Horizontal Attacks using K-Means: Comparison with Traditional Analysis Methods

Horizontal SCA Attacks against $kP$ Algorithm Using K-Means and PCA

“…In [4] and here we performed the horizontal attacks against an FPGA implementation of our kP designs using the measured power trace of a single kP execution. We ported our 3 ECC designs to a Spartan 6 FPGA [10] running at 4 MHz.…”

“…Let 𝑋 be the observation matrix with 𝑙 observations and 𝑑 features as shown in (3). Let 𝒙 𝑗 be the 𝑗 𝑡ℎ observation vector with 𝑑 features as described in (4). Further let us define 𝒙 𝑖 to be an 𝑖 𝑡ℎ feature vector with 𝑙 observations of the following form:…”

“…In [5] we described the implementation details of our 3 different kP designs and evaluated their resistance against horizontal differential SCA attacks using statistical analysis. In [4] the K-means was evaluated as a mean for the extraction of the secret scalar k (further also denoted as key) using the same designs. In this paper we evaluate the applicability and effectiveness of Principal Component Analysis (PCA) as a mean for the secret revealing i.e.…”

“…as an attacking method alternative to K-means. We applied exactly the same steps for the preparation of traces as in [4] and [3].…”

“…In ECDSA an attacker can easy calculate the private key if the scalar 𝑘 used for the signature generation is known to the attacker [3]. Thus, the goal of an attacker is to reveal the scalar k. In our previous paper [4] we have shown that a machine learning algorithm K-means is a successful method for revealing the secret scalar k attacking a single PT. We have noticed that another unsupervised method for dimensionality reduction and data visualization, called Principal Component Analysis (PCA), can also be used to extract the secret scalar k analysing a single measured kP trace.…”