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

We propose a fully functional identity-based encryption (IBE) scheme. The scheme has chosen ciphertext security in the random oracle model assuming a variant of the computational Diffie--Hellman problem. Our system is based on bilinear maps between groups. The Weil pairing on elliptic curves is an example of such a map. We give precise definitions for secure IBE schemes and give several applications for such systems.

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Identity-Based Encryption from the Weil Pairing

In several distributed systems a user should only be able to access data if a user posses a certain set of credentials or attributes. Currently, the only method for enforcing such policies is to employ a trusted server to store the data and mediate access control. However, if any server storing the data is compromised, then the confidentiality of the data will be compromised. In this paper we present a system for realizing complex access control on encrypted data that we call ciphertext-policy attribute-based encryption. By using our techniques encrypted data can be kept confidential even if the storage server is untrusted; moreover, our methods are secure against collusion attacks. Previous attribute-based encryption systems used attributes to describe the encrypted data and built policies into user's keys; while in our system attributes are used to describe a user's credentials, and a party encrypting data determines a policy for who can decrypt. Thus, our methods are conceptually closer to traditional access control methods such as role-based access control (RBAC). In addition, we provide an implementation of our system and give performance measurements.

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Ciphertext-Policy Attribute-Based Encryption

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).

/pdf/attribute-based-encryption-for-fine-grained-access-control-3fjqefx4um.pdf

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

In image processing, algorithms for object classification are typically based around machine learning. From the algorithm developer’s perspective, these can involve a considerable amount of effort and expertise to develop, which makes them commercially valuable. On the other hand, other parties may want to make use of these algorithms to classify their images, while protecting the privacy of their data. In this paper, we show how non-linear Support Vector Machines (SVMs) can be practically used for image classification on data encrypted with a Somewhat Homomorphic Encryption (SHE) scheme. Previous work has shown how an SVM with a linear kernel can be computed on encrypted data, but this only has limited applicability. By enabling SVMs with polynomial kernels, a much larger class of applications are possible with more accuracy in classification results.

Image Classification using non-linear Support Vector Machines on Encrypted Data.

Elliptic Curves in Cryptography: Curve Examples

We consider the problem of computing the intersection of private datasets of two parties, where the datasets contain lists of elements taken from a large domain. This problem has many applications for online collaboration. We present protocols, based on the use of homomorphic encryption and balanced hashing, for both semi-honest and malicious environments. For lists of length k, we obtain O(k) communication overhead and O(k ln ln k) computation. The protocol for the semihonest environment is secure in the standard model, while the protocol for the malicious environment is secure in the random oracle model. We also consider the problem of approximating the size of the intersection, show a linear lower-bound for the communication overhead of solving this problem, and provide a suitable secure protocol. Lastly, we investigate other variants of the matching problem, including extending the protocol to the multi-party setting as well as considering the problem of approximate matching.

Advances in Cryptology - EUROCRYPT 2012

Solving discriminant form equations via unit equations

Verifiable Oblivious Pseudorandom Functions (VOPRFs) are protocols that allow a client to learn verifiable pseudorandom function (PRF) evaluations on inputs of their choice. The PRF evaluations are computed by a server using their own secret key. The security of the protocol prevents both the server from learning anything about the client’s input, and likewise the client from learning anything about the server’s key. VOPRFs have many applications including password-based authentication, secret-sharing, anonymous authentication and efficient private set intersection. In this work, we construct the first round-optimal (online) VOPRF protocol that retains security from well-known subexponential lattice hardness assumptions. Our protocol requires constructions of non-interactive zero-knowledge arguments of knowledge (NIZKAoK). Using recent developments in the area of post-quantum zero-knowledge arguments of knowledge, we show that our VOPRF may be securely instantiated in the quantum random oracle model. We construct such arguments as extensions of prior work in the area of lattice-based zero-knowledge proof systems.

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Nigel P. Smart

Papers

Image Classification using non-linear Support Vector Machines on Encrypted Data.

Elliptic Curves in Cryptography: Curve Examples

Advances in Cryptology - EUROCRYPT 2012

Solving discriminant form equations via unit equations

Round-Optimal Verifiable Oblivious Pseudorandom Functions from Ideal Lattices