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Communication Efficient Secret Sharing

Communication Efficient Secret Sharing

A secret sharing scheme is a method to store information securely and reliably. Particularly, in the threshold secret sharing scheme (due to Shamir), a secret is divided into shares, encoded and distributed to parties, such that any large enough collection of parties can decode the secret, and a smaller (then threshold) set of parties cannot collude to deduce any information about the secret. While Shamir’s scheme was studied for more than 35 years, the question of minimizing its communication bandwidth was not considered. Specifically, assume that a user (or a collection of parties) wishes to decode the secret by receiving information from a set of parties; the question we study is how to minimize the total amount of communication between the user and the parties. We prove a tight lower bound on the amount of communication necessary for decoding, and construct secret sharing schemes achieving the bound. The key idea for achieving optimal communication bandwidth is to let the user receive information from more than the necessary number of parties. In contrast, the current paradigm in secret sharing schemes is to decode from a minimum set of parties. Hence, existing secret sharing schemes are not optimal in terms of communication bandwidth. In addition, we consider secure distributed storage where our proposed communication efficient secret sharing schemes improve disk access complexity during decoding.
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Efficient Verifiable Dynamic Threshold Secret Sharing Scheme Based on Elliptic Curves

Efficient Verifiable Dynamic Threshold Secret Sharing Scheme Based on Elliptic Curves

One way to provide both secrecy and availability for a given secret (highly sensitive information) is to employ secret sharing schemes. A secret sharing scheme is a method of distributing a secret among a set of participants (shareholders) by giving each participant a share (shadow) in such a way that only authorized subsets of participants (defined by the access structure Г) can reconstruct the secret from pooling their shares, but any unauthorized subset of them cannot. Specifically, in a (t, n)-threshold secret sharing (TSS) scheme, a secret s is distributed as shares among n participants in such a way that any group of at least t participants can recover the secret s, while no groups having at most t – 1 participants can uniquely determine the secret s.
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An Efficient Secret Sharing-based Storage System for Cloud-based Internet of Things

An Efficient Secret Sharing-based Storage System for Cloud-based Internet of Things

cryptographic scheme that smart devices can share data securely with others at the edge of cloud-assisted IoTs with checking the integrity of decrypted data in data sharing and downloading phase. Furthermore, they proposed data-searching scheme to search desired data/shared data by authorized users on storage where all data are in encrypted form.

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Proposal of a Secure Modbus RTU communication with Adi Shamir’s secret sharing method

Proposal of a Secure Modbus RTU communication with Adi Shamir’s secret sharing method

The first attempt of implementing the secure Modbus RTU protocol was on a device developed in the Department of Electrical Engineering and Mechatronics at the University of Debrecen. It is a data acquisition and control device which has several types of peripherals. The microcontroller, driving the device is an Atmel ATxmega 128a type. The firmware written by students of the department previously was made in Basic language. For the limited development time, the secure protocol was implemented in this Basic firmware. The data to be encrypted was supplied by eight PTC thermoresistors, because the thermic data is a frequent feature of SCADA communication networks. These thermic sensors measured the temperature of the MSc laboratory of the department, where the system was installed. The master of the network was a personal computer, with a simple Modbus client software running, and logging the gathered data to a comma separated text file. In this test, we only examined the applicability of the protocols on the slave’s side, for in our opinion it is the most critical point in the protocols development to be implementable on a relatively low performance device (such as the used data acquisition device). The physical layer of the network was RS485 2-wire bus, the end node connected with the master via a Moxa Serial-to-USB converter device. Figure 7. shows the structure of the example network.
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An Efficient Data Hiding Approach on Digital Color Image for Secret Communication

An Efficient Data Hiding Approach on Digital Color Image for Secret Communication

Abstract: In this research paper I have proposed the method of an efficient data hiding approach on digital color image for secret communication. The method is applicable for confidential data transfer, secret communication, copyright protection for digital media and military purpose. Steganography process is used for this. Steganography is the process of hiding secret information behind the original cover file. This file may be audio, video or image file. In this system the digital image is taken as input image and preprocessing of input image is done with the help of MATLAB. Any noise present in image is detected and removed in the image preprocessing technique. A given input image is converted into three different planes i.e. red, green and blue plane. After the plane separation embedding process takes place. Also one password is added at the time of embedding process as well as data extraction process, so that no one can easily hack the data. Chaos algorithm is used for data encryption. After the embedding process stego image is formed. In the data extraction process we have to get back original information. So that Chaos decryption algorithm is used to retrieve secret data and cover image. The primary idea of this project is to increase data hiding capacity and reduce image quality degradation.
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An  Efficient $t$-Cheater  Identifiable  Secret  Sharing  Scheme  with  Optimal  Cheater  Resiliency

