Lattices are geometric objects that can be pictorially described as the set of intersection points of an infinite, regular n-dimensional grid. De spite their apparent simplicity, lattices hide a rich combinatorial struc ture, which has attracted the attention of great mathematicians over the last two centuries. Not surprisingly, lattices have found numerous ap plications in mathematics and computer science, ranging from number theory and Diophantine approximation, to combinatorial optimization and cryptography. The study of lattices, specifically from a computational point of view, was marked by two major breakthroughs: the development of the LLL lattice reduction algorithm by Lenstra, Lenstra and Lovasz in the early 80's, and Ajtai's discovery of a connection between the worst-case and average-case hardness of certain lattice problems in the late 90's. The LLL algorithm, despite the relatively poor quality of the solution it gives in the worst case, allowed to devise polynomial time solutions to many classical problems in computer science. These include, solving integer programs in a fixed number of variables, factoring polynomials over the rationals, breaking knapsack based cryptosystems, and finding solutions to many other Diophantine and cryptanalysis problems."

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.

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.

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.

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 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 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.

Lattices are geometric objects that can be pictorially described as the set of intersection points of an infinite, regular n-dimensional grid. De spite their apparent simplicity, lattices hide a rich combinatorial struc ture, which has attracted the attention of great mathematicians over the last two centuries. Not surprisingly, lattices have found numerous ap plications in mathematics and computer science, ranging from number theory and Diophantine approximation, to combinatorial optimization and cryptography. The study of lattices, specifically from a computational point of view, was marked by two major breakthroughs: the development of the LLL lattice reduction algorithm by Lenstra, Lenstra and Lovasz in the early 80's, and Ajtai's discovery of a connection between the worst-case and average-case hardness of certain lattice problems in the late 90's. The LLL algorithm, despite the relatively poor quality of the solution it gives in the worst case, allowed to devise polynomial time solutions to many classical problems in computer science. These include, solving integer programs in a fixed number of variables, factoring polynomials over the rationals, breaking knapsack based cryptosystems, and finding solutions to many other Diophantine and cryptanalysis problems."

TCC2010, the7thTheoryofCryptographyConference, washeldatETHZurich, Zurich, Switzerland, during February 9-11, 2010. TCC 2010 was sponsored by theInternationalAssociationofCryptologicResearch(IACR)andwasorganized in cooperation with the Information Security and Cryptography group at ETH Zurich.The GeneralChairsof the conferencewereMartin Hirt andUeli Maurer. The conference received 100 submissions, of which the Program Committee selected 33 for presentation at the conference. The Best Student Paper Award was given to Kai-Min Chung and Feng-Hao Liu for their paper "ParallelRepe- tion Theorems for Interactive Arguments." These proceedings consist of revised versions of those 33 papers. The revisions were not reviewed, and the authors bearfull responsibility forthe contentsoftheir papers.Inadditionto the regular papers, the conference featured two invited talks: "Secure Computation and Its Diverse Applications," given by Yuval Ishai and "Privacy-Enhancing Crypt- raphy: From Theory Into Practice," given by Jan Camenisch. Abstracts of the invited talks are also included in this volume. As in previous years, TCC received a steady stream of high-quality s- missions. Consequently, the selection process was very rewarding, but also very challenging, as a number of good papers could not be accepted due to lack of space. I would like to thank the TCC Steering Committee, and its Chair Oded Goldreich, for entrusting me with the responsibility of selecting the conference program.Since its inception, TCChas been verysuccessfulin attracting someof the best work in theoretical cryptography every year and o?ering a compelling program to its audience. I am honored I had the opportunity to contribute to the continuation of the success of the conference.