be used to share a new set of secrets.At the same time,the proposed scheme had fewer public parameters,and it did not require secure communication channels.

A General Threshold Signature Scheme Based on Elliptic Curve

Based on Elliptic Curve cryptosystem, a threshold signature scheme characterized by (k,l) joint verification for (t,n) signature is put forward. After being signed by a signer company employing (t, n) threshold signature scheme, the informationmis transmitted to a particular verifier company, and then the signature is verified through the cooperation ofkones from the verifier company withlmembers, so as to realize a directional transmission between different companies. Finally, the application examples of the company encryption communication system, the generating polynomial of company private key and public key were given. The security of this scheme is based on Shamir threshold scheme and Elliptic Curve system, and due to the advantages of Elliptic Curve, the scheme enjoys wider application in practice.

A General Threshold Signature and Authenticated Encryption Scheme Based on ElGamal System

Based on ElGamal system, a group-oriented threshold signature and authenticated encryption scheme was put forward. After being signed by a signer group employing threshold signature scheme, the message was transmitted to a particular verifier group, and then the signature was verified through the cooperation of ones from the verifier group with members. Similarly, a general authenticated encryption scheme characterized by joint verification was put forward through integrating threshold signature scheme and message recovery technique together; After being encrypted singed by any ones from a group with members, the message was transmitted to a particular verifier group with members, and then recovered through the cooperation of any ones from the verifier group. The security of this scheme is based on Shamir threshold scheme and ElGamal system. It realized the directional transmission of message between different groups and enjoyed the characteristics of reduced communication load and lowered calculation complexity, etc. DOI: http://dx.doi.org/10.11591/telkomnika.v11i7.2828 Full Text: PDF

Extending the Shamir threshold secret sharing scheme for sharing simultanneously several secrets

Secret sharing schemes are very important techniques for the key management in cryptography and for the distributed computation. In 1979, Shamir [6] proposed a threshold secret sharing scheme in which one secret is divided into w pieces (shares) and are delivered to w users such that only groups of t or more users (t < w) could cooperately reconstruct the secret. In this paper, by extending the method of Shamir, we present a scheme for sharing simultaneously several secrets which is more effective in using memory space and computation time w.r.t the consecutive application of several times the Shamir’s original scheme for each secret to be shared.

Remarks on the Classical Threshold Secret Sharing Schemes

We survey some results related to classical secret sharing schemes defined in Shamir [10] and Blakley [1], and developed in Brickell [2] and Lai and Ding [4]. Using elementary symmetric polynomials, we describe in a unified way which allocations of identities to participants define Shamir's threshold scheme, or its generalization by Lai and Ding, with a secret placed as a fixed coefficient of the scheme polynomial. This characterization enabled proving in Schinzel et al. [8], [9] and Spiez et al. [13] some new and non-trivial properties of such schemes. Also a characterization of matrices corresponding to the threshold secret sharing schemes of Blakley and Brickell's type is given. Using Gaussian elimination we provide an algorithm to construct all such matrices which is efficient in the case of relatively small matrices. The algorithm may be useful in constructing systems where dynamics is important (one may generate new identities using it). It can also be used to construct all possible MDS codes. MSC: primary 94A62; secondary 11T71; 11C20