Shamir's Scheme Research Articles

MAN[sbnd]C: A masked autoencoder neural cryptography based encryption scheme for CT scan images

Sharing medical images securely is very important towards keeping patients’ data confidential. In this paper we propose MANC: a Masked Autoencoder Neural Cryptography based encryption scheme for sharing medical images. The proposed technique builds upon recently proposed masked autoencoders. In the original paper, the masked autoencoders are used as scalable self-supervised learners for computer vision which reconstruct portions of originally patched images. Here, the facility to obfuscate portions of input image and the ability to reconstruct original images is used an encryption-decryption scheme. In the final form, masked autoencoders are combined with neural cryptography consisting of a tree parity machine and Shamir Scheme for secret image sharing. The proposed technique MANC helps to recover the loss in image due to noise during secret sharing of image.•Uses recently proposed masked autoencoders, originally designed as scalable self-supervised learners for computer vision, in an encryption-decryption setup.•Combines autoencoders with neural cryptography - the advantage our proposed approach offers over existing technique is that (i) Neural cryptography is a new type of public key cryptography that is not based on number theory, requires less computing time and memory and is non-deterministic in nature, (ii) masked auto-encoders provide additional level of obfuscation through their deep learning architecture.•The proposed scheme was evaluated on dataset consisting of CT scans made public by The Cancer Imaging Archive (TCIA). The proposed method produces better RMSE values between the input the encrypted image and comparable correlation values between the input and the output image with respect to the existing techniques.

Threshold secret sharing with geometric algebras

In this work, we propose a geometric algebra‐based variation of a well‐known threshold secret‐sharing scheme introduced by Adi Shamir in 1979. Secret sharing is a cryptographic primitive which allows a secret input to be divided into multiple shares which are then sent to a collection of parties. The shares are generated so that only “authorized” sets of shares can reconstruct the secret. In Shamir's scheme, any sufficiently large set of shares can reconstruct the secret. The minimum number of shares which can obtain the secret is called the threshold, and any number of shares smaller than the threshold reveals nothing about the secret. The shares are generated such that each party can perform computations, generating a new set of shares that, when reconstructed, are equivalent to performing those exact computations directly on the secret input data. Our variant changes the domain from which secrets are taken: A finite field with prime order is replaced by a geometric algebra over a finite field of prime order. This change preserves the important security properties of Shamir's scheme, namely, idealness (secrets and shares are chosen from the same space) and perfectness (“unauthorized” sets of shares learn nothing about the secret). Our scheme allows secret sharing to be seamlessly added to the arsenal of GA‐based applications. Our extension of Shamir's secret scheme was first worked out for geometric algebras. It appears, however, that in fact it works for other algebras, a situation worthy to be explored in future work. For definiteness, in this paper, we restrict the analysis to the case of geometric algebras.

Application of Recursive Algorithm on Shamir's Scheme Reconstruction for Cheating Detection and Identification

Information data protection is necessary to ward off and overcome various fraud attacks that may be encountered. A secret sharing scheme that implements cryptographic methods intends to maintain the security of confidential data by a group of trusted parties is the answer. In this paper, we choose the application of recursive algorithm on Shamir-based linear scheme as the primary method. In the secret reconstruction stage and since the beginning of the share distribution stage, these algorithms have been integrated by relying on a detection parameter to ensure that the secret value sought is valid. Although the obtained scheme will be much simpler because it utilizes the Vandermonde matrix structure, the security aspect of this scheme is not reduced. Indeed, it is supported by two detection parameters formulated from a recursive algorithm to detect cheating and identify the cheater(s). Therefore, this scheme is guaranteed to be unconditionally secure and has a high time efficiency (polynomial running time).

ПОСТРОЕНИЕ И РЕАЛИЗАЦИЯ НЕКОТОРЫХ СОВЕРШЕННЫХ ПРОВЕРЯЕМЫХ СХЕМ РАЗДЕЛЕНИЯ СЕКРЕТА

Most of the existing public key cryptosystems are potentially vulnerable to cryptographic attacks as they rely on the problems of discrete logarithm and factorization of integers. There is now a need for algorithms that will resist attacks on quantum computers. The article describes the implementation of Shamir’s post-quantum secret sharing scheme using long arithmetic that can be applied in modern cryptographic modules. The implementation of the Pedersen – Shamir scheme is described, which allows preserving the property of the perfection of the Shamir scheme by introducing testability. The article presents graphs reflecting the influence of the verifiability property in the Shamir secret sharing scheme on the speed of its operation.

