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Photonic neural networks offer a promising alternative to traditional electronic systems for machine learning accelerators due to their low latency and energy efficiency. However, the challenge of implementing the backpropagation algorithm…
We describe a group theoretic analysis of Shor's algorithm and other related hidden subgroup problems in mathematics and relate these to symmetries of molecular and condensed phase assemblies. By recasting Shor's algorithm through the lens…
We develop matrix cryptography based on linear recurrent sequences of any order that allows securing encryption against brute force and chosen plaintext attacks. In particular, we solve the problem of generalizing error detection and…
Key Encapsulation Mechanisms (KEMs) are a set of cryptographic techniques that are designed to provide symmetric encryption key using asymmetric mechanism (public key). In the current study, we concentrate on design and analysis of key…
The interest in homomorphic encryption/decryption is increasing due to its excellent security properties and operating facilities. It allows operating on data without revealing its content. In this work, we suggest using homomorphism for…
Let $G_1$ be a cyclic multiplicative group of order $n$. It is known that the Diffie-Hellman problem is random self-reducible in $G_1$ with respect to a fixed generator $g$ if $\phi(n)$ is known. That is, given $g, g^x\in G_1$ and having…
Finding low-weight multiples of a binary polynomial is a difficult problem arising in the context of stream ciphers cryptanalysis. The classical algorithm to solve this problem is based on a time memory trade-off. We will present an…
The breakthrough of achieving fully homomorphic encryption sparked enormous studies on where and how to apply homomorphic encryption schemes so that operations can be performed on encrypted data without the secret key while still obtaining…
In this work, we unveil an analogy between well-known lattice based learning with error problem and ill-posed inverse problems. We show that LWE problem is a structured inverse problem. Further, we propose a symmetric encryption scheme…
The evolution of encryption algorithms have led to the development of very complicated and highly versatile algorithms that sacrifice efficiency for better and harder to decrypt results. But by the application of a genetic schema to the…
The Ring Learning-With-Errors (LWE) problem, whose security is based on hard ideal lattice problems, has proven to be a promising primitive with diverse applications in cryptography. There are however recent discoveries of faster algorithms…
High-speed long polynomial multiplication is important for applications in homomorphic encryption (HE) and lattice-based cryptosystems. This paper addresses low-latency hardware architectures for long polynomial modular multiplication using…
This paper studies the problem of reconstructing binary matrices that are only accessible through few evaluations of their discrete X-rays. Such question is prominently motivated by the demand in material science for developing a tool for…
This paper introduces a newly developed private key cryptosystem and a public key cryptosystem. In the first one, each letter is encrypted with a different key. Therefore, it is a kind of a one-time pad. The second one is inspired by the…
In this paper, we present efficient algorithms for solving the Diophantine equation $f(x, y) = m$ for an arbitrary definite binary quadratic form $f$, given the factorization of $m$. While Cornacchia's algorithm to solve $x^2 + dy^2 = m$ is…
This paper aims to provide an efficient implementation of encrypted linear dynamic controllers that perform recursive multiplications on a Ring-Learning With Errors (Ring-LWE) based cryptosystem. By adopting a system-theoretical approach,…
One of the possible generalizations of the discrete logarithm problem to arbitrary groups is the so-called conjugacy search problem (sometimes erroneously called just the conjugacy problem): given two elements a, b of a group G and the…
In this letter, we consider a problem of reconstructing an unknown discrete signal taking values in a finite alphabet from incomplete linear measurements. The difficulty of this problem is that the computational complexity of the…
We consider the problems of Private and Secure Matrix Multiplication (PSMM) and Fully Private Matrix Multiplication (FPMM), for which matrices privately selected by a master node are multiplied at distributed worker nodes without revealing…
We propose a new symmetric cryptographic scheme based on functional invariants defined over discrete oscillatory functions with hidden parameters. The scheme encodes a secret integer through a four-point algebraic identity preserved under…