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- Christophe Nègre
- INDOCRYPT
- 2005

This paper explores elliptic curve cryptosystems over fields of small odd characteristic p = 3 or 5. We establish formulas multiplying by p a random point on an ordinary curve defined over Fpn ,… (More)

- Jean-Claude Bajard, Laurent Imbert, Christophe Nègre
- IEEE Transactions on Computers
- 2006

In this paper, we propose a complete set of algorithms for the arithmetic operations in finite fields of prime medium characteristic. The elements of the fields IFpk are represented using the newly… (More)

- M. Anwar Hasan, Nicolas Meloni, Ashkan Hosseinzadeh Namin, Christophe Nègre
- IEEE Transactions on Computers
- 2012

In this paper, we present a new method for parallel binary finite field multiplication which results in subquadratic space complexity. The method is based on decomposing the building blocks of the… (More)

- Christophe Nègre
- International Conference on Information…
- 2005

Finite field arithmetic has advantageous space and time complexity when the field is constructed with a sparse polynomial. Katti and Brennan in (May, 20023) introduced a new type of polynomial, which… (More)

- M. Anwar Hasan, Christophe Nègre
- IEEE Transactions on Computers
- 2013

Computing the product of a Toeplitz matrix and a vector arises in various applications including cryptography. In this paper, we consider Toeplitz matrices and vectors with entries in… (More)

- Kwang Ho Kim, Chol Ok Lee, Christophe Nègre
- INDOCRYPT
- 2014

We present new formulas for the arithmetic on the binary Edwards curves which are much faster than the-state-of-the-art. The representative speedup are 3M +2D+S for a point addition, D+S for a mixed… (More)

- Jithra Adikari, M. Anwar Hasan, Christophe Nègre
- Selected Areas in Cryptography
- 2012

For the first time ever, the FPGA based cryptoprocessor presented in [12] makes it possible to compute an eta pairing at the 128-bit security level in less than one millisecond. The high performance… (More)

- M. Anwar Hasan, Ashkan Hosseinzadeh Namin, Christophe Nègre
- IEEE Transactions on Very Large Scale Integration…
- 2012

In the recent past, subquadratic space complexity multipliers have been proposed for binary fields defined by irreducible trinomials and some specific pentanomials. For such multipliers, alternative… (More)

- Christophe Nègre, Thomas Plantard
- ACISP
- 2008

In 2004, Bajard, Imbert and Plantard introduced a new system of representation to perform arithmetic modulo a prime integer p, the Adapted Modular Number System (AMNS). In this system, the elements… (More)

- Jean-Claude Bajard, Laurent Imbert, Christophe Nègre, Thomas Plantard
- IEEE Symposium on Computer Arithmetic
- 2003