Deteksi dan Identifikasi Pelaku Kecurangan Skema Pembagian Rahasia Linear Berbasis Skema Shamir

The method that can be used to maintain security of secret in the form of cryptographic keys is by using secret sharing scheme (SSS). This method is first proposed by Adi Shamir in 1979, where the proposed scheme is a (k, n) threshold scheme. Shamir scheme is a perfect scheme under the assumption that all shareholders present their original share. However, if there are dishonest shareholders who present faked shares then the honest shareholders get nothing but a faked secret. Secret sharing scheme based on linear scheme is a scheme that can detect and identify cheaters who submit faked shares at the secret reconstruction. Detectability of this scheme when and identifiability when under the assumption that all shareholders present their shares randomly. After conducting a security analysis of the proposed scheme, it is obtained that to succeed in attack with cheaters who work together to fool honest shareholders then a new polynomial g(x) such that g(1) = , g(2) = , …, g(k - 1) = and a new detector that has the same value as detector d are needed.

Minimizing Latency for Secure Coded Computing Using Secret Sharing via Staircase Codes

We consider the setting of a Master server, M, who possesses confidential data (e.g., personal, genomic or medical data) and wants to run intensive computations on it, as part of a machine learning algorithm for example. The Master wants to distribute these computations to untrusted workers who have volunteered or are incentivized to help with this task. However, the data must be kept private and not revealed to the individual workers. Some of the workers may be stragglers, e.g., slow or busy, and will take a random time to finish the task assigned to them. We are interested in reducing the delays experienced by the Master. We focus on linear computations as an essential operation in many iterative algorithms such as principal component analysis, support vector machines and other gradient-descent based algorithms. A classical solution is to use a linear secret sharing scheme, such as Shamir's scheme, to divide the data into secret shares on which the workers can perform linear computations. However, classical codes can provide straggler mitigation assuming a worst-case scenario of a fixed number of stragglers. We propose a solution based on new secure codes, called Staircase codes, introduced previously by two of the authors. Staircase codes allow flexibility in the number of stragglers up to a given maximum, and universally achieve the information theoretic limit on the download cost by the Master, leading to latency reduction. Under the shifted exponential model, we find upper and lower bounds on the Master's mean waiting time. We derive the distribution of the Master's waiting time, and its mean, for systems with up to two stragglers. For systems with any number of stragglers, we derive an expression that can give the exact distribution, and the mean, of the waiting time of the Master. We show that Staircase codes always outperform classical secret sharing codes.

Linear Subspace Cryptanalysis of Harn’s Secret Sharing-Based Group Authentication Scheme

Shamir's secret sharing is used as an important underlying primitive in many other cryptographic schemes, such as group authentication and group key agreement schemes. Although Shamir secret sharing has unconditional security, it is not necessarily the case for the protocols founded on that. A common imperfect assumption in such schemes is to be satisfied of only hiding the polynomials coefficients from the adversary. In this direction, we present a new method that can be potentially used for cryptanalysis of some Shamir's secret sharing-based schemes. This method is called the linear subspace cryptanalysis, in which the attack problem is made equivalent to the problem of studying the belongingness of a vector to a given linear subspace. Using the proposed method, we analyse the Harn's group authentication protocol, which is a remarkable scheme recently designed based on Shamir's scheme. This scheme has two main variants: one-time asynchronous and multiple-time asynchronous. In the one-time variant, it has been evaluated by the designer that the number of group members should be bounded to n <; kt + 1, in order to make the scheme resistant against outside attacks. This constraint has been relaxed in the multiple-time variant, backed by the hardness of the discrete logarithm problem. In this paper, we show that neither confining the number of group members nor using discrete logarithm have made the one-time and multiple-time variants of this scheme resistant against impersonation attack. We show that, in both cases, an outside attacker can impersonate an authorized group member in a polynomial time, when at least t + k-1 authorized members are participating in the group authentication session. The main observation, based on which the attack works, is that the dimension of the linear subspace spanned by the Lagrange components for any predefined set of users never exceeds t +k-1.

