Related papers: Algorithmic Obfuscation over GF($2^m$)
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…
Hardware IP protection has been one of the most critical areas of research in the past years. Recently, attacks on hardware IPs (such as reverse engineering or cloning) have evolved as attackers have developed sophisticated techniques.…
Gate camouflaging is a technique for obfuscating the function of a circuit against reverse engineering attacks. However, if an adversary has pre-existing knowledge about the set of functions that are viable for an application, random…
Binary field extensions are fundamental to many applications, such as multivariate public key cryptography, code-based cryptography, and error-correcting codes. Their implementation requires a foundation in number theory and algebraic…
In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…
A finite impulse response (FIR) filter is a ubiquitous block in digital signal processing applications. Its characteristics are determined by its coefficients, which are the intellectual property (IP) for its designer. However, in a…
We introduce a new approach to computation on encrypted data -- Encrypted Operator Computing (EOC) -- as an alternative to Fully Homomorphic Encryption (FHE). Given a plaintext vector $|{x}\rangle$, $x\in \{0,1\}^n$, and a function $F(x)$…
Quantum computing leverages quantum mechanics to achieve computational advantages over classical hardware, but the use of third-party quantum compilers in the Noisy Intermediate-Scale Quantum (NISQ) era introduces risks of intellectual…
An abelian variety over a number field is called L-abelian variety if, for any element of the absolute Galois group of a number field L, the conjugated abelian variety is isogenous to the given one by means of an isogeny that preserves the…
In the past two decades, Elliptic Curve Cryptography (ECC) have become increasingly advanced. ECC, with much smaller key sizes, offers equivalent security when compared to other asymmetric cryptosystems. In this survey, an comprehensive…
Using the action of the Galois group of a normal extension of number fields, we generalize and symmetrize various fundamental statements in algebra and algebraic number theory concerning splitting types of prime ideals, factorization types…
Quantum circuit obfuscation is becoming increasingly important to prevent theft and reverse engineering of quantum algorithms. As quantum computing advances, the need to protect the intellectual property contained in quantum circuits…
We bring in here a novel algebraic approach for attacking the McEliece cryptosystem. It consists in introducing a subspace of matrices representing quadratic forms. Those are associated with quadratic relationships for the component-wise…
Federated learning has been proposed as a privacy-preserving machine learning framework that enables multiple clients to collaborate without sharing raw data. However, client privacy protection is not guaranteed by design in this framework.…
In this paper we give a unified approach in categorical setting to the problem of finding the Galois closure of a finite cover, which includes as special cases the familiar finite separable field extensions, finite unramified covers of a…
While the advent of Graph Neural Networks (GNNs) has greatly improved node and graph representation learning in many applications, the neighborhood aggregation scheme exposes additional vulnerabilities to adversaries seeking to extract…
In 1972, Serre showed that the adelic Galois representation associated to a non-CM elliptic curve over a number field has open image in GL_2(\hat{Z}). In Greicius' thesis, he develops necessary and sufficient criteria for determining when…
Elliptic curve multiplications can be improved by replacing the standard ladder algorithm's base 2 representation of the scalar multiplicand, with mixed-base representations with power-of-2 bases, processing the n bits of the current digit…
Integrated circuits (ICs) are essential to modern electronic systems, yet they face significant risks from physical reverse engineering (RE) attacks that compromise intellectual property (IP) and overall system security. While IC camouflage…
Polynomial multiplication is a bottleneck in most of the public-key cryptography protocols, including Elliptic-curve cryptography and several of the post-quantum cryptography algorithms presently being studied. In this paper, we present a…