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

Secure Accounting and Auditing on the Web.

A common method for increasing the usability and uplifting the security of pseudorandom function families (PRFs) is to 'hash' the inputs into a smaller domain before applying the PRF. This approach, known as 'Levin's trick', is used to achieve 'PRF domain extension' (using a short,e.g,fixed, input length PRF to get a variable-length PRF), and more recently to transform non-adaptive PRFs to adaptive ones. Such reductions, however, are vulnerable to a 'birthday attack': after $\sqrt{|\mathcal{U}}$ queries to the resulting PRF, where $\mathcal{U}$ being the hash function range, a collision (i.e., two distinct inputs have the same hash value) happens with high probability. As a consequence, the resulting PRF is insecure against an attacker making this number of queries.

In this work we show how to go beyond the birthday attack barrier, by replacing the above simple hashing approach with a variant of cuckoo hashing — a hashing paradigm typically used for resolving hash collisions in a table, by using two hash functions and two tables, and cleverly assigning each element into one of the two tables. We use this approach to obtain: (i) A domain extension method that requires just two calls to the original PRF, can withstand as many queries as the original domain size and has a distinguishing probability that is exponentially small in the non cryptographic work. (ii) A security-preserving reduction from non-adaptive to adaptive PRFs.

/pdf/hardness-preserving-reductions-via-cuckoo-hashing-1sbz3ime6s.pdf

Hardness preserving reductions via cuckoo hashing

We consider the well known string matching problem where a text and pattern are given and the problem is to determine if the pattern appears as a substring in the text. The setting we investigate is where the pattern and the text are preprocessed separately at two different sites. At some point in time the two sites wish to determine if the pattern appears in the text (this is the on-line stage). We provide preprocessing and on-line algorithms such that the preprocessing algorithm runs in linear time and requires linear storage and the on-line complexity is logarithmic in the text. We also give an application of the algorithm to parallel data compression, and show how to implement the Lempel Ziv algorithm in logarithmic time with linear number of processors.

String matching with preprocessing of text and pattern

We address the message authentication problem in two seemingly different communication models. In the first model, the sender and receiver are connected by an insecure channel and by a low-bandwidth auxiliary channel, that enables the sender to ldquomanuallyrdquo authenticate one short message to the receiver (for example, by typing a short string or comparing two short strings). We consider this model in a setting where no computational assumptions are made, and prove that for any there exists a -round protocol for authenticating -bit messages, in which only bits are manually authenticated, and any adversary (even computationally unbounded) has probability of at most to cheat the receiver into accepting a fraudulent message. Moreover, we develop a proof technique showing that our protocol is essentially optimal by providing a lower bound of on the required length of the manually authenticated string. The second model we consider is the traditional message authentication model. In this model, the sender and the receiver share a short secret key; however, they are connected only by an insecure channel. We apply the proof technique above to obtain a lower bound of on the required Shannon entropy of the shared key. This settles an open question posed by Gemmell and Naor (Advances in Cryptology-CRYPTO '93, pp. 355-367, 1993). Finally, we prove that one-way functions are necessary (and sufficient) for the existence of protocols breaking the above lower bounds in the computational setting.

/pdf/tight-bounds-for-unconditional-authentication-protocols-in-4tyhnrxznz.pdf

Tight Bounds for Unconditional Authentication Protocols in the Manual Channel and Shared Key Models

The bounded storage model (BSM) bounds the storage space of an adversary rather than its running time. It utilizes the public transmission of a long random string R of length r, and relies on the assumption that an eavesdropper cannot possibly store all of this string. Encryption schemes in this model achieve the appealing property of everlasting security. In short, this means that an encrypted message remains secure even if the adversary eventually gains more storage or gains knowledge of (original) secret keys that may have been used. However, if the honest parties do not share any private information in advance, then achieving everlasting security requires high storage capacity from the honest parties (storage of Ω(√r); as shown in [9]). We consider the idea of a hybrid bounded storage model were computational limitations on the eavesdropper are assumed up until the time that the transmission of R has ended. For example, can the honest parties run a computationally secure key agreement protocol in order to agree on a shared private key for the BSM, and thus achieve everlasting security with low memory requirements? We study the possibility and impossibility of everlasting security in the hybrid bounded storage model. We start by formally defining the model and everlasting security for this model. We show the equivalence of two flavors of definitions: indistinguishability of encryptions and semantic security. On the negative side. we show that everlasting security with low storage requirements cannot be achieved by black-box reductions in the hybrid BSM. This serves a.s a further indication to the hardness of achieving low storage everlasting security, adding to previous results of this nature [9,15]. On the other hand, we show two augmentations of the model that allow for low storage everlasting security. The first is by adding a random oracle to the model, while the second bounds the accessibility of the adversary to the broadcast string R. Finally, we show that in these two modified models, there also exist bounded storage oblivious transfer protocols with low storage requirements.

Moni Naor

Papers

Secure Accounting and Auditing on the Web.

Hardness preserving reductions via cuckoo hashing

String matching with preprocessing of text and pattern

Tight Bounds for Unconditional Authentication Protocols in the Manual Channel and Shared Key Models

On Everlasting Security in the Hybrid Bounded Storage Model