Titlebook: Mathematical Modelling for Next-Generation Cryptography; CREST Crypto-Math Pr Tsuyoshi Takagi,Masato Wakayama,Dung Hoang Duong Book 2018 Sp

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On Analysis of Recovering Short Generator Problems via Upper and Lower Bounds of Dirichlet ,-Functior and lower bounds of Dirichlet .-functions which will be applied to security analysis of ideal lattice-based cryptography for cyclotomic fields explained in Part 2 (S. Okumura, On analysis of recovering short generator problems via upper and lower bounds of Dirichlet .-functions : Part 2 [.]).

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Spectra of Group-Subgroup Pair Graphs fact, we give an explicit formula of the eigenvalues of such graphs when the corresponding subgroups are abelian in terms of the characters of the subgroups as well as give a lower bound estimation for the second largest eigenvalues.

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Recent Progress on Coppersmith’s Lattice-Based Method: A Surveyeral strategy could not fully capture the algebraic structure of the target polynomials. Thus, some sophisticated techniques that can deeply exploit the algebraic relations have been proposed. In this paper, we give a survey of these recent approaches for lattice constructions, and also give small examples to show how these approaches work.

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Code-Based Zero-Knowledge Protocols and Their Applicationsf of plaintext knowledge for the code-based public key encryption schemes: the one by McEliece and the one by Niederreiter, respectively. Finally, we briefly discuss verifiable encryption and digital signatures as applications.

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Uniform Random Number Generation and Secret Key Agreement for General Sources by Using Sparse Matrictroduce the notion of the balanced-coloring property and the collision-resistance property. We next apply these properties to the problems. Since an ensemble of sparse matrices (with logarithmic column weight) over a finite field satisfies these properties, we can construct a code achieving the fundamental limits by using sparse matrices.

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A Mixed Integer Quadratic Formulation for the Shortest Vector Problemce of the shortest vector problem. This approach is a potential technique to improve the performance of the state-of-the-art software for mixed integer programming problems. In fact, we observe that this technique improves the numerical performance for TU Darmstadt’s benchmark instances with the dimension up to 49.

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2198-350X thematical physics.Contributes to a better understanding of This book presents the mathematical background underlying security modeling in the context of next-generation cryptography. By introducing new mathematical results in order to strengthen information security, while simultaneously presenting

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Book 2018tical results in order to strengthen information security, while simultaneously presenting fresh insights and developing the respective areas of mathematics, it is the first-ever book to focus on areas that have not yet been fully exploited for cryptographic applications such as representation theor

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