Related papers: Pell hyperbolas in DLP-based cryptosystems
Security of cryptographic protocols can be analysed by creating a model in a formal language and verifying the model in a tool. All such tools focus on the last part of the analysis, verification, and the interpretation of the specification…
We present novel homomorphic encryption schemes for integer arithmetic, intended for use in secure single-party computation in the cloud. These schemes are capable of securely computing only low degree polynomials homomorphically, but this…
One of the advantages of adopting a Model Based Development (MBD) process is that it enables testing and verification at early stages of development. However, it is often desirable to not only verify/falsify certain formal system…
Polar codes are a new class of error correcting linear block codes, whose generator matrix is specified by the knowledge of transmission channel parameters, code length and code dimension. Moreover, regarding computational security, it is…
Developers and organizations are using Large Language Models (LLMs) to generate security-critical code more frequently than ever, including cryptographic solutions for their products. This study presents an empirical evaluation of…
In this paper, we have proposed a modified cryptographic scheme based on the application of recursive matrices as key in ECC and ElGamal. For encryption, we consider mapping analogous to affine Hill cipher in which a plaintext matrix has…
The role of discrete (or point-group) symmetries is discussed in the framework of the Cluster Shell Model which describes the splitting of single-particle levels in the deformed field of cluster potentials. We discuss the classification of…
This paper aims to create a secure environment for networked control systems composed of multiple dynamic entities and computational control units via networking, in the presence of disclosure attacks. In particular, we consider the…
Distributions on integers are ubiquitous in probabilistic modeling but remain challenging for many of today's probabilistic programming languages (PPLs). The core challenge comes from discrete structure: many of today's PPL inference…
There are several public key establishment protocols as well as complete public key cryptosystems based on allegedly hard problems from combinatorial (semi)group theory known by now. Most of these problems are search problems, i.e., they…
Cryptocurrencies are poised to revolutionize the modern economy by democratizing commerce. These currencies operate on top of blockchain-based distributed ledgers. Existing permissionless blockchain-based protocols offer unparalleled…
The discrete logarithm problem in a finite group is the basis for many protocols in cryptography. The best general algorithms which solve this problem have time complexity of $\mathcal{O}(\sqrt{N}\log N)$, and a space complexity of…
The increased use of cryptography to protect our personal information makes us want to understand the security of cryptosystems. The security of many cryptosystems relies on solving the discrete logarithm, which is thought to be relatively…
We investigate questions related to the minimal degree of invariants of finitely generated diagonalizable groups. These questions were raised in connection to security of a public key cryptosystem based on invariants of diagonalizable…
We analyze the security of two-way quantum key distribution using arbitrary finite-dimensional systems, considering both individual and collective eavesdropping attacks, without the effective use of entangled states, by incorporating two…
In this paper, we study the problem of sampling random supersingular elliptic curves with unknown endomorphism rings. This problem has recently gained considerable attention as many isogeny-based cryptographic protocols require such…
Let f be an arbitrary positive integer valued function. The goal of this note is to show that one can construct a finitely generated group in which the discrete log problem is polynomially equivalent to computing the function f. In…
In this work, we present homomorphic encryption-based vaults (Haults), a permissioned privacy-preserving smart wallet protocol for VM-enabled blockchains that keeps users' balances confidential, as well as the amounts transacted to other…
Homomorphic encryption (HE) is widely adopted in untrusted environments such as federated learning. A notable limitation of conventional single-key HE schemes is the stringent security assumption regarding collusion between the parameter…
Differential privacy is often applied with a privacy parameter that is larger than the theory suggests is ideal; various informal justifications for tolerating large privacy parameters have been proposed. In this work, we consider partial…