Related papers: A New Cryptosystem Based On Hidden Order Groups
Recent oracle separations [Kretschmer, TQC'21, Kretschmer et. al., STOC'23] have raised the tantalizing possibility of building quantum cryptography from sources of hardness that persist even if the polynomial hierarchy collapses. We…
In this paper, we consider the problem of secret key generation for multiple parties. Multi-user networks usually require a trusted party to efficiently distribute keys to the legitimate users and this process is a weakness against…
Deciding if a graph is a Hamilton graph, also named the Hamilton cycle problem, is important for discrete mathematics and computer science. Due to no characterization to identify Hamilton graphs effectively, there are no tractable…
This work presents a new, simple O(log^2|G|) algorithm, the Fibonacci cube algorithm, for producing random group elements in black box groups. After the initial O(log^2|G|) group operations, epsilon-uniform random elements are produced…
Distribution grid agents are obliged to exchange and disclose their states explicitly to neighboring regions to enable distributed optimal power flow dispatch. However, the states contain sensitive information of individual agents, such as…
Circulant matrices are an important tool widely used in coding theory and cryptography. A circulant matrix is a square matrix whose rows are the cyclic shifts of the first row. Such a matrix can be efficiently stored in memory because it is…
Collaborative filtering (CF) is a long-standing problem of recommender systems. Many novel methods have been proposed, ranging from classical matrix factorization to recent graph convolutional network-based approaches. After recent fierce…
We generalize the classical definition of effectively closed subshift to finitely generated groups. We study classical stability properties of this class and then extend this notion by allowing the usage of an oracle to the word problem of…
We give efficient data-oblivious algorithms for several fundamental geometric problems that are relevant to geographic information systems, including planar convex hulls and all-nearest neighbors. Our methods are "data-oblivious" in that…
Let $G$ be a finite group of odd order admitting an involutory automorphism $\phi$. We obtain two results bounding the exponent of $[G,\phi]$. Denote by $G_{-\phi}$ the set $\{[g,\phi]\,\vert\, g\in G\}$ and by $G_{\phi}$ the centralizer of…
We develop matrix cryptography based on linear recurrent sequences of any order that allows securing encryption against brute force and chosen plaintext attacks. In particular, we solve the problem of generalizing error detection and…
An order-revealing encryption scheme gives a public procedure by which two ciphertexts can be compared to reveal the ordering of their underlying plaintexts. We show how to use order-revealing encryption to separate computationally…
General cryptographic schemes are presented where keys can be one-time or ephemeral. Processes for key exchange are derived. Public key cryptographic schemes based on the new systems are easily established. Authentication and signature…
We solve the dynamic Predecessor Problem with high probability (whp) in constant time, using only $n^{1+\delta}$ bits of memory, for any constant $\delta > 0$. The input keys are random wrt a wider class of the well studied and practically…
Polycyclic groups are natural generalizations of cyclic groups but with more complicated algorithmic properties. They are finitely presented and the word, conjugacy, and isomorphism decision problems are all solvable in these groups.…
Recent active studies have demonstrated that cryptography without one-way functions (OWFs) could be possible in the quantum world. Many fundamental primitives that are natural quantum analogs of OWFs or pseudorandom generators (PRGs) have…
One of the most basic techniques in algorithm design consists of breaking a problem into subproblems and then proceeding recursively. In the case of graph algorithms, one way to implement this approach is through separator sets. Given a…
Optimal power flow (OPF) is an important problem for power generation and it is in general non-convex. With the employment of renewable energy, it will be desirable if OPF can be solved very efficiently so its solution can be used in real…
We provide a new provably-secure steganographic encryption protocol that is proven secure in the complexity-theoretic framework of Hopper et al. The fundamental building block of our steganographic encryption protocol is a "one-time…
A pseudorandom code is a keyed error-correction scheme with the property that any polynomial number of encodings appear random to any computationally bounded adversary. We show that the pseudorandomness of any code tolerating a constant…