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- Nigel P. Smart, Frederik Vercauteren
- IACR Cryptology ePrint Archive
- 2009

We present a fully homomorphic encryption scheme which has both relatively small key and ciphertext size. Our construction follows that of Gentry by producing a fully homomorphic scheme from a “somewhat” homomorphic scheme. For the somewhat homomorphic scheme the public and private keys consist of two large integers (one of which is shared by both the… (More)

- Florian Hess, Nigel P. Smart, Frederik Vercauteren
- IEEE Transactions on Information Theory
- 2006

In this paper, we simplify and extend the Eta pairing, originally discovered in the setting of supersingular curves by Barreto , to ordinary curves. Furthermore, we show that by swapping the arguments of the Eta pairing, one obtains a very efficient algorithm resulting in a speed-up of a factor of around six over the usual Tate pairing, in the case of… (More)

- Nigel P. Smart
- IACR Cryptology ePrint Archive
- 2001

We describe an ID based authenticated two pass key agreement protocol which makes use of the Weil pairing The protocol is described and its properties are discussed including the ability to add key con rmation

- Craig Gentry, Shai Halevi, Nigel P. Smart
- IACR Cryptology ePrint Archive
- 2012

We describe a working implementation of leveled homomorphic encryption (with or without bootstrapping) that can evaluate the AES-128 circuit. This implementation is built on top of the HElib library, whose design was inspired by an early version of this work. Our main implementation (without bootstrapping) takes about 4 minutes and 3GB of RAM, running on a… (More)

- Benny Pinkas, Thomas Schneider, Nigel P. Smart, Stephen C. Williams
- ASIACRYPT
- 2009

Secure multi-party computation has been considered by the cryptographic community for a number of years. Until recently it has been a purely theoretical area, with few implementations with which to test various ideas. This has led to a number of optimisations being proposed which are quite restricted in their application. In this paper we describe an… (More)

- Liqun Chen, Zhaohui Cheng, Nigel P. Smart
- International Journal of Information Security
- 2006

In recent years, a large number of identity- based key agreement protocols from pairings have been proposed. Some of them are elegant and practical. However, the security of this type of protocol has been surprisingly hard to prove, even in the random oracle model. The main issue is that a simulator is not able to deal with reveal queries, because it… (More)

- Steven D. Galbraith, Kenneth G. Paterson, Nigel P. Smart
- Discrete Applied Mathematics
- 2006

Many research papers in pairing based cryptography treat pairings as a “black box”. These papers build cryptographic schemes making use of various properties of pairings. If this approach is taken, then it is easy for authors to make invalid assumptions concerning the properties of pairings. The cryptographic schemes developed may not be realizable in… (More)

- Ivan Damgård, Valerio Pastro, Nigel P. Smart, Sarah Zakarias
- IACR Cryptology ePrint Archive
- 2011

We propose a general multiparty computation protocol secure against an active adversary corrupting up to n−1 of the n players. The protocol may be used to compute securely arithmetic circuits over any finite field Fpk . Our protocol consists of a preprocessing phase that is both independent of the function to be computed and of the inputs, and a much more… (More)

- Pierrick Gaudry, Florian Hess, Nigel P. Smart
- Journal of Cryptology
- 2001

In this paper we look in detail at the curves which arise in the method of Galbraith and Smart for producing curves in the Weil restriction of an elliptic curve over a finite field of characteristic 2 of composite degree. We explain how this method can be used to construct hyperelliptic cryptosystems which could be as secure as cryptosystems based on the… (More)

- Nigel P. Smart, Frederik Vercauteren
- Des. Codes Cryptography
- 2011

At PKC 2010 Smart and Vercauteren presented a variant of Gentry’s fully homomorphic public key encryption scheme and mentioned that the scheme could support SIMD style operations. The slow key generation process of the Smart–Vercauteren system was then addressed in a paper by Gentry and Halevi, but their key generation method appears to exclude the SIMD… (More)