Bounds for Visual Cryptography Schemes

In this paper, we investigate the best pixel expansion of the various models of visual cryptography schemes. In this regard, we consider visual cryptography schemes introduced by Tzeng and Hu [13]. In such a model, only minimal qualified sets can recover the secret image and that the recovered secret image can be darker or lighter than the background. Blundo et al. [4] introduced a lower bound for the best pixel expansion of this scheme in terms of minimal qualified sets. We present another lower bound for the best pixel expansion of the scheme. As a corollary, we introduce a lower bound, based on an induced matching of hypergraph of qualified sets, for the best pixel expansion of the aforementioned model and the traditional model of visual cryptography realized by basis matrices. Finally, we study access structures based on graphs and we present an upper bound for the smallest pixel expansion in terms of strong chromatic index

Approximate Degree, Secret Sharing, and Concentration Phenomena

The epsilon-approximate degree deg~_epsilon(f) of a Boolean function f is the least degree of a real-valued polynomial that approximates f pointwise to within epsilon. A sound and complete certificate for approximate degree being at least k is a pair of probability distributions, also known as a dual polynomial, that are perfectly k-wise indistinguishable, but are distinguishable by f with advantage 1 - epsilon. Our contributions are: - We give a simple, explicit new construction of a dual polynomial for the AND function on n bits, certifying that its epsilon-approximate degree is Omega (sqrt{n log 1/epsilon}). This construction is the first to extend to the notion of weighted degree, and yields the first explicit certificate that the 1/3-approximate degree of any (possibly unbalanced) read-once DNF is Omega(sqrt{n}). It draws a novel connection between the approximate degree of AND and anti-concentration of the Binomial distribution. - We show that any pair of symmetric distributions on n-bit strings that are perfectly k-wise indistinguishable are also statistically K-wise indistinguishable with at most K^{3/2} * exp (-Omega (k^2/K)) error for all k < K <= n/64. This bound is essentially tight, and implies that any symmetric function f is a reconstruction function with constant advantage for a ramp secret sharing scheme that is secure against size-K coalitions with statistical error K^{3/2} * exp (-Omega (deg~_{1/3}(f)^2/K)) for all values of K up to n/64 simultaneously. Previous secret sharing schemes required that K be determined in advance, and only worked for f=AND. Our analysis draws another new connection between approximate degree and concentration phenomena. As a corollary of this result, we show that for any d deg~_{1/3}(f). These upper and lower bounds were also previously only known in the case f=AND

Naturally Rehearsing Passwords

We introduce quantitative usability and security models to guide the design of password management schemes --- systematic strategies to help users create and remember multiple passwords. In the same way that security proofs in cryptography are based on complexity-theoretic assumptions (e.g., hardness of factoring and discrete logarithm), we quantify usability by introducing usability assumptions. In particular, password management relies on assumptions about human memory, e.g., that a user who follows a particular rehearsal schedule will successfully maintain the corresponding memory. These assumptions are informed by research in cognitive science and validated through empirical studies. Given rehearsal requirements and a user's visitation schedule for each account, we use the total number of extra rehearsals that the user would have to do to remember all of his passwords as a measure of the usability of the password scheme. Our usability model leads us to a key observation: password reuse benefits users not only by reducing the number of passwords that the user has to memorize, but more importantly by increasing the natural rehearsal rate for each password. We also present a security model which accounts for the complexity of password management with multiple accounts and associated threats, including online, offline, and plaintext password leak attacks. Observing that current password management schemes are either insecure or unusable, we present Shared Cues--- a new scheme in which the underlying secret is strategically shared across accounts to ensure that most rehearsal requirements are satisfied naturally while simultaneously providing strong security. The construction uses the Chinese Remainder Theorem to achieve these competing goals

Visual Pixel Expansion of Secret Image

Two common drawbacks of the visual cryptography scheme VCS are the large pixel expansion of each share image and the small contrast of the recovered secret image In this paper we propose a step construction to construct VCSOR and VCSXOR for general access structure by applying 2 2 -VCS recursively where a participant may receive multiple share images The proposed step construction generates VCSOR and VCSXOR which have optimal pixel expansion and contrast for each qualified set in the general access structure in most cases Our scheme applies a technique to simplify the access structure which can reduce the average pixel expansion APE in most cases compared with many of the results in the literature Finally we give some experimental results and comparisons to show the effectiveness of the proposed schem

On Split-State Quantum Tamper Detection and Non-Malleability

Tamper-detection codes (TDCs) and non-malleable codes (NMCs) are now fundamental objects at the intersection of cryptography and coding theory. Both of these primitives represent natural relaxations of error-correcting codes and offer related security guarantees in adversarial settings where error correction is impossible. While in a TDC, the decoder is tasked with either recovering the original message or rejecting it, in an NMC, the decoder is additionally allowed to output a completely unrelated message. In this work, we study quantum analogs of one of the most well-studied adversarial tampering models: the so-called split-state tampering model. In the $t$-split-state model, the codeword (or code-state) is divided into $t$ shares, and each share is tampered with "locally". Previous research has primarily focused on settings where the adversaries' local quantum operations are assisted by an unbounded amount of pre-shared entanglement, while the code remains unentangled, either classical or separable. We construct quantum TDCs and NMCs in several $\textit{resource-restricted}$ analogs of the split-state model, which are provably impossible using just classical codes. In particular, against split-state adversaries restricted to local (unentangled) operations, local operations and classical communication, as well as a "bounded storage model" where they are limited to a finite amount of pre-shared entanglement. We complement our code constructions in two directions. First, we present applications to designing secret sharing schemes, which inherit similar non-malleable and tamper-detection guarantees. Second, we discuss connections between our codes and quantum encryption schemes, which we leverage to prove singleton-type bounds on the capacity of certain families of quantum NMCs in the split-state model

Visual cryptography with cheating shares

Visual cryptography is a technique that applies the human visual system to decode encrypted information, such as text, image and number, without any sophisticated devices and computing capabilities. Therefore, compared with the traditional cryptography, it is apparent that it saves a large amount of time and money on devices and computations. Also, visual cryptography provides the convenience for humans to carry out decryption with a portal card which is significant to the business application. In the past decade, visual cryptography has been thoroughly researched not only on its contrast and subpixel expansion, but also on its applications. The main contribution of this thesis is the security of visual cryptography related to the dishonest shareholders. This is the first known work concerning this variety of potentially secure problem. In the previous papers, the shareholders are inherently honest. However, in the real world, it is impossible to guarantee that every shareholder would be honest forever(e.g., because of the interest of business or military, some shareholders might change to be the traitors). Therefore, a new method based on visual authentication[16] is proposed and the improvement is also made. In this thesis, we also review the previous papers on different fields of the visual cryptography