An Efficient $t$-Cheater Identifiable Secret Sharing Scheme with Optimal Cheater Resiliency

In this paper, we present an efficient k-out-of-n secret sharing scheme, which can identify up to t rushing cheaters, with probability at least 1 − , where 0 < < 1/2, provided t < k/2. This is the optimal number of cheaters that can be tolerated in the setting of public cheater identification, on which we focus in this work. In our scheme, the set of all possible shares V i satisfies the condition that |V i | =

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Efficient and Information-Theoretical Secure Verifiable Secret Sharing over Bilinear Groups

Efficient and Information-Theoretical Secure Verifiable Secret Sharing over Bilinear Groups

Proof From Theorem 2, we learn that the adversary can not get any information about the secret polynomial f(x) given the public commitments. Nevertheless according to the algo- rithm of distribution, to acquire the share owned by an honest participant, the adversary has no choice but compute f(x) merely using the shares of the corrupted participants. With- out loss of generality we suppose that the corrupted players are U 1 , · · · , U k and k < t. The adversary has to compute all coefficients a 1 , · · · , a t −1 of f(x) from the following system of

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Shared Cryptographic Scheme with Efficient Data Recovery and Compression for Audio Secret Sharing

Shared Cryptographic Scheme with Efficient Data Recovery and Compression for Audio Secret Sharing

The original motivation for audio secret sharing are: (1) To safeguard cryptographic keys from loss or to be get stolen, it is desirable to create backup copies of key's, although these copies are themselves a security risk. Secret sharing scheme addresses this issue by allowing enhanced reliability without increased security risk, (2) They also facilitate distributed trust or shared control for critical activities by requiring cooperation by t out of n users for access to a critical action and, (3) The idea of secret sharing is to start with a secret, and divide it into pieces called as shares which are distributed amongst users or participants ,such that the pooled shares of specific subsets of users allow reconstruction or recovery of the original secret. This may be considered as a key distribution technique, facilitating one-time key establishment, wherein the recovered key is pre-defined (static), and in the basic case, same for all groups.
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Nearly optimal robust secret sharing

Nearly optimal robust secret sharing

Cramer et al. [11] introduce the notion of algebraic ma- nipulation detection (AMD) codes, which is a natural variant of error-detection codes in situations where the adversary’s perturbations on a codeword are chosen independently of the codeword. By using this primitive as a pre-code in Shamir’s secret sharing scheme (or any secret sharing scheme with linear decoder), they are able to make the scheme robust against adversarial manipulations. The key difference in their model is the notion of robustness; i.e., the requirement is that if the adversary corrupts any of the shares, the reconstruction should detect the adversary and fail (rather than output the correct share) with high probability. More recently, Lewko and Pastro [12] defined a variation of robust secret sharing in which the robustness requirement is against local adversaries. That is, the error in each share corrupted by the adversary can only depend on the particular share being corrupted. They show that even in this restricted model, the minimum required share length is k + log(1/η) − O(1) (under the standard threshold assumption that any set of t+1 must reconstruct the secret with probability at least 1−η). Furthermore, they construct efficient schemes in the local model that attains a nearly optimal share length of k + O(log(1/η)).
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Nearly  Optimal  Robust  Secret  Sharing

Nearly Optimal Robust Secret Sharing

In another recent work, Cramer et al. [CDD + 15] combine AMD codes with universal hash functions and (folded) list decodable codes to construct a secret sharing scheme with potentially constant share length (more precisely, share length Θ(1 + log(1/η)/n)). Their construction is with respect to a randomly chosen hash function from a universal family and is thus a Monte-Carlo construction. That is, the code construction relies on the probabilistic method (and thus may not result in the desired secret sharing scheme with unfortunate choices of the randomness), however the encoder and decoders are efficient once the randomness of the code construction is set to an appropriate choice. Moreover, this construction considers the “ramp model” in which it is not necessary to be able to reconstruct the secret from any t + 1 of the shares. This relaxation is in fact necessary for any secret sharing scheme with share length smaller than the secret length k.
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A Review on Visual Secret Sharing Schemes

