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.

/pdf/identity-based-encryption-from-the-weil-pairing-1x4254f2zc.pdf

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.

/pdf/ciphertext-policy-attribute-based-encryption-q09jxdyx4n.pdf

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.

/pdf/short-signatures-from-the-weil-pairing-5ajupg0cpi.pdf

Short Signatures from the Weil Pairing

Schoof's Algorithm and Extensions

We consider the issue of securing dark pools/markets in thefinancial services sector. Currently, these markets are executed via trusted third parties, which opens potential for market operators to conduct fraud. We present a potential solution to this problem by using Multi-Party Computation (MPC) to enable a trusted third party to be emulated in software for three popular market mechanisms: continuous double auction (CDA), periodic auction (PA), and scheduled volume matching (SVM). Our experiments show that whilst the predominate market clearing mechanism of CDA is not currently viable when executed using MPC, SVM (a popular market mechanism for dark pools) is viable. We present experimental validation of this conclusion by presenting the expected throughputs for such markets in two popular MPC paradigms: the two party dishonest majority setting, and the honest majority three party setting.

MPC Joins the Dark Side.

We present a methodology to achieve low latency homomorphic operations on approximations to complex numbers, by encoding a complex number as an evaluation of a polynomial at a root of unity. We then use this encoding to evaluate a Discrete Fourier Transform (DFT) on data which has been encrypted using a Somewhat Homomorphic Encryption (SHE) scheme, with up to three orders of magnitude improvement in latency over previous methods. We are also able to deal with much larger input sizes than previous methods. Due to the fact that the entire DFT algorithm is an algebraic operation over the underlying ring of the SHE scheme (for a suitably chosen ring), our method for the DFT utilizes exact arithmetic over the complex numbers, as opposed to approximations.

Faster Homomorphic Evaluation of Discrete Fourier Transforms.

In this paper we examine the hard problems underlying asymmetric pairings, their precise relationships and how they affect a number of existing protocols. Furthermore, we present a new model for the elliptic curve groups used in asymmetric pairings, which allows both an efficient pairing and an efficiently computable isomorphism.

/pdf/on-computable-isomorphisms-in-efficient-asymmetric-pairing-124kd6netv.pdf

On Computable Isomorphisms in Efficient Asymmetric Pairing Based Systems.

We use the theory of Witt vectors to develop an algebraic approach for studying the NTRU primitive with q parameter equal to a power of two. This results in a system of nonlinear algebraic equations over $\mathbb{F}_{2}$ having many symmetries, which is reminiscent of the approach of Courtois, Murphy, Pieprzyk, Robshaw and others for studying the structure of block ciphers such as the AES. We study whether this approach to NTRU provides any immediate security threat and conclude that under the most favourable assumptions, the method is of asymptotic interest but is completely impractical at current or likely future parameter sizes.

/pdf/an-algebraic-approach-to-ntru-q-2-n-via-witt-vectors-and-182mrubfjl.pdf

Nigel P. Smart

Papers

Schoof's Algorithm and Extensions

MPC Joins the Dark Side.

Faster Homomorphic Evaluation of Discrete Fourier Transforms.

On Computable Isomorphisms in Efficient Asymmetric Pairing Based Systems.

An algebraic approach to NTRU ( q = 2 n ) via Witt vectors and overdetermined systems of nonlinear equations