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

As more sensitive data is shared and stored by third-party sites on the Internet, there will be a need to encrypt data stored at these sites. One drawback of encrypting data, is that it can be selectively shared only at a coarse-grained level (i.e., giving another party your private key). We develop a new cryptosystem for fine-grained sharing of encrypted data that we call Key-Policy Attribute-Based Encryption (KP-ABE). In our cryptosystem, ciphertexts are labeled with sets of attributes and private keys are associated with access structures that control which ciphertexts a user is able to decrypt. We demonstrate the applicability of our construction to sharing of audit-log information and broadcast encryption. Our construction supports delegation of private keys which subsumesHierarchical Identity-Based Encryption (HIBE).

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Attribute-based encryption for fine-grained access control of encrypted data

We introduce a short signature scheme based on the Computational Diffie-Hellman assumption on certain elliptic and hyperelliptic curves. The signature length is half the size of a DSA signature for a similar level of security. Our short signature scheme is designed for systems where signatures are typed in by a human or signatures are sent over a low-bandwidth channel.

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Short Signatures from the Weil Pairing

After two decades of research and development, elliptic curve cryptography now has widespread exposure and acceptance. Industry, banking, and government standards are in place to facilitate extensive deployment of this efficient public-key mechanism. Anchored by a comprehensive treatment of the practical aspects of elliptic curve cryptography (ECC), this guide explains the basic mathematics, describes state-of-the-art implementation methods, and presents standardized protocols for public-key encryption, digital signatures, and key establishment. In addition, the book addresses some issues that arise in software and hardware implementation, as well as side-channel attacks and countermeasures. Readers receive the theoretical fundamentals as an underpinning for a wealth of practical and accessible knowledge about efficient application. Features & Benefits: * Breadth of coverage and unified, integrated approach to elliptic curve cryptosystems * Describes important industry and government protocols, such as the FIPS 186-2 standard from the U.S. National Institute for Standards and Technology * Provides full exposition on techniques for efficiently implementing finite-field and elliptic curve arithmetic* Distills complex mathematics and algorithms for easy understanding* Includes useful literature references, a list of algorithms, and appendices on sample parameters, ECC standards, and software toolsThis comprehensive, highly focused reference is a useful and indispensable resource for practitioners, professionals, or researchers in computer science, computer engineering, network design, and network data security.

https://cdn.preterhuman.net/texts/cryptography/Hankerson,%20Menezes,%20Vanstone.%20Guide%20to%20elliptic%20curve%20cryptography%20(Springer,%202004)(ISBN%20038795273X)(332s)_CsCr_.pdf

Guide to Elliptic Curve Cryptography

We present the first efficient Identity-Based Encryption (IBE) scheme that is fully secure without random oracles We first present our IBE construction and reduce the security of our scheme to the decisional Bilinear Diffie-Hellman (BDH) problem Additionally, we show that our techniques can be used to build a new signature scheme that is secure under the computational Diffie-Hellman assumption without random oracles

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Efficient identity-based encryption without random oracles

We present hierarchical identity-based encryption schemes and signature schemes that have total collusion resistance on an arbitrary number of levels and that have chosen ciphertext security in the random oracle model assuming the difficulty of the Bilinear Diffie-Hellman problem.

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Hierarchical ID-Based Cryptography

We study the problem of finding efficiently computable non-degenerate multilinear maps from G1 to G2, where G1 and G2 are groups of the same prime order, and where computing discrete logarithms in G1 is hard. We present several applications to cryptography, explore directions for building such maps, and give some reasons to believe that finding examples with n > 2 may be difficult.

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Applications of Multilinear Forms to Cryptography.

For certain security applications, including identity based encryption and short signature schemes, it is useful to have abelian varieties with security parameters that are neither too small nor too large. Supersingular abelian varieties are natural candidates for these applications. This paper determines exactly which values can occur as the security parameters of supersingular abelian varieties (in terms of the dimension of the abelian variety and the size of the finite field), and gives constructions of supersingular abelian varieties that are optimal for use in cryptography.

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Supersingular Abelian Varieties in Cryptology

A system and method are disclosed for securing binding updates in a wireless telecommunications system. A public key is generating using a home address value of the mobile host. Thereafter, a home agent, such as a router, generates a private key using public cryptographic parameters, that corresponds to the mobile host and the public key. The correspondent node uses the public key to encrypt a shared key and sends the shared key to the mobile host. The mobile host decrypts the shared key using the private key and uses the shared key to sign the binding update. Thereafter, the correspondent node utilizes the shared key to verify the authenticity of the binding update.

Alice Silverberg

Papers

Hierarchical ID-Based Cryptography

Applications of Multilinear Forms to Cryptography.

Supersingular Abelian Varieties in Cryptology

Securing binding update using address based keys

Fields of definition for homomorphisms of abelian varieties