Abstract-The contribution of the present work relies on an innovative and judicious combination of several optimization techniques for achieving high performance when using automatic vectorization and hybrid MPI/OpenMP parallelism in a Particle-in-Cell (PIC) code. The domain of application is plasma physics: the code simulates 2d2v Vlasov-Poisson systems on Cartesian grids with periodic boundary conditions. Overall, our code processes 65 million particles/second per core on Intel Haswell (without hyper-threading) and achieves a good weak scaling up to 0.4 trillion particles on 8,192 cores.The optimizations mainly consist in using (i) a structure of arrays for the particles, (ii) an efficient data structure for the electric field and the charge density, and (iii) an appropriate code for automatic vectorization of the charge accumulation and of the positions' update. In particular, we use space-filling curves to enhance data locality while enabling vectorization: starting from a redundant cell-based data structure for the electric field and for the charge density, we compare several space-filling curves for an efficient ordering of these data and we obtain a gain of 36% in the number of L2 and L3 cache misses when using a Morton curve instead of the classical rowmajor one. In addition, by proposing a specific writing of the updating positions code we achieve a 31% time improvement in that step. The optimizations bring an overall gain in the execution time of 42% with respect to a standard code. The parallelization of the particle loops is simply performed by means of both distributed and shared memory paradigms, without domain decomposition. We explain the weak and the strong scalings of the code bounded as expected by the overhead of the MPI communications.

In [2], 1D×1D two-species Vlasov-Poisson simulations are performed by the semi-Lagrangian method. Thanks to a classical first order dispersion analysis, we are able to check the validity of their simulations; the extension to second order is performed and shown to be relevant for explaining further details. In order to validate multi-dimensional effects, we propose a 2D × 2D single species test problem that has true 2D effects coming from the sole second order dispersion analysis. Finally, we perform, in the same code, full 2D × 2D non linear two-species simulations with mass ratio 0:01, and consider the mixing of semi-Lagrangian and Particle-in-Cell methods.

Abstract. The Particle-in-Cell (PIC) method allows solving partial differential equation through simulations, with important applications in plasma physics. To simulate thousands of billions of particles on clusters of multicore machines, prior work has proposed hybrid algorithms that combine domain decomposition and particle decomposition with carefully optimized algorithms for handling particles processed on each multicore socket. Regarding the multicore processing, existing algorithms either suffer from suboptimal execution time, due to sorting operations or use of atomic instructions, or suffer from suboptimal space usage. In this paper, we propose a novel parallel algorithm for two-dimensional PIC simulations on multicore hardware that features asymptotically-optimal memory consumption, and does not perform unnecessary accesses to the main memory. In practice, our algorithm reaches 65% of the maximum bandwidth, and shows excellent scalability on the classical Landau damping and two-stream instability test cases.

Particle-in-Cell (PIC) codes are widely used for plasma simulations. On recent multi-core hardware, performance of these codes is often limited by memory bandwidth. We describe a multi-core PIC algorithm that achieves close-to-minimal number of memory transfers with the main memory, while at the same time exploiting SIMD instructions for numerical computations and exhibiting a high degree of OpenMPlevel parallelism. Our algorithm keeps particles sorted by cell at every time step, and represents particles from a same cell using a linked list of fixed-capacity arrays, called chunks. Chunks support either sequential or atomic insertions, the latter being used to handle fast-moving particles. To validate our code, called Pic-Vert, we consider a 3d electrostatic Landau-damping simulation as well as a 2d3v transverse instability of magnetized electron holes. Performance results on a 24-core Intel Skylake hardware confirm the effectiveness of our algorithm, in particular its high throughput and its ability to cope with fast moving particles.1 Let t denote the single-core execution time. Assume 0.5% of sequential execution, and 99.5% using 64 cores. The parallel execution time is: 0.005t + 0.995t/64 = 1.32t/64.

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Relativistic cryptography is a proposal for achieving unconditional security that exploits the fact that no information carrier can travel faster than the speed of light. It is based on spacetime constraints but doesn't require quantum hardware. Nevertheless, it was unclear whether this proposal is realistic or not. Recently, Alikhani et al. [ABC + 21] performed an implementation of a relativistic zero-knowledge for NP. Their implemented scheme shows the feasibility of relativistic cryptography but it is only secure against classical adversaries. In this work, we present a new relativistic protocol for NP which is secure against quantum adversaries and which is efficient enough so that it can be implemented on everyday laptops and internet connections. We use Stern's zeroknowledge scheme for the Syndrome Decoding problem, which was used before in post-quantum cryptography. The main technical contribution is a generalization of the consecutive measurement framework of [CL17] to prove the security of our scheme against quantum adversaries, and we perform an implementation that demonstrates the feasibility and efficiency of our proposed scheme.