A Review on Visual Secret Sharing Schemes

The increase in usage of the internet and advancements in the network technologies makes the communication becomes more crucial in many application areas. In multimedia communication, images are the most preferred source. They may cause certain risk from unauthorized sources. Hence there is a demand in information security to protect secret images or important data from being tampered or grabbed. Secret sharing scheme has turn into an important concept in information protection and security. The Visual Secret Sharing (VSS) schemes encode original image into a number of share images. The original image can be recovered by superimposing collected shares. The Visual Cryptography (VC) is a secret sharing method that encodes original image into n shadow or share images and circulated among participants. Original image can be reconstructed by the human visual system (HVS) while superimposing or stacking k (k ≥ n) or more share images and fewer than k shares never give information about the original secret.
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An Explication of Multifarious Secret Sharing Schemes

An Explication of Multifarious Secret Sharing Schemes

able to reconstruct the secret whenever it is necessary. The term pro-active refers to the fact that it's not necessary for a breach of security to occur before secrets are refreshed, the refreshment is done periodically (and hence, proactively). Several PSSS have been proposed. Bai [26] used matrix projection method and Shamirs [5] scheme to get a new PSSS. Optimum secret sharing is described by Zhengjun [27]. They extend the secret s in the Shamir‟s scheme to an array of three elements, (s, e0, e1), and construct two equations for checking validity. Each item in the equations should be reconstructed using Lagrange‟s interpolation. In this paper, the schemes are revisited by introducing a public hash function to construct equations for checking validity. The revisited scheme is more efficient because they only extend the secret to an array of two elements.
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Secret Sharing using Image Hashing

Secret Sharing using Image Hashing

This paper presents a cryptographic technique that encrypts secret information using a coding image by transforming the pixels of this image from the intensity domain to the characters domain using a hash function. In the proposed technique, the coding image will be used to encrypt the secret information at the sender and decrypt it at the receiver using the pixels whose intensity values are transformed to characters. A matrix of characters corresponding to the coding image is generated where each character in this matrix corresponds to a pixel in the coding image and each character in the secret information is mapped to a character in the matrix of characters. The locations of characters in the matrix of characters that correspond to pixels in the coding image and correspond to characters in the secret information forms the pixels map. The pixels map is encrypted using a secret key before being sent to the receiver on a secure communication channel different from that used to send the coding image and at different times. Upon receiving the coding image and the encrypted pixels map the receiver uses the secret key to decrypt the pixels map and uses the coding image and the hash function to generate the matrix of characters. Each location in the pixels map is used to retrieve a character from the matrix of characters in order to decrypt the secret information. Experimental results showed the effectiveness and the efficiency of the proposed algorithm where a message was encrypted using a coding image without modifying its pixels and it was decrypted without errors.
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On  the  Power  of  Amortization  in  Secret  Sharing: $d$-Uniform  Secret  Sharing   and  CDS  with  Constant  Information  Rate

On the Power of Amortization in Secret Sharing: $d$-Uniform Secret Sharing and CDS with Constant Information Rate

in the sense that one can apply a PSM protocol to hide all of Alice’s and Bob’s input (both the private and public parts). Adapting known PSM protocols to the partial PSM model in a way that communication complexity is reduced, does not seem like an easy task. As explained in Section 6, CDS turns out to be a natural tool for accomplishing this task. In Section 6 we reduce partial PSM to CDS with an overhead that is roughly linear in the domain of the private input. (We obtain better results for families of predicates that can be computed by small/shallow Boolean circuits.) Our results improve upon the reduction of [AARV17] whose overhead is exponential in the domain of the private parts.
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Secure and Efficient Steganography Scheme using 2 out of 2 Secret Sharing Method

Secure and Efficient Steganography Scheme using 2 out of 2 Secret Sharing Method

sharing and steganography. The requirements of an efficient steganographic algorithm are good embedding capacity, less chance of steganalysis and good imperceptibility after embedding. Basically the objective of the watermarking approach is to provide copyright protection and image authentication [21]. Fingerprinting is also an approach which are generally used to track unique copies of the object which are going to be supplied to different customers. By this way a trusted third party can revoke the licence of the distribution authority [20]. In watermarking and fingerprinting the fact that information is hidden inside the files may be public knowledge – sometimes it may even be visible – while in steganography the imperceptibility of the information is crucial [19]. A successful attack on a steganographic system consists of an adversary observing that there is information hidden inside a file, while a successful attack on a watermarking or fingerprinting system would not be to detect the mark, but to remove it [20]. Steganography became famous only because of the certain loopholes in the existing cryptography approaches. Because of many rules provided by the government, strength of cryptography became more weaker [22][23], hence the focus of researchers are transferred to other security mechanism.
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Non-Malleable  Secret  Sharing

