Related papers: Lattices, Homomorphic Encryption, and CKKS
Currently deployed public-key cryptosystems will be vulnerable to attacks by full-scale quantum computers. Consequently, "quantum resistant" cryptosystems are in high demand, and lattice-based cryptosystems, based on a hard problem known as…
Verifiable Homomorphic Encryption (VHE) is a cryptographic technique that integrates Homomorphic Encryption (HE) with Verifiable Computation (VC). It serves as a crucial technology for ensuring both privacy and integrity in outsourced…
Post-quantum cryptography has gained attention due to the need for secure cryptographic systems in the face of quantum computing. Code-based and lattice-based cryptography are two prominent approaches, both heavily studied within the NIST…
In this paper, we study the connextion between lattice and Riesz homomorphisms in Riesz spaces. We prove, under a certain condition, that any lattice homomorphism on Riesz space is a Riesz homomorphism. This fits in the type of results by…
Homomorphic encryption is a cryptographic paradigm allowing to compute on encrypted data, opening a wide range of applications in privacy-preserving data manipulation, notably in AI. Many of those applications require significant linear…
The advent of quantum computing necessitates the transition of worldwide cryptosystems to post-quantum cryptography (PQC), which is founded upon the problem of finding short vectors in high-dimensional structured lattices. It is assumed…
We introduce a novel method and implementation architecture to train neural networks which preserves the confidentiality of both the model and the data. Our method relies on homomorphic capability of lattice based encryption scheme. Our…
Homomorphic encryption provides many opportunities for privacy-aware processing, including with methods related to machine learning. Many of our existing cryptographic methods have been shown in the past to be susceptible to side channel…
An exercise in implementing Scale Invariant Feature Transform using CKKS Fully Homomorphic encryption quickly reveals some glaring limitations in the current FHE paradigm. These limitations include the lack of a standard comparison operator…
This thesis is a study of quantum error-correction codes from an algebraic perspective. We concern ourselves not only with quantum codes but also protocols to perform logical quantum computation using such codes. We derive new methods of…
Constructing cryptographic schemes with tight or almost-tight security has long been one of the central problems in theoretical cryptography. At ASIACRYPT 2016, Boyen and Li posed an open problem: whether it is possible to construct a…
In this paper, we evaluate the different fully homomorphic encryption schemes, propose an implementation, and numerically analyze the applicability of gradient descent algorithms to solve quadratic programming in a homomorphic encryption…
We propose a multi-bit leveled fully homomorphic encryption scheme using multivariate polynomial evaluations. The security of the scheme depends on the hardness of the Learning with Errors (LWE) problem. For homomorphic multiplication, the…
In this paper we present two reductions between variants of the Code Equivalence problem. We give polynomial-time Karp reductions from Permutation Code Equivalence (PCE) to both Linear Code Equivalence (LCE) and Signed Permutation Code…
In this work, we study the solution of shortest vector problems (SVPs) arising in terms of learning with error problems (LWEs). LWEs are linear systems of equations over a modular ring, where a perturbation vector is added to the right-hand…
Homomorphic encryption (HE) applied to a networked controller enables secure operation, but in most cases it allows for addition and multiplication over integers only, because of computation efficiency. Several related results deal with…
Homomorphic encryption (HE) is a promising cryptographic technique for enabling secure collaborative machine learning in the cloud. However, support for homomorphic computation on ciphertexts under multiple keys is inefficient. Current…
In this work, we abstract some key ingredients in previous LWE- and RLWE-based key exchange protocols, by introducing and formalizing the building tool, referred to as key consensus (KC) and its asymmetric variant AKC. KC and AKC allow two…
Fully Homomorphic Encryption (FHE) represents a paradigm shift in cryptography, enabling computation directly on encrypted data and unlocking privacy-critical computation. Despite being increasingly deployed in real platforms, the…
Homomorphic Encryption (HE) enables computation on encrypted data without decryption, making it a cornerstone of privacy-preserving computation in untrusted environments. As HE sees growing adoption in sensitive applications such as secure…