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In the evolving landscape of cryptographic security, the robustness of Elliptic Curve Cryptography (ECC) against side-channel analysis (SCA) attacks is of paramount importance due to the widespread use of ECC and the growing sophistication…

Elliptic Curve Scalar Multiplication denoted as kP operation is the basic operation in all Elliptic Curve based cryptographic protocols. The atomicity principle and different atomic patterns for kP algorithms were proposed in the past as…

In this work, we investigate the security of Elliptic Curve Cryptosystem (ECC) implementations against Side-Channel Analysis (SCA). ECC is well known for its efficiency and strong security, yet vulnerable to SCA which exploits physical…

In this work we discuss the resistance of atomic pattern algorithms for elliptic curve point multiplication against simple side channel analysis attacks using our own implementation as an example. The idea of the atomicity principle is to…

Scalar multiplication kP is a critical operation in Elliptic Curve Cryptosystems (ECC), often targeted by Side-Channel Analysis (SCA). Despite strategies based on atomic patterns to enhance security, the binary kP algorithms remain…

In the past years, research on Shor's algorithm for solving elliptic curves for discrete logarithm problems (Shor's ECDLP), the basis for cracking elliptic curve-based cryptosystems (ECC), has started to garner more significant interest. To…

In this paper we address the problem of protecting elliptic curve scalar multiplication implementations against side-channel analysis by using the atomicity principle. First of all we reexamine classical assumptions made by scalar…

We propose a novel approach for performing side-channel attacks on elliptic curve cryptography. Unlike previous approaches and inspired by the ``activity detection'' literature, we adopt a long-short-term memory (LSTM) neural network to…

In this paper we report on the results of selected horizontal SCA attacks against two open-source designs that implement hardware accelerators for elliptic curve cryptography. Both designs use the complete addition formula to make the point…

We perform logical and physical resource estimation for computing binary elliptic curve discrete logarithms using Shor's algorithm on fault-tolerant quantum computers. We adopt a windowed approach to design our circuit implementation of the…

Scalar multiplication kP is the operation most frequently targeted in Elliptic Curve (EC) cryptosystems. To protect against single-trace Side-Channel Analysis (SCA) attacks, the atomicity principle and various atomic block patterns have…

The goal of this paper is to revisit Kernel Principal Component Analysis (KPCA) through dualization of a difference of convex functions. This allows to naturally extend KPCA to multiple objective functions and leads to efficient…

Specific quantum algorithms exist to-in theory-break elliptic curve cryptographic protocols. Implementing these algorithms requires designing quantum circuits that perform elliptic curve arithmetic. To accurately judge a cryptographic…

We consider a quantum polynomial-time algorithm which solves the discrete logarithm problem for points on elliptic curves over $GF(2^m)$. We improve over earlier algorithms by constructing an efficient circuit for multiplying elements of…

We consider the problem of checking whether an elliptic curve defined over a given number field has complex multiplication. We study two polynomial time algorithms for this problem, one randomized and the other deterministic. The randomized…

Elliptic curves are planar curves which can be used to define an abelian group. The efficient computation of discrete logarithms over this group is a longstanding problem relevant to cryptography. It may be possible to efficiently compute…

Precise suites of benchmarks are required to assess the progress of early fault-tolerant quantum computers at economically impactful applications such as cryptanalysis. Appropriate challenges exist for factoring but those for elliptic curve…

In this paper, we propose an elliptic curve key generation processor over GF(2m) and GF(P) with Network-on-Chip (NoC) design scheme based on binary scalar multiplication algorithm. Over the Two last decades, Elliptic Curve Cryptography…

Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…

Quantum computers have the potential to break classical cryptographic systems by efficiently solving problems such as the elliptic curve discrete logarithm problem using Shor's algorithm. While resource estimates for factoring-based…