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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)

- Jürgen Bierbrauer, Charalambos A. Charalambides, +15 authors Frederik Vercauteren
- 2005

- 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)

- Frederik Vercauteren
- IEEE Transactions on Information Theory
- 2008

In this paper, we introduce the concept of an optimal pairing, which by definition can be computed using only <i>log</i> <sub>2</sub> <i>r</i>/¿(<i>k</i>) basic Miller iterations, with <i>r</i> the order of the groups involved and <i>k</i> the embedding degree. We describe an algorithm to construct optimal ate pairings on all parametrized families of… (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)

- Junfeng Fan, Frederik Vercauteren
- IACR Cryptology ePrint Archive
- 2012

In this paper we port Brakerski’s fully homomorphic scheme based on the Learning With Errors (LWE) problem to the ring-LWE setting. We introduce two optimised versions of relinearisation that not only result in a smaller relinearisation key, but also faster computations. We provide a detailed, but simple analysis of the various homomorphic operations, such… (More)

- Antoine Joux, Reynald Lercier, Nigel P. Smart, Frederik Vercauteren
- CRYPTO
- 2006

In this paper, we study several variations of the number field sieve to compute discrete logarithms in finite fields of the form Fpn , with p a medium to large prime. We show that when n is not too large, this yields a Lpn(1/3) algorithm with efficiency similar to that of the regular number field sieve over prime fields. This approach complements the recent… (More)

- Dan Page, Frederik Vercauteren
- IEEE Trans. Computers
- 2006

Current fault attacks against public key cryptography focus on traditional schemes such as RSA and ECC, and to a lesser extent primitives such as XTR. However, bilinear maps, or pairings, have presented theorists with a new and increasingly popular way of constructing cryptographic protocols. Most notably, this has resulted in efficient methods for Identity… (More)

- Steven D. Galbraith, Florian Hess, Frederik Vercauteren
- IEEE Transactions on Information Theory
- 2007

In this paper, we discuss some applications of the pairing inversion problem and outline some potential approaches for solving it. Our analysis of these approaches gives further evidence that pairing inversion is a difficult problem.

In this paper we propose an efficient and compact processor for a ring-LWE based encryption scheme. We present three optimizations for the Number Theoretic Transform (NTT) used for polynomial multiplication: we avoid preprocessing in the negative wrapped convolution by merging it with the main algorithm, we reduce the fixed computation cost of the twiddle… (More)