There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

From the Publisher:
A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols; more than 200 tables and figures; more than 1,000 numbered definitions, facts, examples, notes, and remarks; and over 1,250 significant references, including brief comments on each paper.

Handbook of Applied Cryptography

PROBLEM TO BE SOLVED: To solve the problem, wherein it is impossible for an electronic content information provider to provide commercially secure and effective method, for a configurable general-purpose electronic commercial transaction/distribution control system. SOLUTION: In this system, having at least one protected processing environment for safely controlling at least one portion of decoding of digital information, a secure content distribution method comprises a process for encapsulating digital information in one or more digital containers; a process for encrypting at least a portion of digital information; a process for associating at least partially secure control information for managing interactions with encrypted digital information and/or digital container; a process for delivering one or more digital containers to a digital information user; and a process for using a protected processing environment, for safely controlling at least a portion of the decoding of the digital information. COPYRIGHT: (C)2006,JPO&NCIPI

https://apps.dtic.mil/dtic/tr/fulltext/u2/a423264.pdf

Systems and Methods for Secure Transaction Management and Electronic Rights Protection

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

We propose a fully functional identity-based encryption scheme (IBE). The scheme has chosen ciphertext security in the random oracle model assuming an elliptic curve variant of the computational Diffie-Hellman problem. Our system is based on the Weil pairing. We give precise definitions for secure identity based encryption schemes and give several applications for such systems.

/pdf/identity-based-encryption-from-the-weil-pairing-sfqdyadlbb.pdf

Identity-Based Encryption from the Weil Pairing

The papers in this volume were presented at the 5th Innovations in Theoretical Computer Science (ITCS 2014) conference, sponsored by the ACM Special Interest Group on Algorithms and Computation Theory (SIGACT). The conference was held in Princeton, New Jersey, USA, January 11--14, 2014. ITCS (previously known as ICS) seeks to promote research that carries a strong conceptual message, for instance, introducing a new concept or model, opening a new line of inquiry within traditional or cross-interdisciplinary areas, or introducing new techniques or new applications of known techniques).

The call for papers welcomed all submissions, whether aligned with current theory of computation research directions or deviating from them. Altogether 116 submissions were received worldwide. Of these the program committee selected 48 papers. The accepted papers cover a wide range of topics in theoretical computer science, including algorithms, complexity, cryptography, learning, data privacy, quantum, physical and biological computing and relations between computing and social sciences. In addition to the selected papers the committee invited Professor Peter Winkler of Dartmouth to give an evening talk and we are grateful for his acceptance. Another evening was devoted to "Graduating Bits" - short talks by recent graduates.

The program committee consisted of 24 members (plus the chair): Deeparnab Chakrabarty (Microsoft Research India), Timothy Chan (University of Waterloo), Costis Daskalakis (MIT), Yuval Emek (ETH and Technion), Kousha Etessami (University of Edinburgh), Yuval Filmus (University of Toronto and Simons Institute, Berkeley), Arpita Ghosh (Cornell University), Monika Henzinger (University of Vienna), Sandy Irani (University of California Irvine), Michael nKearns (University of Pennsylvania), Lap Chi Lau (The Chinese University of Hong Kong), Nati Linial (Hebrew University of Jerusalem), Kobbi Nissim (Ben-Gurion University), Rasmus Pagh (IT University of Copenhagen), Shubhangi Saraf (Rutgers University), Ola Svensson (EPFL), Vinod Vaikuntanathan (University of Toronto and MIT), Jan Vondrak (IBM Almaden Research Center), Manfred Warmuth (University of California, Santa Cruz), Daniel Wichs (Northeastern University), Udi Wieder (Microsoft Research SVC), Ryan Williams (Stanford University), Ronald de Wolf (CWI and University of Amsterdam), David Xiao (CNRS and Universite Paris 7). I wish to express my admiration for their hard work of reading, evaluating and debating the merits of the submissions. The many individuals who assisted the reviewing process as subreviewers and extended the expertise of the committee deserve acknowledgments as well.

Proceedings of the 5th conference on Innovations in theoretical computer science

On Chosen Ciphertext Security of Multiple Encryptions.

We are interested in constructing short two-message arguments for various languages, where the complexity of the verifier is small e.g. linear in the input size, or even sublinear if the input is coded appropriately.

In 2000 Aiello et al. suggested the tantalizing possibility of obtaining such arguments for all of NP. These have proved elusive, despite extensive efforts. Our work builds on the compiler of Kalai and Raz, which takes as input an interactive proof system consisting of several rounds and produces a two-message argument system. The proof of soundness of their compiler relies on superpolynomial hardness assumptions.

In this work we obtain a succinct two-message argument system for any language in NC, where the verifier's work is linear or even polylogarithmic. Soundness relies on any standard polynomially hard private information retrieval scheme or fully homomorphic encryption scheme. This is the first non trivial two-message succinct argument system that is based on a standard polynomial-time hardness assumption. We obtain this result by proving that the compiler is sound under standard polynomial hardness assumptions if the verifier in the original protocol runs in logarithmic space and public coins. We obtain our two-message argument by applying the compiler to an interactive proof protocol of Goldwasser, Kalai and Rothblum. On the other hand, we prove that under standard assumptions there is a sound interactive proof protocol that, when run through the compiler, results in a protocol that is not sound.

Spooky Interaction and its Discontents: Compilers for Succinct Two-Message Argument Systems.

To distinguish between random generation in bounded, as opposed to expected, polynomial time, a model of Probabalisic Turing Machine (PTM) with the ability to make random choices with any (small) rational bias is necessary. This ability is equivalent to that of being able to simulate rolling any k-sided die (where |k| is polynomial in the length of the input). We would like to minimize the amount of hardware required for a machine with this capability. This leads to the problem of efficiently simulating a family of dice with as few different types of biased coins as possible.

On Dice and Coins: Models of Computation for Random Generation

We describe an implicit data structure for n multikey records that supports searching for a record, under any key, in the asymptotically optimal search time O(log n). This improves on [Mun87] in which Munro describes an implicit data structure for the problem of storing n k-key records so that search on any key can be performed in O(logkn(log log n)k-1) comparisons. The theoretical tools we develop also yield practical schemes that either halve the number of memory references over obvious solutions to the non-implicit version of the problem, or alternatively reduce the number of pointers involved significantly.

Moni Naor

Papers

Proceedings of the 5th conference on Innovations in theoretical computer science

On Chosen Ciphertext Security of Multiple Encryptions.

Spooky Interaction and its Discontents: Compilers for Succinct Two-Message Argument Systems.

On Dice and Coins: Models of Computation for Random Generation

Storing and searching a multikey table