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A survey of pseudorandomness, the theory of efficiently generating objects that look random despite being constructed using little or no randomness. This theory has significance for areas in computer science and mathematics, including computational complexity, algorithms, cryptography, combinatorics, communications, and additive number theory.
A pseudorandom generator is an easy-to-compute function that stretches a short random string into a much longer string that "looks" just like a random string to any efficient adversary. One immediate application of a pseudorandom generator is the construction of a private key cryptosystem that is secure against chosen plaintext attack. There do not seem to be natural examples of functions that are pseudorandom generators. On the other hand, there do seem to be a variety of natural examples of another basic primitive: the one-way function. A function is one-way if it is easy to compute but hard for any efficient adversary to invert on average. The first half of the book shows how to construct a pseudorandom generator from any one-way function. Building on this, the second half of the book shows how to construct other useful cryptographic primitives, such as private key cryptosystems, pseudorandom function generators, pseudorandom permutation generators, digital signature schemes, bit commitment protocols, and zero-knowledge interactive proof systems. The book stresses rigorous definitions and proofs.
Cryptography is one of the most active areas in current mathematics research and applications. This book focuses on cryptography along with two related areas: the study of probabilistic proof systems, and the theory of computational pseudorandomness. Following a common theme that explores the interplay between randomness and computation, the important notions in each field are covered, as well as novel ideas and insights.
The primer assumes basic familiarity with the notion of efficient algorithms and with elementary probability theory, but provides a basic introduction to all notions that are actually used. as a result, the primer is essentially self-contained, although the interested reader is at times referred to other sources for more detail. --Book Jacket.
This book constitutes the proceedings of the International Conference on Trusted Systems, held in Beijing, China, in December 2009.
This book is based on the invited talks of the "RICAM-Workshop on Finite Fields and Their Applications: Character Sums and Polynomials" held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 2-7, 2012. Finite fields play important roles in many application areas such as coding theory, cryptography, Monte Carlo and quasi-Monte Carlo methods, pseudorandom number generation, quantum computing, and wireless communication. In this book we will focus on sequences, character sums, and polynomials over finite fields in view of the above mentioned application areas: Chapters 1 and 2 deal with sequences mainly constructed via characters and analyzed using bounds on character sums. Chapters 3, 5, and 6 deal with polynomials over finite fields. Chapters 4 and 9 consider problems related to coding theory studied via finite geometry and additive combinatorics, respectively. Chapter 7 deals with quasirandom points in view of applications to numerical integration using quasi-Monte Carlo methods and simulation. Chapter 8 studies aspects of iterations of rational functions from which pseudorandom numbers for Monte Carlo methods can be derived. The goal of this book is giving an overview of several recent research directions as well as stimulating research in sequences and polynomials under the unified framework of character theory.
Conference on Cryptologic Research, CRYPTO 2020, which was held during August 17–21, 2020. Crypto has traditionally been held at UCSB every year, but due to the COVID-19 pandemic it will be an online event in 2020. The 85 papers presented in the proceedings were carefully reviewed and selected from a total of 371 submissions. They were organized in topical sections as follows: Part I: Security Models; Symmetric and Real World Cryptography; Hardware Security and Leakage Resilience; Outsourced encryption; Constructions. Part II: Public Key Cryptanalysis; Lattice Algorithms and Cryptanalysis; Lattice-based and Post Quantum Cryptography; Multi-Party Computation. Part III: Multi-Party Computation; Secret Sharing; Cryptanalysis; Delay functions; Zero Knowledge.
Cryptography is concerned with the construction of schemes that withstand any abuse. A cryptographic scheme is constructed so as to maintain a desired functionality, even under malicious attempts aimed at making it deviate from its prescribed behavior. The design of cryptographic systems must be based on firm foundations, whereas ad hoc approaches and heuristics are a very dangerous way to go. These foundations were developed mostly in the 1980s, in works that are all co-authored by Shafi Goldwasser and/or Silvio Micali. These works have transformed cryptography from an engineering discipline, lacking sound theoretical foundations, into a scientific field possessing a well-founded theory, which influences practice as well as contributes to other areas of theoretical computer science. This book celebrates these works, which were the basis for bestowing the 2012 A.M. Turing Award upon Shafi Goldwasser and Silvio Micali. A significant portion of this book reproduces some of these works, and another portion consists of scientific perspectives by some of their former students. The highlight of the book is provided by a few chapters that allow the readers to meet Shafi and Silvio in person. These include interviews with them, their biographies and their Turing Award lectures.
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.
The three volume-set, LNCS 10991, LNCS 10992, and LNCS 10993, constitutes the refereed proceedings of the 38th Annual International Cryptology Conference, CRYPTO 2018, held in Santa Barbara, CA, USA, in August 2018. The 79 revised full papers presented were carefully reviewed and selected from 351 submissions. The papers are organized in the following topical sections: secure messaging; implementations and physical attacks prevention; authenticated and format-preserving encryption; cryptoanalysis; searchable encryption and differential privacy; secret sharing; encryption; symmetric cryptography; proofs of work and proofs of stake; proof tools; key exchange; symmetric cryptoanalysis; hashes and random oracles; trapdoor functions; round optimal MPC; foundations; lattices; lattice-based ZK; efficient MPC; quantum cryptography; MPC; garbling; information-theoretic MPC; oblivious transfer; non-malleable codes; zero knowledge; and obfuscation.