Karim Bigou

Université de Bretagne Occidentale        Lab-STICC

Département Informatique U.F.R. Sciences et Techniques, Université de Bretagne Occidentale, 20 avenue Le Gorgeu C.S. 93837, 29238 BREST Cedex 3, France
(+33) (0)2 98 01 67 97

Current Position

Since September 2016, I am assistant professor at Université de Bretagne Occidentale in the computer science department. I do my research in the ARCAD team of the SHARP department of Lab-STICC laboratory, working on computer arithmetic for cryptographic implementations, in hardware (FPGA) and software (multicore processors).


Since September 2021, I am in charge of the 2nd year of the computer science bachelor (licence in french) of Université de Bretagne Occidentale (UBO). I am currently teaching in the computer science departement of UBO the following courses:

Formerly teached at UBO:

I did various courses (vacations) in 2014-2016 at IUT Lannion in the DUT Informatique about Operating Systems, Computer Architecture, Network Architecture, Object-oriented programming or Algorithmics and C Programming.


Current Research Interests

PhD Students

Former PhD Students


International Journal and Conference Articles

French Conference Articles



The main objective of this PhD thesis is to speedup elliptic curve cryptography (ECC) computations, using the residue number system (RNS). A state-of-art of RNS for cryptographic computations is presented. Then, several new RNS algorithms, faster than state-of-art ones, are proposed. First, a new RNS modular inversion algorithm is presented. This algorithm leads to implementations from 5 to 12 times faster than state-of-art ones, for the standard cryptographic parameters evaluated. Second, a new algorithm for RNS modular multiplication is proposed. In this algorithm, computations are split into independant parts, which can be reused in some computations when operands are reused, for instance to perform a square. It reduces the number of precomputations by 25 % and the number of elementary multiplications up to 10 %, for some cryptographic applications (for example with the discrete logarithm). Using the same idea, an exponentiation algorithm is also proposed. It reduces from 15 % to 22 % the number of elementary multiplications, but requires more precomputations than state-of-art. Third, another modular multiplication algorithm is presented, requiring only one RNS base, instead of 2 for the state-of-art. This algorithm can be used for ECC and well-chosen fields, it divides by 2 the number of elementary multiplications, and by 4 the number of precomputations to store. Partial FPGA implementations of our algorithm halves the area, for a computation time overhead of, at worse, 10 %, compared to state-of-art algorithms. Finally, a method for fast multiple divisibility tests is presented, which can be used in hardware for scalar recoding to accelerate some ECC computations.


GDR ASR (Groupe De Recherche Architecture, Systèmes et Réseaux) award 2013 of the best scientific contributions of young researchers, section Architecture, for the work Improving Modular Inversion in RNS using the Plus-Minus Method (given during ComPAS 2014).

Some Talk Slides

News and events

Conferences 2024