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

Two computer scientists have created a video game about mice and elephants that can make computer encryption properly secure---as long as you play it randomly.

/pdf/games-for-extracting-randomness-30l13oyn1v.pdf

Games for extracting randomness

Non-oblivious hashing, where the information gathered by performing “unsuccessful” probes determines the probe strategy, is introduced and used to obtain the following results for static lookup on full tables: An O(1) worst case scheme that requires only logarithmic additional memory (improving on the [FKS84] linear space upper bound).An almost sure O(1) probabilistic worst case scheme, without any additional memory (improving on previous logarithmic time upper bounds).Enhancements to hashing: Solving (a) and (b) in the multikey record environment, search can be performed under any key in time O(1); finding the nearest neighbor, the rank, etc. in logarithmic time.Our non-oblivious upper bounds are much better than the appropriate oblivious lower bounds.

Non-oblivious hashing

We construct efficiently computable sequences of random-looking graphs that preserve properties of the canonical random graphs G (2n,p(n)). We focus on first-order graph properties, namely properties that can be expressed by a formula φ in the language where variables stand for vertices and the only relations are equality and adjacency (e.g. having an isolated vertex is a first-order property ∃x∀y(¬EDGE(x, y))). Random graphs are known to have remarkable structure w.r.t. first order properties, as indicated by the following 0/1 law: for a variety of choices of p(n), any fixed first-order property φ holds for G (2n,p(n)) with probability tending either to 0 or to 1 as n grows to infinity.

We first observe that similar 0/1 laws are satisfied by G (2n,p(n)) even w.r.t. sequences of formulas {φn}n∈ℕ with bounded quantifier depth, ${\it depth}(\phi_{n}) \leq {\frac {1}{{\rm lg} (1/p(n))}}$. We also demonstrate that 0/1 laws do not hold for random graphs w.r.t. properties of significantly larger quantifier depth. For most choices of p(n), we present efficient constructions of huge graphs with edge density nearly p(n) that emulate G (2n,p(n)) by satisfying ${\it \Theta} ({\frac {1}{{\rm lg} (1/p(n))}})-0/1$ laws. We show both probabilistic constructions (which also have other properties such as K-wise independence and being computationally indistinguishable from G (N,p(n)) ), and deterministic constructions where for each graph size we provide a specific graph that captures the properties of G (2n,p(n)) for slightly smaller quantifier depths.

/pdf/efficiently-constructible-huge-graphs-that-preserve-first-3ro6kzwxhj.pdf

Efficiently constructible huge graphs that preserve first order properties of random graphs

Given a distributed network of processors represented by an undirected graph G=(V, E) and a file size k, the problem of distributing an arbitrary file w of k bits among all nodes of the network G is considered. Memory devices are to be assigned to the node of G such that, by accessing the memory of its own and of its adjacent nodes, each node can reconstruct the contents of w. The objective is to minimize the total size memory in the network. A file distribution scheme that realizes this objective for k>>log Delta /sub G/, where Delta /sub G/, stands for the maximum degree in G, is presented. For this range of k, the total size of memory required by the suggested scheme approaches an integer programming lower bound on that size. >

/pdf/optimal-file-sharing-in-distributed-networks-30jvbgjwbi.pdf

Optimal file sharing in distributed networks

Kearns et al. [18] defined two notions for learning a distribution D. The first is with generator, where the learner presents a generator that outputs a distribution identical or close to D, The other is with an evahtat or, where the learner presents a procedure that on input z evaluates correctly (or approximates) the probability that x is generated by D. They showed an example where efficient learning by a generator is possible , but learning by an evaluator is computationally infeasible. Though it may seem that generation is, in general, easier than evaluation, in this paper we show that the converse may be true: we provide a class of distributions where efficient learning with an evaluator is possible, but coming up with a generator that approximates the given distribution is infeasible. We also show that some distributions may be learned (with either a generator or an evaluator) to within any ~ > 0, but the learned hypothesis must be of size proportional to l/e. This is in contrast to the distribution-free PAC model where the size of the hypothesis can always be proportional to log I/c. Permission to make digital/hard copies of all or patt of thk material for personal or classrmm use is granted without fee provided that the copies a-mnot ~de or dktributad for profit or commercial advantage, the copY-nght notice, the title of the publication and ita date appear, and notice is 1 Introduction The problem of learning a distribution D from several independent samples from D occupies a large part of Statistics and Pattern Recognition, However, only recently did Kearns et al. [18] put it in a comput ational setting. They distinguished between two notions of learning-evaluation and generation. In evaluation the goal of the learner is to be able to evaluate (or approximate) D[y]-the probability that D generates II, given y. In generation the goal of the learner is to construct a distribution D1 (i.e. a machine or a circuit whose output distribution is D' on uniformly random inputs) such that D' is as close as possible to D. In the setting of [18] there is a class of distributions Dn over {O, I}n. Members of Dn are generated by polynomial sized circuits. Such a class may be learned efficiently with a generator (with confidence 6 and approximation e): assuming that D ED. but is unknown, then given enough samples there is an (efi-cient) …

Moni Naor

Papers

Games for extracting randomness

Non-oblivious hashing

Efficiently constructible huge graphs that preserve first order properties of random graphs

Optimal file sharing in distributed networks

Evaluation may be easier than generation (extended abstract)