Methods increasing inherent resistance of ECC designs against horizontal attacks

Due to the nature of applications such as critical infrastructure and the Internet of Things etc. side channel analysis attacks are becoming a serious threat. Side channel analysis attacks take advantage from the fact that the behaviour of crypto implementations can be observed and provides hints that simplify revealing keys. A new type of SCA is the so called horizontal differential SCA. In this paper we investigate two different approaches to increase the inherent resistance of our hardware accelerator for the kP operation. The first approach aims at reducing the impact of the addressing in our design by realizing a regular schedule of the addressing. In the second approach, we investigated how the formula used to implement the multiplication of GF(2n)-elements influences the results of horizontal DPA attacks against a Montgomery kP-implementation. We implemented 5 designs with different partial multipliers, i.e. based on different multiplication formulae. We used two different technologies, i.e. a 130 and a 250 nm technology, to simulate power traces for our analysis. We show that the implemented multiplication formula influences the success of horizontal attacks significantly. The combination of these two approaches leads to the most resistant design. For the 250 nm technology only 2 key candidates could be revealed with a correctness of about 70% which is a huge improvement given the fact that for the original design 7 key candidates achieved a correctness of more than 90%. For our 130 nm technology no key candidate was revealed with a correctness of more than 60%

Resistance of the Montgomery Ladder Against Simple SCA: Theory and Practice

The Montgomery kP algorithm i.e. the Montgomery ladder is reported in literature as resistant against simple SCA due to the fact that the processing of each key bit value of the scalar k is done using the same sequence of operations. We implemented the Montgomery kP algorithm using Lopez-Dahab projective coordinates for the NIST elliptic curve B-233. We instantiated the same VHDL code for a wide range of clock frequencies for the same target FPGA and using the same compiler options. We measured electromagnetic traces of the kP executions using the same input data, i.e. scalar k and elliptic curve point P, and measurement setup. Additionally, we synthesized the same VHDL code for two IHP CMOS technologies, for a broad spectrum of frequencies. We simulated the power consumption of each synthesized design during an execution of the kP operation, always using the same scalar k and elliptic curve point P as inputs. Our experiments clearly show that the success of simple electromagnetic analysis attacks against FPGA implementations as well as the one of simple power analysis attacks against synthesized ASIC designs depends on the target frequency for which the design was implemented and at which it is executed significantly. In our experiments the scalar k was successfully revealed via simple visual inspection of the electromagnetic traces of the FPGA for frequencies from 40 to 100 MHz when standard compile options were used as well as from 50 MHz up to 240 MHz when performance optimizing compile options were used. We obtained similar results attacking the power traces simulated for the ASIC. Despite the significant differences of the here investigated technologies the designs’ resistance against the attacks performed is similar: only a few points in the traces represent strong leakage sources allowing to reveal the key at very low and very high frequencies. For the “middle” frequencies the number of points which allow to successfully reveal the key increases when increasing the frequency

Horizontal DEMA Attack as the Criterion to Select the Best Suitable EM Probe

Implementing cryptographic algorithms in a tamper resistant way is an extremely complex task as the algorithm used and the target platform have a significant impact on the potential leakage of the implementation. In addition the quality of the tools used for the attacks is of importance. In order to evaluate the resistance of a certain design against electromagnetic emanation attacks – as a highly relevant type of attacks – we discuss the quality of different electromagnetic (EM) probes as attack tools. In this paper we propose to use the results of horizontal attacks for comparison of measurement setup and for determining the best suitable instruments for measurements. We performed horizontal differential electromagnetic analysis (DEMA) attacks against our ECC design that is an im-plementation of the Montgomery kP algorithm for the NIST elliptic curve B-233. We experimented with 7 different EM probes under same conditions: attacked FPGA, design, inputs, measurement point and measurement equipment were the same, excepting EM probes. The used EM probe influences the success rate of performed attack significantly. We used this fact for the comparison of probes and for determining the best suitable one

Resilience in the Cyberworld: Definitions, Features and Models

Resilience is a feature that is gaining more and more attention in computer science and computer engineering. However, the definition of resilience for the cyber landscape, especially embedded systems, is not yet clear. This paper discusses definitions provided by different authors, on different years and with different application areas the field of computer science/computer engineering. We identify the core statements that are more or less common to the majority of the definitions, and based on this we give a holistic definition using attributes for (cyber-) resilience. In order to pave a way towards resilience engineering, we discuss a theoretical model of the life cycle of a (cyber-) resilient system that consists of key actions presented in the literature. We adapt this model for embedded (cyber-) resilient systems

On the Complexity of Attacking Elliptic Curve Based Authentication Chips

In this paper we discuss the difficulties of mounting successful attacks against crypto implementations if essential information is missing. We start with a detailed description of our attack against our own design, to highlight which information is needed to increase the success of an attack, i.e. we use it as a blueprint to the following attack against commercially available crypto chips. We would like to stress that our attack against our own design is very similar to what happens during certification e.g. according to the Common Criteria Standard as in those cases the manufacturer needs to provide detailed information. If attacking commercial designs without signing NDAs, we were forced to intensively search the Internet for information about the designs. We were able to reveal information on the processing sequence during the authentication process even as detailed as identifying the clock cycles in which the individual key bits are processed. But we could not reveal the private keys used by the attacked commercial authentication chips 100% correctly. Moreover, as we did not knew the used keys we could not evaluate the success of our attack. To summarize, the effort of such an attack is significantly higher than the one of attacking a well-known implementation

Reversal of Impaired Hippocampal Long-Term Potentiation and Contextual Fear Memory Deficits in Angelman Syndrome Model Mice by ErbB Inhibitors

Our findings suggest that neuregulin-ErbB4 signaling is involved in synaptic plasticity and memory impairments in AS model mice, suggesting that ErbB inhibitors have therapeutic potential for the treatment of A