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

On-line machine scheduling has been studied extensively, but the fundamental issue of fairness in scheduling is still mostly open. In this paper we explore the issue in settings where there are long-lived processes which should be repeatedly scheduled for various tasks throughout the lifetime of a system. For any such instance we develop a notion ofdesiredload of a process, which is a function of the tasks it participates in. Theunfairnessof a system is the maximum, taken over all processes, of the difference between the desired load and the actual load.An example of such a setting is thecarpool problemsuggested by Fagin and Williams IBM Journal of Research and Development27(2) (1983), 133?139]. In this problem, a set ofnpeople form a carpool. On each day a subset of the people arrive and one of them is designated as the driver. A scheduling rule is required so that the driver will be determined in a “fair” way.We investigate this problem under various assumptions on the input distribution. We also show that the carpool problems can capture several other problems of fairness in scheduling.

Fairness in scheduling

We study the sample complexity of learning threshold functions under the constraint of differential privacy. It is assumed that each labeled example in the training data is the information of one individual and we would like to come up with a generalizing hypothesis $h$ while guaranteeing differential privacy for the individuals. Intuitively, this means that any single labeled example in the training data should not have a significant effect on the choice of the hypothesis. This problem has received much attention recently; unlike the non-private case, where the sample complexity is independent of the domain size and just depends on the desired accuracy and confidence, for private learning the sample complexity must depend on the domain size $X$ (even for approximate differential privacy). Alon et al. (STOC 2019) showed a lower bound of $\Omega(\log^*|X|)$ on the sample complexity and Bun et al. (FOCS 2015) presented an approximate-private learner with sample complexity $\tilde{O}\left(2^{\log^*|X|}\right)$. In this work we reduce this gap significantly, almost settling the sample complexity. We first present a new upper bound (algorithm) of $\tilde{O}\left(\left(\log^*|X|\right)^2\right)$ on the sample complexity and then present an improved version with sample complexity $\tilde{O}\left(\left(\log^*|X|\right)^{1.5}\right)$.\n\nOur algorithm is constructed for the related interior point problem, where the goal is to find a point between the largest and smallest input elements. It is based on selecting an input-dependent hash function and using it to embed the database into a domain whose size is reduced logarithmically; this results in a new database, an interior point of which can be used to generate an interior point of the original database in a differentially private manner.

/pdf/privately-learning-thresholds-closing-the-exponential-gap-3pgy3ww0hb.pdf

Privately Learning Thresholds: Closing the Exponential Gap

We propose simple, realistic protocols for polling that allow the responder to plausibly repudiate his response, while at the same time allow accurate statistical analysis of poll results. The protocols use simple physical objects (envelopes or scratch-off cards) and can be performed without the aid of computers. One of the main innovations of this work is the use of techniques from theoretical cryptography to rigorously prove the security of a realistic, physical protocol. We show that, given a few properties of physical envelopes, the protocols are unconditionally secure in the universal composability framework.

/pdf/polling-with-physical-envelopes-a-rigorous-analysis-of-a-2x3gi25fsc.pdf

Polling with physical envelopes: a rigorous analysis of a human-centric protocol

The following file distribution problem is considered: Given a network of processors represented by an undirected graph $G=(V,E)$ and a file size $k$, an arbitrary file w of $k$ bits is to be distributed among all nodes of $G$. To this end, each node is assigned a memory device such that by accessing the memory of its own and of its adjacent nodes, the node can reconstruct the contents of w. The objective is to minimize the total size of memory in the network. This paper presents a file distribution scheme which realizes this objective for $k \gg \log \Delta_G$, where $\Delta_G$ stands for the maximum degree in $G$: For this range of $k$, the total memory size required by the suggested scheme approaches an integer programming lower bound on that size. The scheme is also constructive in the sense that given $G$ and $k$, the memory size at each node in $G$, as well as the mapping of any file w into the node memory devices, can be computed in time complexity which is polynomial in $k$ and $|V|$. Furthermore, each node can reconstruct the contents of such a file w in $O(k^2)$ bit operations. Finally, it is shown that the requirement of $k$ being much larger than $\log \Delta_G$ is necessary in order to have total memory size close to the integer programming lower bound.

/pdf/optimal-file-sharing-in-distributed-networks-22nxvyl1kj.pdf

Optimal File Sharing in Distributed Networks

This work presents threshold tracing schemes. Tracing schemes trace the source of keys which are used in pirate decoders for sensitive or proprietary data (such as pay-TV programs). Previous tracing schemes were designed to operate against any decoder which decrypts with a non-negligible success probability. We introduce threshold tracing schemes which are only designed to trace the source of keys of decoders which decrypt with probability greater than some threshold q (which is a parameter). These schemes present a dramatic reduction in the overhead compared to the previous constructions of tracing schemes. We argue that in many applications it is only required to protect against pirate decoders which have a decryption probability very close to 1 (for example, TV decoders). In such applications it is therefore very favorable to use threshold tracing schemes.

Moni Naor

Papers

Fairness in scheduling

Privately Learning Thresholds: Closing the Exponential Gap

Polling with physical envelopes: a rigorous analysis of a human-centric protocol

Optimal File Sharing in Distributed Networks

Threshold traitor tracing