## 1 Introduction
Later, it was accepted as a standard by the International Standards Organization (ISO-14888-3), American National Standards Institute (ANSI X9.62), and Institute of Electrical and Electronics Engineers (IEEE 1363), and as the U.S. Government Federal Information Processing Standard (FIPS 186) [13]. The main advantage of using Elliptic Curve Cryptography over RSA is its short key size. The same level of security can be achieved using a 256-bit key for ECDSA as can be achieved using a 3072-bit-long key for RSA [14]. The modern cryptosystems are extremely hard to break. It would take more years than the number for which Earth has existed to solve the complex mathematic problems that are the basis of modern cryptography (factorisation of big numbers, discrete logarithm problem (DLP), or elliptic curve discrete logarithm problem (ECDLP)) or to brute-force modern ciphers using the largest super computers available to men. However, there are ways to compromise their security in merely hours. The cryptographic operations can be implemented either as software libraries or as auxiliary hardware components. They require additional processing time, more energy consumption, or larger chip area, which is especially problematic in resource-constrained IoT or WSN devices. The processing of cryptographic primitives is inevitably correlated to the transistor-switching activity of the underlying hardware, whether it comprises a dedicated circuitry or a part of a general-purpose processing pipeline. Dynamic power consumption, the electromagnetic field emanation, heat dissipation, and, above all, the timing information are just some of many side channels, which can be leveraged to uncover the secret. The first one to present how this could be accomplished was [PERSON], in 1996 [15], who showed how to break the RSA and Data Encryption Standard (DES) algorithms using only timing and power consumption information. This was considered the beginning of Side Channel Analysis (SCA), a branch of cryptoanalysis focusing on finding new ways to leverage side channels to uncover secrets in cryptosystems, but also on finding new methods to mitigate potential attacks and implement countermeasures. Since 2012, when the famous AlexNet [16] Convolutional Neural Network (CNN) won the ImageNet competition, machine learning has gained popularity also among the SCA community. The supervised learning paradigm of feeding the neural networks with large amounts of data and corresponding labels fits perfectly into the profiling scenarios of SCA, where electromagnetic traces (EMTs) or power traces (PTs) of multiple cryptographic operations are recorded and the corresponding secret values are provided as labels. While the profiling attacks make sense in SCA attacks against AES, in public-key cryptography, the secret key is ephemeral and only a single recording of a cryptographic operation with given inputs is possible. Especially dangerous are attacks against signature generation if the secret--not the private key of the sender but a randomly generated big number--can be revealed, analyzing only a single execution trace of the cryptographic operation. Knowledge of the secret random number applied for the signature generation allows one to calculate, easily, the private key of the sender. Our work is an extension of a conference paper [17], published in the 26 th Euromicro Conference Series on Digital System Design (DSD), proposing a semi-supervised non-profiled side channel analysis attack against an Elliptic Curve Scalar Multiplication (ECSM) hardware implementation. The analysis combines a horizontal attack to derive initial key candidates and a highly regularized Support Vector Machine (SVM) classification step to iteratively correct those candidates. We have also discovered another work [18] discussing a similar framework, which we describe in the related work section, outlining the differences with our approach. Our contributions in this work are as follows:  
1. We present a summary of existing horizontal non-profiled solutions against ECSM implementations. 2.