Related papers: Pell hyperbolas in DLP-based cryptosystems
We study the use of polyhedral discretizations for the solution of heat diffusion and elastodynamic problems in computer graphics. Polyhedral meshes are more natural for certain applications than pure triangular or quadrilateral meshes,…
Akleylek et al. [S. Akleylek, L. Emmungil and U. Nuriyev, A mod ified algorithm for peer-to-peer security, journal of Appl. Comput. Math., vol. 6(2), pp.258-264, 2007.], introduced a modified public-key encryption scheme with steganographic…
We provide a survey on the Hidden Subgroup Problem (HSP), which plays an important role in studying the security of public-key cryptosystems. We first review the abelian case, where Kitaev's algorithm yields an efficient quantum solution to…
The point of this paper is to use affine automorphisms from algebraic geometry to build cryptographic multivariate mappings. We will construct groups G,H, both isomorphic to the cyclic group with a prime number of elements and multilinear…
This article introduces differentially private log-location-scale (DP-LLS) regression models, which incorporate differential privacy into LLS regression through the functional mechanism. The proposed models are established by injecting…
We describe a cryptographic protocol in which Wheeler's delayed choice experiment is used to generate the key distribution. The protocol, which uses photons polarized only along one axis, is secure against general attacks.
Large language models (LLMs) employ safety mechanisms to prevent harmful outputs, yet these defenses primarily rely on semantic pattern matching. We show that encoding harmful prompts as coherent mathematical problems -- using formalisms…
We analyze the security and reliability of a recently proposed class of public-key cryptosystems against attacks by unauthorized parties who have acquired partial knowledge of one or more of the private key components and/or of the…
Secure computation often benefits from the use of correlated randomness to achieve fast, non-cryptographic online protocols. A recent paradigm put forth by Boyle $\textit{et al.}$ (CCS 2018, Crypto 2019) showed how pseudorandom correlation…
Differential privacy (DP) has arisen as the state-of-the-art metric for quantifying individual privacy when sensitive data are analyzed, and it is starting to see practical deployment in organizations such as the US Census Bureau, Apple,…
Most cryptosystems are defined over finite algebraic structures where arithmetic operations are performed modulo natural numbers. This applies to private key as well as to public key ciphers. No secure cryptosystems defined over the field…
Infrastructures are group-like objects that make their appearance in arithmetic geometry in the study of computational problems related to number fields and function fields over finite fields. The most prominent computational tasks of…
Differential privacy (DP) has a wide range of applications for protecting data privacy, but designing and verifying DP algorithms requires expert-level reasoning, creating a high barrier for non-expert practitioners. Prior works either rely…
This work presents a dual system-level parameterization (D-SLP) method for closed-loop system identification. The recent system-level synthesis framework parameterizes all stabilizing controllers via linear constraints on closed-loop…
We prove that the path-finding problem in $\ell$-isogeny graphs and the endomorphism ring problem for supersingular elliptic curves are equivalent under reductions of polynomial expected time, assuming the generalised Riemann hypothesis.…
Protocols satisfying Local Differential Privacy (LDP) enable parties to collect aggregate information about a population while protecting each user's privacy, without relying on a trusted third party. LDP protocols (such as Google's RAPPOR)…
Linear codes have diverse applications in secret sharing schemes, secure two-party computation, association schemes, strongly regular graphs, authentication codes and communication. There are a large number of linear codes with few weights…
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…
Cryptography is the science of using mathematics to encrypt and decrypt data. Cryptography enables you to store sensitive information or transmit it across insecure networks so that it cannot be read by anyone except the intended recipient.…
Big data has been a pervasive catchphrase in recent years, but dealing with data scarcity has become a crucial question for many real-world deep learning (DL) applications. A popular methodology to efficiently enable the training of DL…