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

I have developed "tennis elbow" from lugging this book around the past four weeks, but it is worth the pain, the effort, and the aspirin. It is also worth the (relatively speaking) bargain price. Including appendixes, this book contains 894 pages of text. The entire panorama of the neural sciences is surveyed and examined, and it is comprehensive in its scope, from genomes to social behaviors. The editors explicitly state that the book is designed as "an introductory text for students of biology, behavior, and medicine," but it is hard to imagine any audience, interested in any fragment of neuroscience at any level of sophistication, that would not enjoy this book. The editors have done a masterful job of weaving together the biologic, the behavioral, and the clinical sciences into a single tapestry in which everyone from the molecular biologist to the practicing psychiatrist can find and appreciate his or

Principles of Neural Science

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

This paper presents a secure (tamper-resistant) algorithm for watermarking images, and a methodology for digital watermarking that may be generalized to audio, video, and multimedia data. We advocate that a watermark should be constructed as an independent and identically distributed (i.i.d.) Gaussian random vector that is imperceptibly inserted in a spread-spectrum-like fashion into the perceptually most significant spectral components of the data. We argue that insertion of a watermark under this regime makes the watermark robust to signal processing operations (such as lossy compression, filtering, digital-analog and analog-digital conversion, requantization, etc.), and common geometric transformations (such as cropping, scaling, translation, and rotation) provided that the original image is available and that it can be successfully registered against the transformed watermarked image. In these cases, the watermark detector unambiguously identifies the owner. Further, the use of Gaussian noise, ensures strong resilience to multiple-document, or collusional, attacks. Experimental results are provided to support these claims, along with an exposition of pending open problems.

http://dns2.asia.edu.tw/~ysho/YSHO-English/2000%20Engineering/PDF/IEE%20Tra%20Ima%20Pro6,%201673.pdf

Secure spread spectrum watermarking for multimedia

We present an e-cash scheme which provides a trade-off between anonymity and efficiency, by amortizingth e cost of zero-knowledge and signature computation in the cash generation phase.Our work solves an open problem of Okamoto in divisible e-cash. Namely, we achieve results similar to those of Okamoto, but (1) based on traditional complexity assumptions (rather than ad hoc ones), and (2) within a much crisper definitional framework that highlights the anonymity properties, and (3) in a simple fashion.

Amortized E-Cash

We present a new, decentralized, efficient, and secure digital cryptocurrency, in which the ordinary users themselves keep turns to ensure that the systems works well. ∗sergeyg@mit.edu †silvio@csail.mit.edu

/pdf/democoin-a-publicly-verifiable-and-jointly-serviced-103n222m3c.pdf

Democoin: A Publicly Verifiable and Jointly Serviced Cryptocurrency.

We relate the strategy sets that a player ends up with after refining his own strategies according to two very different models of rationality: namely, utility maximization and regret minimization.

Bridging Utility Maximization and Regret Minimization

We investigate the resilience of some classical mechanisms to alternative specifications of preferences and information structures. Specifically, we analyze the Vickrey mechanism for auctions of multiple identical goods when the only information a player $i$ has about the profile of true valuations, $\theta^*$, consists of a set of distributions, from one of which $\theta_i^*$ has been drawn. 
In this setting, the players no longer have complete preferences, and the Vickrey mechanism is no longer dominant-strategy. However, we prove that its efficiency performance is excellent, and essentially optimal, in undominated strategies.

Knightian Robustness of the Vickrey Mechanism.

