Thomas Izard Email & Phone Number

Code protection through obfuscationData protection

Région De Montpellier, France

In charge of Evarix, the Matlab/Scilab to optimized C++ compiler

Montpellier

Compilation - High-Performance Computing

Région De Montpellier, France

Graph theory, networks

Parallel Arithmetic Operators for Public Key Cryptography (in French)Protocols for asymmetric cryptography require arithmetic computations in several mathematical structures. In particular, many of them need computations in finite structures, imposing an efficient modular arithmetic. These modular calculations are composed of multiprecision operations between operands of sizes large enough to insure the required level of security (between several hundred and several thousand of bits). Finally, some protocols need arithmetic operations in the group of points of an elliptic curve, which are themselves composed of modular computations. The sizes of the keys used by the protocols make the arithmetic computations expansive in terms of execution time. Nowadays, current architectures have several computing units, which are distributed over the processors and GPU. These resources are now easily programmable using dedicated languages such as OpenMP or CUDA. This thesis focuses on the definition of parallel algorithms to take advantage of all the computing resources of multi-core shared-memory architectures. Parallelism at the lowest arithmetic level gives a moderate speedup since the sizes of the operands are not large enough so that the arithmetic intensity hides the latencies induced by the parallelism. We propose algorithms for parallelization at higher arithmetic levels: parallel algorithms for modular multiplication and scalar multiplication on elliptic curves. For modular multiplication, we study in particular several schedulings of modular computations. We also propose a two-level parallelization, at modular and multiprecision levels. This "coarse-grained" parallelism allows in practice a more substantial speedup. We also present a parallelization of modular and elliptic curves operations on GPU. Finally, we introduce a method to optimize scalar multiplication on elliptic curves for small scalars.

Région De Montpellier, France

Lirmm - Montpellier

Since introduced by Koblitz and Miller, the use of elliptic curve cryptography, motivated byits reduced key sizes, has spread and has become an interesting alternative to other asymetriccryptographic protocols. Security of this cryptosystem relies on the so-called elliptic curve dis-crete logarithm problem, with scalar, or point multiplication as the base operation. This kind ofoperation is expensive, especially with numbers of 160 bits or more. In this report, we proposean automatic method for optimizing this point multiplication operation, for small scalars. Ourmethod uses simple and efficient heuristics in order to reduce the number of operations we haveto perform. Thanks to our method, optimizations which were performed by hand can be appliedconsistently for a large set of small scalars and give better results than those computed by classicmultiplication algorithms.

Région De Montpellier, France

Kaunas Lithuania

Badge Reverse Engineering

Master Of Science (Msc), Computer Science

Licence, Computer Science

Dut, Informatique