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Institute
- Institut für Systemdynamik - ISD (103) (remove)
This work presents a new concept to implement the elliptic curve point multiplication (PM). This computation is based on a new modular arithmetic over Gaussian integer fields. Gaussian integers are a subset of the complex numbers such that the real and imaginary parts are integers. Since Gaussian integer fields are isomorphic to prime fields, this arithmetic is suitable for many elliptic curves. Representing the key by a Gaussian integer expansion is beneficial to reduce the computational complexity and the memory requirements of secure hardware implementations, which are robust against attacks. Furthermore, an area-efficient coprocessor design is proposed with an arithmetic unit that enables Montgomery modular arithmetic over Gaussian integers. The proposed architecture and the new arithmetic provide high flexibility, i.e., binary and non-binary key expansions as well as protected and unprotected PM calculations are supported. The proposed coprocessor is a competitive solution for a compact ECC processor suitable for applications in small embedded systems.
Modeling a suitable birth density is a challenge when using Bernoulli filters such as the Labeled Multi-Bernoulli (LMB) filter. The birth density of newborn targets is unknown in most applications, but must be given as a prior to the filter. Usually the birth density stays unchanged or is designed based on the measurements from previous time steps.
In this paper, we assume that the true initial state of new objects is normally distributed. The expected value and covariance of the underlying density are unknown parameters. Using the estimated multi-object state of the LMB and the Rauch-Tung-Striebel (RTS) recursion, these parameters are recursively estimated and adapted after a target is detected.
The main contribution of this paper is an algorithm to estimate the parameters of the birth density and its integration into the LMB framework. Monte Carlo simulations are used to evaluate the detection driven adaptive birth density in two scenarios. The approach can also be applied to filters that are able to estimate trajectories.
The Montgomery multiplication is an efficient method for modular arithmetic. Typically, it is used for modular arithmetic over integer rings to prevent the expensive inversion for the modulo reduction. In this work, we consider modular arithmetic over rings of Gaussian integers. Gaussian integers are subset of the complex numbers such that the real and imaginary parts are integers. In many cases Gaussian integer rings are isomorphic to ordinary integer rings. We demonstrate that the concept of the Montgomery multiplication can be extended to Gaussian integers. Due to independent calculation of the real and imaginary parts, the computation complexity of the multiplication is reduced compared with ordinary integer modular arithmetic. This concept is suitable for coding applications as well as for asymmetric key cryptographic systems, such as elliptic curve cryptography or the Rivest-Shamir-Adleman system.
In this work, we investigate a hybrid decoding approach that combines algebraic hard-input decoding of binary block codes with soft-input decoding. In particular, an acceptance criterion is proposed which determines the reliability of a candidate codeword. For many received codewords the stopping criterion indicates that the hard-decoding result is sufficiently reliable, and the costly soft-input decoding can be omitted. The proposed acceptance criterion significantly reduces the decoding complexity. For simulations we combine the algebraic hard-input decoding with ordered statistics decoding, which enables near maximum likelihood soft-input decoding for codes of small to medium block lengths.
Multi-dimensional spatial modulation is a multipleinput/ multiple-output wireless transmission technique, that uses only a few active antennas simultaneously. The computational complexity of the optimal maximum-likelihood (ML) detector at the receiver increases rapidly as more transmit antennas or larger modulation orders are employed. ML detection may be infeasible for higher bit rates. Many suboptimal detection algorithms for spatial modulation use two-stage detection schemes where the set of active antennas is detected in the first stage and the transmitted symbols in the second stage. Typically, these detection schemes use the ML strategy for the symbol detection. In this work, we consider a suboptimal detection algorithm for the second detection stage. This approach combines equalization and list decoding. We propose an algorithm for multi-dimensional signal constellations with a reduced search space in the second detection stage through set partitioning. In particular, we derive a set partitioning from the properties of Hurwitz integers. Simulation results demonstrate that the new algorithm achieves near-ML performance. It significantly reduces the complexity when compared with conventional two-stage detection schemes. Multi-dimensional constellations in combination with suboptimal detection can even outperform conventional signal constellations in combination with ML detection.
Spatial modulation is a low-complexity multipleinput/ multipleoutput transmission technique. The recently proposed spatial permutation modulation (SPM) extends the concept of spatial modulation. It is a coding approach, where the symbols are dispersed in space and time. In the original proposal of SPM, short repetition codes and permutation codes were used to construct a space-time code. In this paper, we propose a similar coding scheme that combines permutation codes with codes over Gaussian integers. Short codes over Gaussian integers have good distance properties. Furthermore, the code alphabet can directly be applied as signal constellation, hence no mapping is required. Simulation results demonstrate that the proposed coding approach outperforms SPM with repetition codes.
Many resource-constrained systems still rely on symmetric cryptography for verification and authentication. Asymmetric cryptographic systems provide higher security levels, but are very computational intensive. Hence, embedded systems can benefit from hardware assistance, i.e., coprocessors optimized for the required public key operations. In this work, we propose an elliptic curve cryptographic coprocessors design for resource-constrained systems. Many such coprocessor designs consider only special (Solinas) prime fields, which enable a low-complexity modulo arithmetic. Other implementations support arbitrary prime curves using the Montgomery reduction. These implementations typically require more time for the point multiplication. We present a coprocessor design that has low area requirements and enables a trade-off between performance and flexibility. The point multiplication can be performed either using a fast arithmetic based on Solinas primes or using a slower, but flexible Montgomery modular arithmetic.
Side Channel Attack Resistance of the Elliptic Curve Point Multiplication using Gaussian Integers
(2020)
Elliptic curve cryptography is a cornerstone of embedded security. However, hardware implementations of the elliptic curve point multiplication are prone to side channel attacks. In this work, we present a new key expansion algorithm which improves the resistance against timing and simple power analysis attacks. Furthermore, we consider a new concept for calculating the point multiplication, where the points of the curve are represented as Gaussian integers. Gaussian integers are subset of the complex numbers, such that the real and imaginary parts are integers. Since Gaussian integer fields are isomorphic to prime fields, this concept is suitable for many elliptic curves. Representing the key by a Gaussian integer expansion is beneficial to reduce the computational complexity and the memory requirements of a secure hardware implementation.
Ein Beitrag zum Beobachterentwurf und zur sensorlosen Folgeregelung translatorischer Magnetaktoren
(2020)
Flatness-based feed-forward control of solenoid actuators is considered. For precise motion planning and accurate steering of conventional solenoids, eddy currents cannot be neglected. The system of ordinary differential equations including eddy currents, that describes the nonlinear dynamics of such actuators, is not differentially flat. Thus, a distributed parameter approach based on a diffusion equation is considered, that enables the parametrization of the eddy current by the armature position and its time derivatives. In order to design the feedforward control, the distributed parameter model of the eddy current subsystem is combined with a typical nonlinear lumped parameter model for the electrical and mechanical subsystems of the solenoid. The control design and its application are illustrated by numerical and practical results for an industrial solenoid actuator.