Non-Malleable Secret Sharing

Existing secret-sharing schemes. Most of the secret sharing schemes known are linear [Bei, chapter 4] and have nice algebraic and geometric properties, which are harnessed to obtain efficient sharing and reconstruction procedures. Non-malleable secret sharing schemes on the other hand cannot be linear. To see this, consider a linear secret sharing scheme, in which the secret is a linear combination of the authorized shares. Now if an adversary multiplies each of the authorized shares by 2, the secret, which is a linear combination, also gets multiplied by 2 and non-malleability is lost. In fact, it is easy to see that for any authorized set of shares of linear schemes, the adversary can add an arbitrary value of its choice to the secret by changing only one of the shares. Indeed, the malleability of linear secret sharing schemes, such as polynomials based Shamir’s secret sharing scheme [Sha79], forms the basis of secure multi-party computation protocols [BOGW88]. For our purposes, any such alteration is an “attack” and we try to build secret sharing schemes that necessarily prohibit any such attacks.
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Leakage-Resilient  Secret  Sharing

Leakage-Resilient Secret Sharing

Can we use extractors to get 2-party leakage-resilient schemes? Most existing (1, 2, 2)- LRSSs are based on two source extractors [DP07, DDV10, ADKO15, GK18a]. These constructions rely on the following powerful observation: if the two shares are independent, then conditioning on the entire transcript of a bounded communication protocol preserves the conditional independence between them, and therefore independent source extractors can be invoked for proving leakage- resilience. Unfortunately this idea does not generalize to 2-party collusion protocols even for 3-out- of-3 schemes. Consider 3 bits of leakage corresponding to the 3 subsets of size 2. As we fix the three leaked bits, conditional independence between pairs is lost (unlike the 2-out-of-2 case), and we cannot rely on independent source extractors. We face further challenges when considering 3- out-of-5 schemes. Even without leakage, the five shares cannot be directly modeled as independent sources, as any 3-out-of-5 shares have to encode the same secret. Moreover, leaking even a single bit from any one of the shares may reveal some joint information about other shares, and it is not clear how to rely on extractors.
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Foundations  of  Homomorphic  Secret  Sharing

Foundations of Homomorphic Secret Sharing

• Output Client Complexity: Finally, we remark that our protocols has the feature that the output client is relatively efficient. Its sole job is recovering the randomized encoding from the output shares and then decode the randomized encoding. The latter task has T poly(λ) complexity, and the former has at most T poly(λ) × m complexity, since for every output element, the output client merely needs to add the corresponding output shares from the m servers, due to the additive decoding of HSS. This feature is important for delegating secure computation. Computationally weak (input) clients can share their inputs offline, and computationally weak output clients can recover the outputs efficiently. The most expensive computation is performed by the servers who are computationally powerful. In comparison, protocols following the round-collapsing approach all have high complexity for deriving the outputs, namely T poly(λ) × n 3 per party.
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A SIMPLE AND EFFICIENT VISUAL CRYPTOGRAPHY SCHEME FOR SHARING MULTIPLE SECRET IMAGES

A SIMPLE AND EFFICIENT VISUAL CRYPTOGRAPHY SCHEME FOR SHARING MULTIPLE SECRET IMAGES

www.wjert.org 57 receiver side it takes 1.237009 seconds for 640*480 sized 3 message images).The algorithm encryption and decryption of images uses symmetric key, which allow users to have confidentiality and security in transmission of the image based data. The key used is of size 24bit. This scheme is best suitable for pictures having secret in the form of binary image.

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AN EFFICIENT SECRET SHARING SCHEME FOR QUANTUM KEY DISTRIBUTION

AN EFFICIENT SECRET SHARING SCHEME FOR QUANTUM KEY DISTRIBUTION

We know that a quantum secret sharing scheme is secure against any outside attacker if it is secure against a dishonest participant. Also we know that a dishonest participant can intercept other participant’s particles and resends forged particles or entangle aider particles on the intercepted particles and pilfer the secret information through measuring the aider particles. As discussed above, it is evident from the intercept and resend attack, and entangle and measure attack that neither outside eavesdropper nor dishonest participant can filch the secret information from the transmitted particles because the transmitted particles in our proposed quantum secret sharing scheme are conserved by the decoy particles which are randomly yield in the computational Z -basis or
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