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.

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Identity-Based Encryption from the Weil Pairing

It is shown how to efficiently construct a small probability space on n binary random variables such that for every subset, its parity is either zero or one with “almost” equal probability. They are called $\epsilon $-biased random variables. The number of random bits needed to generate the random variables is $O(\log n + \log \frac{1}{\epsilon })$. Thus, if $\epsilon $ is polynomially small, then the size of the sample space is also polynomial. Random variables that are $\epsilon $-biased can be used to construct “almost” k-wise independent random variables where $\epsilon $ is a function of k.These probability spaces have various applications: l. Derandomization of algorithms: Many randomized algorithms that require only k-wise independence of their random bits (where k is bounded by $O(\log n)$), can be derandomized by using $\epsilon $-biased random variables. 2. Reducing the number of random bits required by certain randomized algorithms, e.g., verification of matrix multiplication. 3. Exhaustive tes...

Small-bias probability spaces: efficient constructions and applications

Differential privacy is a recent notion of privacy tailored to privacy-preserving data analysis [11]. Up to this point, research on differentially private data analysis has focused on the setting of a trusted curator holding a large, static, data set; thus every computation is a "one-shot" object: there is no point in computing something twice, since the result will be unchanged, up to any randomness introduced for privacy. However, many applications of data analysis involve repeated computations, either because the entire goal is one of monitoring, e.g., of traffic conditions, search trends, or incidence of influenza, or because the goal is some kind of adaptive optimization, e.g., placement of data to minimize access costs. In these cases, the algorithm must permit continual observation of the system's state. We therefore initiate a study of differential privacy under continual observation. We identify the problem of maintaining a counter in a privacy preserving manner and show its wide applicability to many different problems.

/pdf/differential-privacy-under-continual-observation-5em03vowyh.pdf

Differential privacy under continual observation

A fundamental problem in designing secure multi-party protocols is how to deal with adaptive adversaries (i.e., adversaries that may choose the corrupted parties during the course of the computation), in a setting where the channels are insecure and secure communication is achieved by cryptographic primitives based on computational limitations of the adversary. It turns out that the power of an adaptive adversary is greatly affected by the amount of information gathered upon the corruption of the party. This amount of information models the extent to which uncorrupted parties are trusted to carry out instructions that cannot be externally verified, such as erasing records of past configurations. It has been shown that if the parties are trusted to erase such records, then adaptivity secure computation can be carried out using known primitives. However, this total trust in parties may be unrealistic in many scenarios. An important question, open since 1986, is whether adaptively secure multi-party computation can be carried out in the "insecure channel" setting, even if no party is thoroughly trusted. Our main result is an affirmative resolution of this question for the case where even uncorrupted parties may deviate from the protocol by keeping record of all past configurations. We first propose a novel property of encryption protocols and show that if an encryption protocol enjoying this property is used, instead of a standard encryption scheme, then known constructions become adaptively secure. Next we constructed, based on standard RSA assumption, an encryption protocol that enjoys this property. We also consider parties that, even when corrupted, may internally deviate from their protocols in arbitrary ways, as long as no external test can detect faulty behavior. We show that in this case no non-trivial protocol can be proven adaptively secure using black-box simulation. This holds even if the communication channels are totally secure.

/pdf/adaptively-secure-multi-party-computation-48xdpa3ak0.pdf

Adaptively secure multi-party computation

We present a solution for the problem of certificate revocation. This solution represents certificate revocation lists by authenticated dictionaries that support: (1) efficient verification whether a certificate is in the list or not and (2) efficient updates (adding/removing certificates from the list). The suggested solution gains in scalability, communication costs, robustness to parameter changes, and update rate. Comparisons to the following solutions (and variants) are included: "traditional" certificate revocation lists (CRLs), Micali's (see Tech. Memo MIT/LCS/TM-542b, 1996) certificate revocation system (CRS), and Kocher's (see Financial Cryptography-FC'98 Lecture Notes in Computer Science. Berlin: Springer-Verlag, 1998, vol.1465, p.172-7) certificate revocation trees (CRT). We also consider a scenario in which certificates are not revoked, but frequently issued for short-term periods. Based on the authenticated dictionary scheme, a certificate update scheme is presented in which all certificates are updated by a common message. The suggested solutions for certificate revocation and certificate update problems are better than current solutions with respect to communication costs, update rate, and robustness to changes in parameters, and are compatible, e.g., with X.500 certificates.

/pdf/certificate-revocation-and-certificate-update-2chfdi4tv9.pdf

Certificate revocation and certificate update

We describe efficient constructions for various cryptographic primitives (both in private-key and in public-key cryptography). We show these constructions to be at least as secure as the decisional version of the Diffie-Hellman assumption or as the assumption that factoring is hard. Our major result is a new construction of pseudo-random functions such that computing their value at any given point involves two multiple products. This is much more efficient than previous proposals. Furthermore, these functions have the advantage of being in TC/sup 0/ (the class of functions computable by constant depth circuits consisting of a polynomial number of threshold gates) which has several interesting applications. The simple algebraic structure of the functions implies additional features. In particular, we show a zero-knowledge proof for statements of the form "y=f/sub s/(x)" and "y/spl ne/f(x)" given a commitment to a key s of a pseudo-random function f/sub s/.

Moni Naor

Papers

Small-bias probability spaces: efficient constructions and applications

Differential privacy under continual observation

Adaptively secure multi-party computation

Certificate revocation and certificate update

Number-theoretic constructions of efficient pseudo-random functions