Number Of Scalar Multiplications Research Articles

Practical Certificate-Less Infrastructure with Application in TLS

We propose highly efficient certificate-less (CL) protocols for the infrastructure used by authenticated key exchange (AKE). The construction is based on elliptic curves (EC) without pairing, which means it can be easily supported by most industrial cryptography libraries on constrained devices. Compared with other pairing-free CL solutions, the new CL-AKE protocol enjoys the least number of scalar multiplications over EC groups. We use a unified game-based model to formalize the security of each protocol, while most previous works only assess the security against a list of attacks, provide informal theorems without proper modeling, or use separate models for protocols in different stages. We also present an efficient integration of the core protocols into the TLS cipher suites and a stand-alone implementation for constrained devices. The performance is evaluated on constrained devices in real-world settings, which further confirms the efficiency of our proposal.

Statistical Pruning for Near-Maximum Likelihood Decoding

In many communications problems, maximum-likelihood (ML) decoding reduces to finding the closest (skewed) lattice point in N-dimensions to a given point xisin C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sup> . In its full generality, this problem is known to be NP-complete. Recently, the expected complexity of the sphere decoder, a particular algorithm that solves the ML problem exactly, has been computed. An asymptotic analysis of this complexity has also been done where it is shown that the required computations grow exponentially in N for any fixed SNR. At the same time, numerical computations of the expected complexity show that there are certain ranges of rates, SNRs and dimensions N for which the expected computation (counted as the number of scalar multiplications) involves no more than N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> computations. However, when the dimension of the problem grows too large, the required computations become prohibitively large, as expected from the asymptotic exponential complexity. In this paper, we propose an algorithm that, for large N, offers substantial computational savings over the sphere decoder, while maintaining performance arbitrarily close to ML. We statistically prune the search space to a subset that, with high probability, contains the optimal solution, thereby reducing the complexity of the search. Bounds on the error performance of the new method are proposed. The complexity of the new algorithm is analyzed through an upper bound. The asymptotic behavior of the upper bound for large N is also analyzed which shows that the upper bound is also exponential but much lower than the sphere decoder. Simulation results show that the algorithm is much more efficient than the original sphere decoder for smaller dimensions as well, and does not sacrifice much in terms of performance