Related papers: Unified Field Multiplier for ECC: Inherent Resista…
In this paper we describe our flexible ECDSA design for elliptic curve over binary extended fields GF(2l). We investigated its resistance against Horizontal Collision Correlation Attacks (HCCA). Due to the fact that our design is based on…
Side-channel analysis attacks, especially horizontal DPA and DEMA attacks, are significant threats for cryptographic designs. In this paper we investigate to which extend different multiplication formulae and randomization of the field…
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 behavior of…
Elliptic Curve Cryptography (ECC) is widely accepted for ensuring secure data exchange between resource-limited IoT devices. The National Institute of Standards and Technology (NIST) recommended implementation, such as B-163, is…
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…
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…
Securing communication channels is especially needed in wireless environments. But applying cipher mechanisms in software is limited by the calculation and energy resources of the mobile devices. If hardware is applied to realize…
A Galois unitary is a generalization of the notion of anti-unitary operators. They act only on those vectors in Hilbert space whose entries belong to some chosen number field. For Mutually Unbiased Bases the relevant number field is a…
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…
A Hopf Galois structure on a finite field extension $L/K$ is a pair $(H,\mu)$, where $H$ is a finite cocommutative $K$-Hopf algebra and $\mu$ a Hopf action. In this paper we present a program written in the computational algebra system…
Galois Field arithmetic blocks are the key components in many security applications, such as Elliptic Curve Cryptography (ECC) and the S-Boxes of the Advanced Encryption Standard (AES) cipher. This paper introduces a novel hardware…
Let $K$ be an imaginary quadratic field and $p$ a prime split in $K$. In this paper we construct an anticyclotomic Euler system for the adjoint representation attached to elliptic modular forms base changed to $K$. We also relate our Euler…
Elliptic curve cryptography (ECC) has emerged as the dominant public-key protocol, with NIST standardizing parameters for binary field GF(2^m) ECC systems. This work presents a hardware implementation of a Hybrid Multiplication technique…
We show that under certain conditions every maximal symmetric subfield of a central division algebra with positive unitary involution $(B,\tau)$ will be a Galois extension of the fixed field of $\tau$ and will "real split" $(B,\tau)$. As an…
A Hopf Galois structure on a finite field extension L/K is given by a finite cocommutative K-Hopf algebra and a Hopf action. In this paper we present an algorithm written in the computational algebra system Magma which gives all Hopf Galois…
Devices employing cryptographic approaches have to be resistant to physical attacks. Side-Channel Analysis (SCA) and Fault Injection (FI) attacks are frequently used to reveal cryptographic keys. In this paper, we present a combined SCA and…
As cyber-physical systems (CPSs) become more dependent on data and communication networks, their vulnerability to false data injection (FDI) attacks has raised significant concerns. Among these, stealthy attacks, those that evade…
Side Channel Analysis attacks take advantage of the information leaked from the implementations of cryptographic algorithms. In this paper we describe two key revealing methods which are based on machine learning algorithms: K-means and…
A representation of finite fields that has proved useful when implementing finite field arithmetic in hardware is based on an isomorphism between subrings and fields. In this paper, we present an unified formulation for multiplication in…
Galois field (GF) arithmetic is used to implement critical arithmetic components in communication and security-related hardware, and verification of such components is of prime importance. Current techniques for formally verifying such…