Related papers: Lattices, Homomorphic Encryption, and CKKS
This letter presents a cryptanalysis of the modified McEliece cryptosystem recently proposed by Moufek, Guenda and Gulliver [24]. The system is based on the juxtaposition of quasi-cyclic LDPC and quasi-cyclic MDPC codes. The idea of our…
The use of Neural Networks (NNs) for sensitive data processing is becoming increasingly popular, raising concerns about data privacy and security. Homomorphic Encryption (HE) has the potential to be used as a solution to preserve data…
Outsourced computation for neural networks allows users access to state of the art models without needing to invest in specialized hardware and know-how. The problem is that the users lose control over potentially privacy sensitive data.…
We obtain variants of the classical Minkowski Theorem on inhomogeneous approximation where we require moreover that the solutions $p, q$ be coprime integers. We link the subject with density exponents of lattice orbits in the real plane.
The growing number of satellites in low Earth orbit (LEO) has increased concerns about the risk of satellite collisions, which can ultimately result in the irretrievable loss of satellites and a growing amount of space debris. To mitigate…
The complexity of the list homomorphism problem for signed graphs appears difficult to classify. Existing results focus on special classes of signed graphs, such as trees and reflexive signed graphs. Irreflexive signed graphs are in a…
This paper explores the use of partially homomorphic encryption (PHE) for encrypted vector similarity search, with a focus on facial recognition and broader applications like reverse image search, recommendation engines, and large language…
In this paper, we study a certain case of a subgraph isomorphism problem. We consider the Hasse diagram of the lattice $M_{k}$ (the unique lattice with $k+2$ elements and one anti-chain of length $k$) and want to find the maximal $k$ for…
In this paper, the authors give the definitions of a coprime sequence and a lever function, and describe the five algorithms and six characteristics of a prototypal public key cryptosystem which is used for encryption and signature, and…
We explore the computational implications of a superposition of spacetimes, a phenomenon hypothesized in quantum gravity theories. This was initiated by Shmueli (2024) where the author introduced the complexity class $\mathbf{BQP^{OI}}$…
Homomorphic encryption is a form of encryption which allows computation to be carried out on the encrypted data without the need for decryption. The success of quantum approaches to related tasks in a delegated computation setting has…
Fully homomorphic encryption (FHE) enables a simple, attractive framework for secure search. Compared to other secure search systems, no costly setup procedure is necessary; it is sufficient for the client merely to upload the encrypted…
This article describes a lightweight additive homomorphic algorithm with the same encryption and decryption keys. Compared to standard additive homomorphic algorithms like Paillier, this algorithm reduces the computational cost of…
The lattice cohomology of a plumbed 3--manifold $M$ associated with a connected negative definite plumbing graph is an important tool in the study of topological properties of $M$, and in the comparison of the topological properties with…
Privacy-preserving machine learning (PPML) is an emerging topic to handle secure machine learning inference over sensitive data in untrusted environments. Fully homomorphic encryption (FHE) enables computation directly on encrypted data on…
With the rapid advancements in quantum computing, traditional cryptographic schemes like Rivest-Shamir-Adleman (RSA) and elliptic curve cryptography (ECC) are becoming vulnerable, necessitating the development of quantum-resistant…
We construct three public key knapsack cryptosystems. Standard knapsack cryptosystems hide easy instances of the knapsack problem and have been broken. The systems considered in the article face this problem: They hide a random (possibly…
We survey known results about the complexity of surjective homomorphism problems, studied in the context of related problems in the literature such as list homomorphism, retraction and compaction. In comparison with these problems,…
In [15], Leonardi and Ruiz-Lopez propose an additively homomorphic public key encryption scheme whose security is expected to depend on the hardness of the learning homomorphism with noise problem (LHN). Choosing parameters for their…
For avoiding the exposure of plaintexts in cloud environments, some homomorphic hashing algorithms have been proposed to generate the hash value of each plaintext, and cloud environments only store the hash values and calculate the hash…