Elliptic curve cryptography (ECC) is one of the commonly used standard methods for encrypting and signing messages which is especially applicable to resource-constrained devices such as sensor nodes that are networked in the Internet of Things. The same holds true for wearable sensors. In these fields of application, confidentiality and data integrity are of utmost importance as human lives depend on them. In this paper, we discuss the resistance of our fast dual-field ECDSA accelerator against side-channel analysis attacks. We present our implementation of a design supporting four different NIST elliptic curves to allow the reader to understand the discussion of the resistance aspects. For two different target platforms—ASIC and FPGA—we show that the application of atomic patterns, which is considered to ensure resistance against simple side-channel analysis attacks in the literature, is not sufficient to prevent either simple SCA or horizontal address-bit DPA attacks. We also evaluated an approach which is based on the activity of the field multiplier to increase the inherent resistance of the design against attacks performed.

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.

While IoT technology makes industries, cities, and homes smarter, it also opens the door to security risks. With the right equipment and physical access to the devices, the attacker can leverage side-channel information, like timing, power consumption, or electromagnetic emanation, to compromise cryptographic operations and extract the secret key. This work presents a side channel analysis of a cryptographic hardware accelerator for the Elliptic Curve Scalar Multiplication operation, implemented in a Field-Programmable Gate Array and as an Application-Specific Integrated Circuit. The presented framework consists of initial key extraction using a state-of-the-art statistical horizontal attack and is followed by regularized Artificial Neural Networks, which take, as input, the partially incorrect key guesses from the horizontal attack and correct them iteratively. The initial correctness of the horizontal attack, measured as the fraction of correctly extracted bits of the secret key, was improved from 75% to 98% by applying the iterative learning.