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Quantum Proofs
  • Language: en
  • Pages: 232

Quantum Proofs

Quantum Proofs provides an overview of many of the known results concerning quantum proofs, computational models based on this concept, and properties of the complexity classes they define. In particular, it discusses non-interactive proofs and the complexity class QMA, single-prover quantum interactive proof systems and the complexity class QIP, statistical zero-knowledge quantum interactive proof systems and the complexity class QSZK, and multiprover interactive proof systems and the complexity classes QMIP, QMIP*, and MIP*. Quantum Proofs is mainly intended for non-specialists having a basic background in complexity theory and quantum information. A typical reader may be a student or researcher in either area desiring to learn about the fundamentals of the (actively developing) theory of quantum interactive proofs.

Geometric Aspects of Functional Analysis
  • Language: en
  • Pages: 350

Geometric Aspects of Functional Analysis

Continuing the theme of the previous volumes, these seminar notes reflect general trends in the study of Geometric Aspects of Functional Analysis, understood in a broad sense. Two classical topics represented are the Concentration of Measure Phenomenon in the Local Theory of Banach Spaces, which has recently had triumphs in Random Matrix Theory, and the Central Limit Theorem, one of the earliest examples of regularity and order in high dimensions. Central to the text is the study of the Poincaré and log-Sobolev functional inequalities, their reverses, and other inequalities, in which a crucial role is often played by convexity assumptions such as Log-Concavity. The concept and properties of...

Mathematics and Computation
  • Language: en
  • Pages: 434

Mathematics and Computation

From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theo...

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
  • Language: en
  • Pages: 794

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques

This book constitutes the joint refereed proceedings of the 13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010, and the 14th International Workshop on Randomization and Computation, RANDOM 2010, held in Barcelona, Spain, in September 2010. The 28 revised full papers of the APPROX 2010 workshop and the 29 revised full papers of the RANDOM 2010 workshop included in this volume, were carefully reviewed and selected from 66 and 61 submissions, respectively. APPROX focuses on algorithmic and complexity issues surrounding the development of efficient approximate solutions to computationally difficult problems. RANDOM is concerned with applications of randomness to computational and combinatorial problems.

Theory of Cryptography
  • Language: en
  • Pages: 661

Theory of Cryptography

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The Best Writing on Mathematics 2021
  • Language: en
  • Pages: 303

The Best Writing on Mathematics 2021

The year’s finest mathematical writing from around the world This annual anthology brings together the year’s finest mathematics writing from around the world—and you don’t need to be a mathematician to enjoy the pieces collected here. These essays—from leading names and fresh new voices—delve into the history, philosophy, teaching, and everyday aspects of math, offering surprising insights into its nature, meaning, and practice, and taking readers behind the scenes of today’s hottest mathematical debates. Here, Viktor Blåsjö gives a brief history of “lockdown mathematics”; Yelda Nasifoglu decodes the politics of a seventeenth-century play in which the characters are geometric shapes; and Andrew Lewis-Pye explains the basic algorithmic rules and computational procedures behind cryptocurrencies. In other essays, Terence Tao candidly recalls the adventures and misadventures of growing up to become a leading mathematician; Natalie Wolchover shows how old math gives new clues about whether time really flows; and David Hand discusses the problem of “dark data”—information that is missing or ignored. And there is much, much more.

Advances in Cryptology – CRYPTO 2013
  • Language: en
  • Pages: 570

Advances in Cryptology – CRYPTO 2013

  • Type: Book
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  • Published: 2013-08-15
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  • Publisher: Springer

The two volume-set, LNCS 8042 and LNCS 8043, constitutes the refereed proceedings of the 33rd Annual International Cryptology Conference, CRYPTO 2013, held in Santa Barbara, CA, USA, in August 2013. The 61 revised full papers presented in LNCS 8042 and LNCS 8043 were carefully reviewed and selected from numerous submissions. Two abstracts of the invited talks are also included in the proceedings. The papers are organized in topical sections on lattices and FHE; foundations of hardness; cryptanalysis; MPC - new directions; leakage resilience; symmetric encryption and PRFs; key exchange; multi linear maps; ideal ciphers; implementation-oriented protocols; number-theoretic hardness; MPC - foundations; codes and secret sharing; signatures and authentication; quantum security; new primitives; and functional encryption.

Advances in Cryptology – CRYPTO 2019
  • Language: en
  • Pages: 865

Advances in Cryptology – CRYPTO 2019

  • Type: Book
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  • Published: 2019-08-09
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  • Publisher: Springer

The three-volume set, LNCS 11692, LNCS 11693, and LNCS 11694, constitutes the refereed proceedings of the 39th Annual International Cryptology Conference, CRYPTO 2019, held in Santa Barbara, CA, USA, in August 2019. The 81 revised full papers presented were carefully reviewed and selected from 378 submissions. The papers are organized in the following topical sections: Part I: Award papers; lattice-based ZK; symmetric cryptography; mathematical cryptanalysis; proofs of storage; non-malleable codes; SNARKs and blockchains; homomorphic cryptography; leakage models and key reuse. Part II: MPC communication complexity; symmetric cryptanalysis; (post) quantum cryptography; leakage resilience; memory hard functions and privacy amplification; attribute based encryption; foundations. Part III: Trapdoor functions; zero knowledge I; signatures and messaging; obfuscation; watermarking; secure computation; various topics; zero knowledge II; key exchange and broadcast encryption.

Advances in Cryptology - CRYPTO 2024
  • Language: en
  • Pages: 511

Advances in Cryptology - CRYPTO 2024

Zusammenfassung: The 10-volume set, LNCS 14920-14929 constitutes the refereed proceedings of the 44th Annual International Cryptology Conference, CRYPTO 2024. The conference took place at Santa Barbara, CA, USA, during August 18-22, 2024. The 143 full papers presented in the proceedings were carefully reviewed and selected from a total of 526 submissions. The papers are organized in the following topical sections: Part I: Digital signatures; Part II: Cloud cryptography; consensus protocols; key exchange; public key encryption; Part III: Public-key cryptography with advanced functionalities; time-lock cryptography; Part IV: Symmetric cryptanalysis; symmetric cryptograph; Part V: Mathematical assumptions; secret sharing; theoretical foundations; Part VI: Cryptanalysis; new primitives; side-channels and leakage; Part VII: Quantum cryptography; threshold cryptography; Part VIII: Multiparty computation; Part IX: Multiparty computation; private information retrieval; zero-knowledge; Part X: Succinct arguments.

Bell Nonlocality
  • Language: en
  • Pages: 239

Bell Nonlocality

The development of quantum technologies has seen a tremendous upsurge in recent years, and the theory of Bell nonlocality has been key in making these technologies possible. Bell nonlocality is one of the most striking discoveries triggered by quantum theory. It states that in some situations, measurements of physical systems do not reveal pre-existing properties; rather, the property is created by the measurement itself. In 1964, John Bell demonstrated that the predictions of quantum theory are incompatible with the assumption that outcomes are predetermined. This phenomenon has been observed beyond any doubt in the last decades. It is an observation that is here to stay, even if quantum th...