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Quantum algorithms can break factoring and discrete logarithm based cryptography and weaken symmetric cryptography and hash functions. In order to estimate the real-world impact of these attacks, apart from tracking the development of…
One of the major issues of cryptography is the cryptanalysis of cipher algorithms. Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required.…
When solving data analysis problems it is important to integrate prior knowledge and/or structural invariances. This paper contributes by a novel framework for incorporating algebraic invariance structure into kernels. In particular, we…
Quantum computers, that may become available one day, would impact many scientific fields, most notably cryptography since many asymmetric primitives are insecure against an adversary with quantum capabilities. Cryptographers are already…
Let $G$ be a complex classical group, and let $V$ be its defining representation (possibly plus a copy of the dual). A foundational problem in classical invariant theory is to write down generators and relations for the ring of…
Several cryptographic protocols constructed based on less-known algorithmic problems, such as those in non-commutative groups, group rings, semigroups, etc., which claim quantum security, have been broken through classical reduction methods…
We introduce a general method for achieving robust group-invariance in group-equivariant convolutional neural networks ($G$-CNNs), which we call the $G$-triple-correlation ($G$-TC) layer. The approach leverages the theory of the…
We propose a symmetric key homomorphic encryption scheme based on the evaluation of multivariate polynomials over a finite field. The proposed scheme is somewhat homomorphic with respect to addition and multiplication. Further, we define a…
Is it possible to convert classical cryptographic reductions into post-quantum ones? It is customary to argue that while this is problematic in the interactive setting, non-interactive reductions do carry over. However, when considering…
Fully homomorphic encryption is a kind of encryption scheme, which enables arbitrary computation on encrypted data without accessing the data. We present the quantum version of fully homomorphic encryption scheme, which is constructed based…
Lattice based encryption schemes and linear code based encryption schemes have received extensive attention in recent years since they have been considered as post-quantum candidate encryption schemes. Though LLL reduction algorithm has…
Recently, heterogeneous Graph Neural Networks (GNNs) have become a de facto model for analyzing HGs, while most of them rely on a relative large number of labeled data. In this work, we investigate Contrastive Learning (CL), a key component…
We study the algebra of complex polynomials which remain invariant under the action of the local Clifford group under conjugation. Within this algebra, we consider the linear spaces of homogeneous polynomials degree by degree and construct…
The present work develops certain analytical tools required to construct and compute invariant kernels on the space of complex covariance matrices. The main result is the $\mathrm{L}^1$--Godement theorem, which states that any invariant…
Unsupervised graph representation learning is a non-trivial topic. The success of contrastive methods in the unsupervised representation learning on structured data inspires similar attempts on the graph. Existing graph contrastive learning…
Block ciphers are versatile cryptographic ingredients that are used in a wide range of applications ranging from secure Internet communications to disk encryption. While post-quantum security of public-key cryptography has received…
We introduce several new quantum algorithms for estimating homological invariants, specifically Betti numbers and persistent Betti numbers, of a simplicial complex given via a structured classical input. At the core of our algorithm lies…
The impossibility of creating perfect identical copies of unknown quantum systems is a fundamental concept in quantum theory and one of the main non-classical properties of quantum information. This limitation imposed by quantum mechanics,…
Post-Quantum Cryptography (PQC) attempts to find cryptographic protocols resistant to attacks using Shor polynomial time algorithm for numerical field problems or Grover search algorithm. A mostly overlooked but valuable line of solutions…
Motivated by a historical combinatorial problem that resembles the well-known Josephus problem, we investigate circular partition algorithms and formulate problems in deterministic finite automata with practical algorithms. The historical…