Data sharing based on error-correcting codes

Secret sharing protocols are used for distributed storing of information. Most often such information are secret keys or passwords of any user. Secret sharing protocols are designed to solve the problem of storing information so that those groups of people, who are allowed to know the secret, can restore the secret, and those groups that are not allowed to know the secret, are not able to recover even by brute-force. More popular threshold secret sharing scheme is Shamir’s distribution scheme. The idea of Shamir's scheme is the fact that for the interpolation polynomial of degree k-1, k points are required. Shamir’s sharing scheme was originally designed for distribution of secret keys. For large amounts of data, sharing and restore processes are very slow. Thus, it is necessary to have a faster threshold secret sharing scheme. Since the secret scheme is based on the redundant information, and error-correcting codes provide redundancy, the idea was came to build a distribution scheme based on these codes. This article describes a new system of secret sharing on the basis of error-correcting codes. The purpose of the study is to develop a high-performance system which will use a different error-correcting code.

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.

Linear (k,n) secret sharing scheme with cheating detection

AbstractLinear (k,n) secret sharing scheme with the capability of detecting cheating is considered in this paper. Linear (k,n) secret sharing scheme is a class of (k,n) secret sharing, where all the n shares of a secret satisfy a linear relationship. It plays an important role in other cryptographic systems, such as multi‐party computation and function sharing schemes. On the other hand, cheating problem in (k,n) secret sharing is an important issue, such that cheaters (dishonest players) submit forged shares during secret reconstruction to fool honest players. During decades of research on cheating prevention, vast (k,n) secret sharing schemes against cheating have been proposed. However, most of these schemes are not linear schemes because it contains redundant information in their shares to achieve cheating detection. Because linear (k,n) secret sharing is an important primitive in threshold cryptography, linear (k,n) secret sharing scheme with the capability of cheating detection is also worthwhile to be discussed. In this paper, we propose a linear (k,n) secret sharing scheme against cheating based on Shamir's original scheme, which possesses the following merits: (1) Our scheme is just a combination of two Shamir's schemes. Therefore, our scheme can be used in other threshold cryptographic systems, which are based on Shamir's scheme. (2) The size of share in the proposed scheme almost reaches its theoretic lower bound in (k,n) secret sharing with cheating detection. (3) In the phase of cheating detection, only one honest player can detect the cheating from other k − 1 cheaters, which achieves a stronger detection effective than the previous linear secret sharing schemes against cheating. Copyright © 2016 John Wiley &amp; Sons, Ltd.

A Novel (K,N) Secret Sharing Scheme from Quadratic Residues for Grayscale Images

A new grayscale image encryption algorithm based on $(k,n)$ threshold secret sharing is proposed. The scheme allows a secret image to be transformed into $n$ shares, where any $k \le n$ shares can be used to reconstruct the secret image, while the knowledge of $k-1$ or fewer shares leaves no sufficient information about the secret image and it becomes hard to decrypt the transmitted image. In the proposed scheme, the pixels of the secret image are first permuted and then encrypted by using quadratic residues. In the final stage, the encrypted image is shared into n shadow images using polynomials of Shamir scheme. The proposed scheme is provably secure and the experimental results shows that the scheme performs well while maintaining high levels of quality in the reconstructed image.

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.

Authentication of grayscale document images using shamir secret sharing scheme.

This paper proposed a new blind authentication method based on the secret sharing technique with a data repair capability for grayscale document images .Shamir proposed threshold secret sharing scheme in which a secret message is transformed in to shares for keeping by participants, and when some of the shares, not necessarily all of them, are collected, the secret message can be lossless recovered.. This secret sharing scheme is useful for reducing the risk of incidental partial data loss. In additional image transformed in to a stego-image in the PNG format with an additional alpha channel for transmission on networks. For tampered block data repairing is applied by reverse Shamir scheme. It also presents the security issues and discuss on keeping high quality visual effect.

English

Generally digital images are mostly used to preserve confidential & important information. But the problem is providing authentication and integrity to these digital images is a very challenging task. Therefore using this paper a new efficient authentication method is proposed to provide for grayscale document images using the Portable Network Graphics (PNG) image with data repair capability. In this concept an authentication signal generated by each block of a grayscale document image and then using Shamir secret sharing scheme grayscale document image authentication signal and binarized block content is combined and transformed into several shares. These several binarized block content shares are then combined into an alpha channel plane then the PNG image is built from combining the grayscale image with alpha channel plan. In this process the authentication for image is achieved as follows; if the authentication signal measured from the current block content does not match that extracted from the shares embedded in the alpha channel plane then that image block is tampered. Then using reverse Shamir scheme, two shares from unmarked blocks are collected and then data repairing is applied. Finally simulation results are provided to prove the concept of proposed method. Keywords— Data hiding, data repair, grayscale document image, image authentication, Portable Network Graphics (PNG) image, secret sharing

