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

We describe efficient constructions for various cryptographic primitives in private-key as well as public-key cryptography. Our main results are two new constructions of pseudo-random functions. We prove the pseudo-randomness of one construction under the assumption that factoring (Blum integers) is hard while the other construction is pseudo-random if the decisional version of the Diffie--Hellman assumption holds. Computing the value of our functions at any given point involves two subset products. This is much more efficient than previous proposals. Furthermore, these functions have the advantage of being in TC0 (the class of functions computable by constant depth circuits consisting of a polynomial number of threshold gates). This fact has several interesting applications. The simple algebraic structure of the functions implies additional features such as a zero-knowledge proof for statements of the form "y = fs(x)" and "y ≠ fs(x)" given a commitment to a key s of a pseudo-random function fs.

Number-theoretic constructions of efficient pseudo-random functions

The problems of authentication and identification have received wide interest in cryptographic research. However, there has been no satisfactory solution for the problem of authentication by a human recipient who does not use any trusted computational device, which arises for example in the context of smartcard-human interaction, in particular in the context of electronic wallets. The problem of identification is ubiquitous in communication over insecure networks.

https://link.springer.com/content/pdf/10.1007%2FBFb0052245.pdf

Visual Authentication and Identification

Chosen-Prefix Collisions for MD5 and Colliding X.509 Certificates for Different Identities.- Non-trivial Black-Box Combiners for Collision-Resistant Hash-Functions Don't Exist.- The Collision Intractability of MDC-2 in the Ideal-Cipher Model.- An Efficient Protocol for Secure Two-Party Computation in the Presence of Malicious Adversaries.- Revisiting the Efficiency of Malicious Two-Party Computation.- Efficient Two-Party Secure Computation on Committed Inputs.- Universally Composable Multi-party Computation Using Tamper-Proof Hardware.- Generic and Practical Resettable Zero-Knowledge in the Bare Public-Key Model.- Instance-Dependent Verifiable Random Functions and Their Application to Simultaneous Resettability.- Conditional Computational Entropy, or Toward Separating Pseudoentropy from Compressibility.- Zero Knowledge and Soundness Are Symmetric.- Mesh Signatures.- The Power of Proofs-of-Possession: Securing Multiparty Signatures against Rogue-Key Attacks.- Batch Verification of Short Signatures.- Cryptanalysis of SFLASH with Slightly Modified Parameters.- Differential Cryptanalysis of the Stream Ciphers Py, Py6 and Pypy.- Secure Computation from Random Error Correcting Codes.- Round-Efficient Secure Computation in Point-to-Point Networks.- Atomic Secure Multi-party Multiplication with Low Communication.- Cryptanalysis of the Sidelnikov Cryptosystem.- Toward a Rigorous Variation of Coppersmith's Algorithm on Three Variables.- An L (1/3?+??) Algorithm for the Discrete Logarithm Problem for Low Degree Curves.- General Ad Hoc Encryption from Exponent Inversion IBE.- Non-interactive Proofs for Integer Multiplication.- Ate Pairing on Hyperelliptic Curves.- Ideal Multipartite Secret Sharing Schemes.- Non-wafer-Scale Sieving Hardware for the NFS: Another Attempt to Cope with 1024-Bit.- Divisible E-Cash Systems Can Be Truly Anonymous.- A Fast and Key-Efficient Reduction of Chosen-Ciphertext to Known-Plaintext Security.- Range Extension for Weak PRFs The Good, the Bad, and the Ugly.- Feistel Networks Made Public, and Applications.- Oblivious-Transfer Amplification.- Simulatable Adaptive Oblivious Transfer.

Advances in Cryptology - EUROCRYPT 2007

Non-Malleable Cryptography (Extended Abstract)

How to represent a graph in memory is a fundamental data structuring question. In the usual representations of an n-vertex graph, the names of the vertices (i.e., integers from 1 to n) betray nothing about the graph itself. Indeed, the names (or labels) on the n vertices are just $\log n$ bit place holders to allow data on the edges to encode the structure of the graph. In this scenario, there is no such waste. By assigning $O(\log n)$ bit labels to the vertices, the structure of the graph is completely encoded, so that, given the labels of two vertices, one can test if they are adjacent in time linear in the size of the labels. Furthermore, given an arbitrary original labeling of the vertices, structure coding labels are found (as above) that are no more than a small constant factor larger than the original labels. These notions are intimately related to vertex-induced universal graphs of polynomial size. For example, planar graphs can be labeled with structure coding labels of size $ < 4\log n$, which i...

Moni Naor

Papers

Number-theoretic constructions of efficient pseudo-random functions

Visual Authentication and Identification

Advances in Cryptology - EUROCRYPT 2007

Non-Malleable Cryptography (Extended Abstract)

Implicit representation of graphs