Robin Larrieu
[ Research | Publications | Software | Talks ]

Postal

Address:

Laboratoire d'informatique

LIX, UMR 7161 CNRS

Campus de l'École polytechnique

1, rue Honoré d'Estienne d'Orves

Bâtiment Alan Turing

CS35003

91120 Palaiseau

Office:

1 rue Honoré d'Estienne d'Orves

Bâtiment Alan Turing

Room 1014

Telephone:

+33(0)1 77 57 80 76

E-mail: larrieu_at_lix.polytechnique.fr

Position:

PhD Student

Research

I started my PhD in October 2016 under the supervision of Joris van der Hoeven and co-advised by Luca de Feo. As its title Fast Finite Field Arithmetic suggests, the focus is on fast algorithms for polynomial arithmetic over finite fields. In a first step, I consider the fundamental problem of polynomial multiplication and how the structure of finite fields can be exploited to speed up this operation. Knowing that fast multiplication is a building block for many other operations, I try in a second step to apply similar techniques to problems of practical interest. This typically includes Gröbner basis computation for polynomial system solving, or general applications in cryptology.

Publications [BibTex file]

Joris van der Hoeven and Robin Larrieu. Fast Gröbner basis computation and polynomial reduction for generic bivariate ideals. Presented in ACA 2018, [Preliminary version], April 2018.

Joris van der Hoeven and Robin Larrieu. Fast reduction of bivariate polynomials with respect to sufficiently regular Gröbner bases. To appear in proceedings of ISSAC 2018, [Preliminary version], April 2018.

Joris van der Hoeven, Robin Larrieu, and Grégoire Lecerf. Implementing Fast Carryless Multiplication. In Johannes Blömer, Ilias S. Kotsireas, Temur Kutsia, and Dimitris E. Simos, editors, Mathematical Aspects of Computer and Information Sciences: 7th International Conference, MACIS 2017, Vienna, Austria, November 15-17, 2017, Proceedings, pages 121–136, Cham, 2017. Springer International Publishing. [Published version], [Preliminary version].

Joris van der Hoeven and Robin Larrieu. The Frobenius FFT. In Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC '17, pages 437–444, New York, NY, USA, 2017. ACM. [Published version], [Preliminary version].

Robin Larrieu. The Truncated Fourier Transform for Mixed Radices. In Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC '17, pages 261–268, New York, NY, USA, 2017. ACM. [Published version], [Preliminary version].

Robin Larrieu and Natarajan Shankar. A framework for high-assurance quasi-synchronous systems. In 2014 Twelfth ACM/IEEE Conference on Formal Methods and Models for Codesign (MEMOCODE), pages 72–83, Oct 2014. [Published version].

Software

A proof-of-concept implementation for algorithms on bivariate Gröbner bases (results presented in ISSAC and ACA 2018). Source code available here.

A fast library for multiplication of polynomials over F2 (joint work with Joris van der Hoeven and Grégoire Lecerf, results presented in MACIS 2017). Integrated to the Justinline library of mathemagix.

Talks

Fast Gröbner basis computation and polynomial reduction for generic bivariate ideals. ACA 2018 (June 2018), Santiago de Compostela, Spain, [PDF].

Implementing Fast Carryless Multiplication. MACIS 2017 (November 2017), Vienna, Austria, [PDF].

The Truncated Fourier Transform for Mixed Radices. ISSAC '17 (July 2017), Kaiserslautern, Germany, [PDF].