In auctions of a single good, the second-price mechanism achieves, in dominant strategies, a revenue benchmark that is naturally high and resilient to any possible collusion. We show how to achieve, to the maximum extent possible, the same properties in combinatorial auctions. ∗This Technical Memo improves on material submitted to FOCS 2007, SODA 2008, and the Library of Congress. 1 The Problem of Guaranteeing Revenue in Combinatorial Auctions 1.1 Combinatorial Auctions and Their Basic Revenue Problem A (non-Bayesian, n × m) combinatorial-auction context is described as follows. There is a set of players N = {1, . . . , n} and a set of m goods G. A valuation is a function from G’s subsets to R+, and each player i has a secret valuation TVi, which we refer to as i’s true valuation. An outcome consists of (1) a profile (i.e., a vector indexed by the players) P = P1, . . . , Pn, where Pi ∈ R+ is the price to be paid by player i, and (2) an allocation A = A0, A1, . . . , An, where Ai is the subset of goods allocated to player i, and A0 the set of unallocated goods. For each outcome (A,P ), the utility of each player i is defined to be TVi(Ai) − Pi; that is, i’s true value of the goods allocated to him minus the price he pays. Note that such a context is fully described by just N , G, and the true-valuation profile TV , since these determine outcomes and utilities. For such a context, a combinatorial-auction mechanism is a (possibly probabilistic) function M mapping a profile of valuations V to an outcome (A,P ) such that Pi = 0 whenever Vi is the null valuation —the opt-out condition. An n ×m context C = (N,G, TV ) and an n ×m mechanism M define a (n ×m) combinatorial auction (C,M): namely, the game G envisaged to be played as follows. First, each player i (independently of the others) chooses a valuation BIDi on inputs TVi, N , and G. Then, an outcome (A,P ) is obtained by evaluating M on BID. We refer to the so chosen valuations as bids, to emphasize that they need not coincide with the players’ true valuations. In such a game, a strategy is a (possibly probabilistic) way for a player to choose his bid. Since the players’ true valuation are not publicly known, generating high revenue requires a careful design of the mechanism. As for any game, in a rational play of an auction the players end up selecting an equilibrium, that is, a profile of strategies σ = (σ1, . . . , σn) such that no player i has an incentive to deviate from his strategy σi if the other players stick to theirs. Accordingly, the basic revenue problem can be informally stated as follows: find a mechanism M such that, for every context C, the resulting combinatorial auction (C,M) yields high revenue for every equilibrium σ the players may reasonably select. Since computational efficiency is not a traditional concern of game theory, we shall not be concerned about M ’s efficiency either. 1.2 The Worst Natural Setting and Natural Solution-Pairs The basic revenue problem for combinatorial auctions is already difficult. Yet, we wish to investigate and provide solutions to a more adversarial version of it: namely, the problem of generating revenue in the worst natural setting. We characterize such a setting by the following three assumptions. • Total Equilibrium Uncertainty. An auction having an equilibrium (or several equilibria) σ yielding high revenue may not “guarantee” high revenue at all. Indeed, as for any other game, an auction typically has plenty of equilibria, and rational players may ultimately select one other than σ. In the worst (rational) setting, we assume that the equilibrium ultimately selected will be the one generating least revenue among those equilibria τ having a “modicum of rationality,” that is, those composed by weakly non-dominated strategies.1 • Total Bayesian Ignorance. In a Bayesian setting, the players’ true valuations are assumed to be drawn from a distribution D. Clearly, knowledge of such a distribution can be very helpful for designing high-revenue mechanisms, particularly when D is of a suitable form.2 In the worst setting, however, no Bayesian information is available. Informally, a strategy τi is weakly dominated for player i if i has another strategy ψi that is always at least as good as τi and sometimes strictly better. For single-good auctions, Myerson [18] has put forward mechanisms that generate optimal revenue essentially whenever the players have independent valuations of the good, a quite general condition. For such a case, he is able to optimally set “minimum winning bids” without undue risk of pricing out players. By contrast, in combinatorial auctions no general distributions for the players’ true valuations are known for which optimal revenue mechanisms exist.

http://dspace.mit.edu/bitstream/handle/1721.1/39420/MIT-CSAIL-TR-2007-052.pdf?sequence=1

Silvio Micali

Papers

Amortized E-Cash

Democoin: A Publicly Verifiable and Jointly Serviced Cryptocurrency.

Bridging Utility Maximization and Regret Minimization

Knightian Robustness of the Vickrey Mechanism.

Collusion-Resilient Revenue In Combinatorial Auctions