Card-Based Zero-Knowledge Proof for Sudoku

In 2009, Gradwohl, Naor, Pinkas, and Rothblum proposed physical zero-knowledge proof protocols for Sudoku. That is, for a puzzle instance of Sudoku, their excellent protocols allow a prover to convince a verifier that there is a solution to the Sudoku puzzle and that he/she knows it, without revealing any information about the solution. The possible drawback is that the existing protocols have a soundness error with a non-zero probability or need special cards (such as scratch-off cards). Thus, in this study, we propose new protocols to perform zero-knowledge proof for Sudoku that use a normal deck of playing cards and have no soundness error. Our protocols can be easily implemented by humans with a reasonable number of playing cards

On Problems Equivalent to (min,+)-Convolution

In the recent years, significant progress has been made in explaining apparent hardness of improving over naive solutions for many fundamental polynomially solvable problems. This came in the form of conditional lower bounds -- reductions from a problem assumed to be hard. These include 3SUM, All-Pairs Shortest Paths, SAT and Orthogonal Vectors, and others. In the (min,+)-convolution problem, the goal is to compute a sequence c, where c[k] = min_i a[i]+b[k-i], given sequences a and b. This can easily be done in O(n^2) time, but no O(n^{2-eps}) algorithm is known for eps > 0. In this paper we undertake a systematic study of the (min,+)-convolution problem as a hardness assumption. As the first step, we establish equivalence of this problem to a group of other problems, including variants of the classic knapsack problem and problems related to subadditive sequences. The (min,+)-convolution has been used as a building block in algorithms for many problems, notably problems in stringology. It has also already appeared as an ad hoc hardness assumption. We investigate some of these connections and provide new reductions and other results

On the Query Complexity of Black-Peg AB-Mastermind

Mastermind is a two players zero sum game of imperfect information. Starting with Erd˝os and Rényi (1963), its combinatorics have been studied to date by several authors, e.g., Knuth (1977), Chvátal (1983), Goodrich (2009). The first player, called “codemaker”, chooses a secret code and the second player, called “codebreaker”, tries to break the secret code by making as few guesses as possible, exploiting information that is given by the codemaker after each guess. For variants that allow color repetition, Doerr et al. (2016) showed optimal results. In this paper, we consider the so called Black-Peg variant of Mastermind, where the only information concerning a guess is the number of positions in which the guess coincides with the secret code. More precisely, we deal with a special version of the Black-Peg game with n holes and k ≥ n colors where no repetition of colors is allowed. We present upper and lower bounds on the number of guesses necessary to break the secret code. For the case k = n, the secret code can be algorithmically identified within less than (n − 3)dlog 2 ne + 5 2 n − 1 queries. This result improves the result of Ker-I Ko and Shia-Chung Teng (1985) by almost a factor of 2. For the case k > n, we prove an upper bound of (n − 2)dlog 2 ne + k + 1. Furthermore, we prove a new lower bound of n for the case k = n, which improves the recent n − log log(n) bound of Berger et al. (2016). We then generalize this lower bound to k queries for the case k ≥ n

Generating Signed Permutations by Twisting Two-Sided Ribbons

We provide a simple and natural solution to the problem of generating all $2^n \cdot n!$ signed permutations of $[n] = \{1,2,\ldots,n\}$. Our solution provides a pleasing generalization of the most famous ordering of permutations: plain changes (Steinhaus-Johnson-Trotter algorithm). In plain changes, the $n!$ permutations of $[n]$ are ordered so that successive permutations differ by swapping a pair of adjacent symbols, and the order is often visualized as a weaving pattern involving $n$ ropes. Here we model a signed permutation using $n$ ribbons with two distinct sides, and each successive configuration is created by twisting (i.e., swapping and turning over) two neighboring ribbons or a single ribbon. By greedily prioritizing $2$-twists of the largest symbol before $1$-twists of the largest symbol, we create a signed version of plain change's memorable zig-zag pattern. We provide a loopless algorithm (i.e., worst-case $\mathcal{O}(1)$-time per object) by extending the well-known mixed-radix Gray code algorithm.Comment: 15 pages, 7 figure

A framework for SLA-centric service-based Utility Computing

Nicht angegebenService oriented Utility Computing paves the way towards realization of service markets, which promise metered services through negotiable Service Level Agreements (SLA). A market does not necessarily imply a simple buyer-seller relationship, rather it is the culmination point of a complex chain of stake-holders with a hierarchical integration of value along each link in the chain. In service value chains, services corresponding to different partners are aggregated in a producer-consumer manner resulting in hierarchical structures of added value. SLAs are contracts between service providers and service consumers, which ensure the expected Quality of Service (QoS) to different stakeholders at various levels in this hierarchy. \emph{This thesis addresses the challenge of realizing SLA-centric infrastructure to enable service markets for Utility Computing.} Service Level Agreements play a pivotal role throughout the life cycle of service aggregation. The activities of service selection and service negotiation followed by the hierarchical aggregation and validation of services in service value chain, require SLA as an enabling technology. \emph{This research aims at a SLA-centric framework where the requirement-driven selection of services, flexible SLA negotiation, hierarchical SLA aggregation and validation, and related issues such as privacy, trust and security have been formalized and the prototypes of the service selection model and the validation model have been implemented. } The formal model for User-driven service selection utilizes Branch and Bound and Heuristic algorithms for its implementation. The formal model is then extended for SLA negotiation of configurable services of varying granularity in order to tweak the interests of the service consumers and service providers. %and then formalizing the requirements of an enabling infrastructure for aggregation and validation of SLAs existing at multiple levels and spanning % along the corresponding service value chains. The possibility of service aggregation opens new business opportunities in the evolving landscape of IT-based Service Economy. A SLA as a unit of business relationships helps establish innovative topologies for business networks. One example is the composition of computational services to construct services of bigger granularity thus giving room to business models based on service aggregation, Composite Service Provision and Reselling. This research introduces and formalizes the notions of SLA Choreography and hierarchical SLA aggregation in connection with the underlying service choreography to realize SLA-centric service value chains and business networks. The SLA Choreography and aggregation poses new challenges regarding its description, management, maintenance, validation, trust, privacy and security. The aggregation and validation models for SLA Choreography introduce concepts such as: SLA Views to protect the privacy of stakeholders; a hybrid trust model to foster business among unknown partners; and a PKI security mechanism coupled with rule based validation system to enable distributed queries across heterogeneous boundaries. A distributed rule based hierarchical SLA validation system is designed to demonstrate the practical significance of these notions