Fair ( t , n ) threshold secret sharing scheme

In the setting of secret sharing, a group of parties wish to run a protocol for recovering the secret when they input their shares. The security requirement include privacy, correctness and others. One desirable property is fairness, which guarantees that if either party gets the secret, then the other party does too. However, basic secret sharing schemes, verifiable secret sharing schemes and publicly verifiable secret sharing schemes do not satisfy the fairness. Moreover, fairness is a central objective of the rational secret sharing scheme. In this work, the authors study the fairness problem of secret reconstruction in a (t, n) secret sharing scheme. They use a new approach to achieve the fairness of the protocol. They first define the fair notion of secret sharing probabilistically. Using the definition, a fair (t, n) secret sharing scheme is proposed, its security and fairness are shown against three different attack types. The proposed scheme is an extension of basic model of secret sharing (Shamir's scheme) and the approach of fairness of Dov Gordon et al.(STOC2008). Theoretical analysis shows that the proposed scheme is more efficient.

Key based Visual Cryptography Scheme using Novel Secret Sharing Technique with Steganography

With rapidly growing network, Internet has become a primary source of transmitting confidential or secret data such as military information, financial documents, etc. In such cases, techniques devoted to protect such kind of information are needed and they play an important role in providing confidential and secure transmission over network. Visual Cryptography is also one of them which is used to hide secret visual information (such as image, text, etc) in which secret sharing scheme is used. Secret sharing is used to encrypt a secret image into customized versions of the original image. There are many secret sharing algorithms in literature including Shamir, Blakley, and Asmuth-Bloom to divide the image into no. of shares. These sharing schemes lead to computational complexity and also generate shares like noisy images. Then afterwards Lin & Tsai proposed a scheme which creates meaningful shares but having same computational complexity as like Shamir's scheme. Along with this, in these schemes, as decryption is done using Human Visual system, the secret can be retrieved by anyone if person get at least k no. of shares. To overcome all above problems, we are suggesting one new method in which a symmetric secret key is used to encrypt the image and then secret shares are generated from this image using Novel secret sharing technique with steganography. So, finally this method will produce meaningful shares and use of secret key will ensure the security of scheme. This scheme can become a reliable solution suitable for today's authentication challenges. Index Terms: Visual cryptography, Secret sharing, steganography.

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

The Research of Secret Image Sharing Based on RS Erasure Code

Secret image sharing is an attractive research problem in information security filed. After more than ten years of development, secret image sharing has become a relatively independent area. Most current secret image sharing scheme used Lagrange interpolation of Shamir scheme as the core idea, but which way will greatly reduce the computational efficiency and system availability without a doubt because of a huge amount of data in images. According to the internal relationship between coding theory and secret sharing technology, the paper proposed a secret image scheme based on coding theory. In addition to have advantages which most secret image sharing schemes based on Lagrange interpolation own, the new method which has a more simple idea reduced computational complexity and easy to extend the field of video and audio, so has a more obvious practical value; The design and realization of the new secret image sharing scheme has indirectly proved the internal relationship between coding and secret sharing scheme.

A Secret-Sharing-Based Method for Authentication of Grayscale Document Images via the Use of the PNG Image With a Data Repair Capability

A new blind authentication method based on the secret sharing technique with a data repair capability for grayscale document images via the use of the Portable Network Graphics (PNG) image is proposed. An authentication signal is generated for each block of a grayscale document image, which, together with the binarized block content, is transformed into several shares using the Shamir secret sharing scheme. The involved parameters are carefully chosen so that as many shares as possible are generated and embedded into an alpha channel plane. The alpha channel plane is then combined with the original grayscale image to form a PNG image. During the embedding process, the computed share values are mapped into a range of alpha channel values near their maximum value of 255 to yield a transparent stego-image with a disguise effect. In the process of image authentication, an image block is marked as tampered if the authentication signal computed from the current block content does not match that extracted from the shares embedded in the alpha channel plane. Data repairing is then applied to each tampered block by a reverse Shamir scheme after collecting two shares from unmarked blocks. Measures for protecting the security of the data hidden in the alpha channel are also proposed. Good experimental results prove the effectiveness of the proposed method for real applications.