Related papers: On non-abelian homomorphic public-key cryptosystem…
Recently, Dor\"oz et al. (2017) proposed a new hard problem, called the finite field isomorphism problem, and constructed a fully homomorphic encryption scheme based on this problem. In this paper, we generalize the problem to the case of…
Cryptographic systems are derived using units in group rings. Combinations of types of units in group rings give units not of any particular type. This includes cases of taking powers of units and products of such powers and adds the…
Encrypted control has been introduced to protect controller data by encryption at the stage of computation and communication, by performing the computation directly on encrypted data. In this article, we first review and categorize recent…
It is well known that quantum computers can efficiently find a hidden subgroup $H$ of a finite Abelian group $G$. This implies that after only a polynomial (in $\log |G|$) number of calls to the oracle function, the states corresponding to…
Since the first theoretically feasible full homomorphic encryption (FHE) scheme was proposed in 2009, great progress has been achieved. These improvements have made FHE schemes come off the paper and become quite useful in solving some…
We present a new scheme for quantum homomorphic encryption which is compact and allows for efficient evaluation of arbitrary polynomial-sized quantum circuits. Building on the framework of Broadbent and Jeffery and recent results in the…
Secure function evaluation (SFE) is the process of computing a function (or running an algorithm) on some data, while keeping the input, output and intermediate results hidden from the environment in which the function is evaluated. This…
Fully homomorphic encryption (FHE) is a powerful encryption technique that allows for computation to be performed on ciphertext without the need for decryption. FHE will thus enable privacy-preserving computation and a wide range of…
Public-key cryptography algorithms have evolved towards increasing computational complexity to hide desired messages, which is accelerating with the development of the Internet and quantum computing. This paper introduces a novel public-key…
Cloud computing emerges as an attractive solution that can be delegated to store and process confidential data. However, several security risks are encountered with such a system as the securely encrypted data should be decrypted before…
Sometimes it is possible to embed an algebraic trapdoor into a block cipher. Building on previous research, in this paper we investigate an especially dangerous algebraic structure, which is called a hidden sum and which is related to some…
In this paper, we propose the first homomorphic based proxy re-encryption (HPRE) solution that allows different users to share data they outsourced homomorphically encrypted using their respective public keys with the possibility to process…
We present a conceptual framework for extending homomorphic encryption beyond arithmetic or Boolean operations into the domain of intuitionistic logic proofs and, by the Curry-Howard correspondence, into the domain of typed functional…
The problem we address is the following: how can a user employ a predictive model that is held by a third party, without compromising private information. For example, a hospital may wish to use a cloud service to predict the readmission…
In this paper we study the MOR cryptosystem. We use the group of unitriangular matrices over a finite field as the non-abelian group in the MOR cryptosystem. We show that a cryptosystem similar to the El-Gamal cryptosystem over finite…
In this paper, we propose a brand new public key encryption scheme in the Lie group that is a non-abelian group. In particular, we firstly investigate the intractability assumptions in the Lie group, including the non-abelian factoring…
We consider deterministic algorithms for the well-known hidden subgroup problem ($\mathsf{HSP}$): for a finite group $G$ and a finite set $X$, given a function $f:G \to X$ and the promise that for any $g_1, g_2 \in G, f(g_1) = f(g_2)$ iff…
Due to the rising privacy demand in data mining, Homomorphic Encryption (HE) is receiving more and more attention recently for its capability to do computations over the encrypted field. By using the HE technique, it is possible to securely…
In this paper we propose right-angled Artin groups as a platform for secret sharing schemes based on the efficiency (linear time) of the word problem. Inspired by previous work of Grigoriev-Shpilrain in the context of graphs, we define two…
A group G is (finitely) co-Hopfian if it does not contain any proper (finite-index) subgroups isomorphic to itself. We study finitely generated groups G that admit a descending chain of proper normal finite-index subgroups, each of which is…