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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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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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.

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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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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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 | =

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

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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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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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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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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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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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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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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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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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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• 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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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.

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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