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*Advanced Topics in Public-Key Encryption
Published in Jonathan Katz, Yehuda Lindell, Introduction to Modern Cryptography, 2020
Consider the following problem. A dealer holds a secret s ∈ {0, 1}ℓ—say, a nuclear-launch code—that it wishes to share among some set of N users P1, …, PN by giving each user a share. Any t users should be able to pool their shares and reconstruct the secret, but no coalition of fewer than t users should get any information about s from their collective shares (beyond whatever information they had about s already). We refer to such a sharing mechanism as a (t, N) -threshold secret-sharing scheme. Such a scheme ensures that s is not revealed without sufficient authorization, while also guaranteeing availability of s when needed (since any t users can reconstruct it). Beyond their direct application, secret-sharing schemes are also a building block of many cryptographic protocols.
Visual Cryptography: Introduction
Published in Shivendra Shivani, Suneeta Agarwal, Jasjit S. Suri, Handbook of Image-Based Security Techniques, 2018
Shivendra Shivani, Suneeta Agarwal, Jasjit S. Suri
Secret sharing has a vital cryptographic application. It is used in scenarios when people, involved in cryptographic processing of private data (secret), are either unreliable, or do not have trust in each other, while they together want to secretly compute some function for their private data. Hence to conceal a secret, it is split into various pieces called shares and distributed among participants, involved in cryptographic processing, in such a way that the secret can only be recovered by certain subsets of the shares. The search for efficient secret sharing schemes is still a great focus of research for cryptographic community.
Key Establishment Protocols
Published in Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone, Handbook of Applied Cryptography, 2018
Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone
The idea of secret sharing is to start with a secret, and divide it into pieces called shares which are distributed amongst users such that the pooled shares of specific subsets of users allow reconstruction of the original secret. This may be viewed as a key pre-distribution technique, facilitating one-time key establishment, wherein the recovered key is pre-determined (static), and, in the basic case, the same for all groups.
Analyzing the efficiency of partially entangled states in Vaidman’s-type games and its applications in Quantum Secret Sharing
Published in International Journal of Computers and Applications, 2019
Secret sharing is the process of splitting a secret message into parts, such that no part of it is sufficient to retrieve the original message [11]. The original idea was to split the information between the two recipients, one of which may be a cheat (unknown to the sender). Only when the two recipients cooperate with each other, they retrieve the original message. The protocol, therefore, assumes that the honest recipient will not allow the dishonest recipient to cheat, hence, splitting the information between the two.
Secret image sharing based on multiphase retrieval algorithm
Published in Journal of Modern Optics, 2020
To protect the security and transmission of image information, image hiding [1], image watermarking [2,3], image encryption [4,5], and optical image security [6,7] have been extensively studied. Unlike these technologies, secret sharing is an alternative method for protecting an image by dividing it into multiple encrypted shares. When sufficient shares are collected, the image can be recovered. In 1976, Shamir proposed a (k,n) secret sharing, where , which hid the secret data in the constant term of a (k–1) degree polynomial to generate the shadows [8]. In 2002, Thien and Lin extended Shamir's scheme to secret image sharing (SIS). To reduce the size of the shadows, all the coefficients of the polynomial were embedded in the pixel values of the secret image to generate n share images; thus, the size of the shadows were reduced to 1/k times that of the original secret image. In the recovery phase, when the value of Lagrange's interpolation was equal to or greater than k shadows, the secret image could be recovered, but when the value of Lagrange's interpolation was less than k shadows, the secret image could not be recovered [9]. Since then, various SIS schemes have been proposed. To improve the efficiency, schemes that can share multiple secret images at a time were proposed [10,11]. To prevent an attacker from impersonating a legitimate user obtaining a resource, SIS schemes with authentication were proposed [12–16]. An SIS scheme generating small-sized share images had the advantages of saving storage space, reducing management costs, accelerating the transmission speed, saving bandwidth, and improving the data hiding efficiency. Therefore, many schemes reducing the size of the shadows were proposed [17–20]. Recently, a progressive SIS scheme was proposed in which the amount of information or the resolution of the secret image can be gradually recovered as the shadows increase [21,22].