Related papers: Constructing elliptic curve isogenies in quantum s…
In this paper, we intend to study the geometric meaning of the discrete logarithm problem defined over an Elliptic Curve. The key idea is to reduce the Elliptic Curve Discrete Logarithm Problem (EC-DLP) into a system of equations. These…
Diffie-Hellman key exchange is at the foundations of public-key cryptography, but conventional group-based Diffie-Hellman is vulnerable to Shor's quantum algorithm. A range of "post-quantum Diffie-Hellman" protocols have been proposed to…
Privacy Preserving Data Mining is a method which ensures privacy of individual information during mining. Most important task involves retrieving information from multiple data bases which is distributed. The data once in the data warehouse…
We will describe an algorithm to construct an elliptic curve $E_{f_q}$ over some prime field $\mathbb{F}_p$ such that such that $|E_{f_q}(\mathbb{F}_p)| = f_q$, where $f_q$ is a probable Fibonacci prime for some prime index $q$. The…
Extraspecial groups form a remarkable subclass of p-groups. They are also present in quantum information theory, in particular in quantum error correction. We give here a polynomial time quantum algorithm for finding hidden subgroups in…
Onion routing provides anonymity by layering encryption so that no relay can link sender to destination. A quantum analogue faces a core obstacle: layered quantum encryption generally requires symmetric encryption schemes, whereas…
This paper introduces a completely new approach to encryption based on group theoretic quantum framework. Quantum cryptography has essentially focused only on key distribution and proceeded with classical encryption algorithm with the…
Nonlinear differential equations model diverse phenomena but are notoriously difficult to solve. While there has been extensive previous work on efficient quantum algorithms for linear differential equations, the linearity of quantum…
Descent via an isogeny on an elliptic curve is used to construct two subrings of the field of rational numbers, which are complementary in a strong sense, and for which Hilbert's Tenth Problem is undecidable. This method further develops…
The orbit problem is at the heart of symmetry reduction methods for model checking concurrent systems. It asks whether two given configurations in a concurrent system (represented as finite strings over some finite alphabet) are in the same…
The main component of (constructive) recognition algorithms for black box groups of Lie type in computational group theory is the construction of unipotent elements. In the existing algorithms unipotent elements are found by random search…
In the Correlation Clustering, also known as Cluster Editing, we are given an undirected n-vertex graph G and a positive integer k. The task is to decide if G can be transformed into a cluster graph, i.e., a disjoint union of cliques, by…
We initiate a systematic study of pseudo-deterministic quantum algorithms. These are quantum algorithms that, for any input, output a canonical solution with high probability. Focusing on the query complexity model, our main contributions…
While efficient algorithms are known for solving many important problems related to groups, no efficient algorithm is known for determining whether two arbitrary groups are isomorphic. The particular case of 2-nilpotent groups, a special…
The task of this paper is to introduce a new lightweight identification protocol based on biometric data and elliptic curves. In fact, we combine biometric data and asymetric cryptography, namely elliptic curves and standard tools to design…
By resorting to basic features of topological knot theory we propose a (classical) cryptographic protocol based on the `difficulty' of decomposing complex knots generated as connected sums of prime knots and their mutants. The scheme…
We present a specialized point-counting algorithm for a class of elliptic curves over F\_{p^2} that includes reductions of quadratic Q-curves modulo inert primes and, more generally, any elliptic curve over F\_{p^2} with a low-degree…
There have been several research works on the hidden shift problem, quantum algorithms for the problem, and their applications. However, all the results have focused on discrete groups with discrete oracle functions. In this paper, we…
In this work we propose an algorithm that numerically evaluates Kleinian hyperelliptic functions associated with a complex curve of genus 2. This algorithm is based upon constructing a sequence of curves with Richelot isogenous Jacobians…
We give a quantum algorithm for a novel type of black-box problem: identifying a hidden $d$-regular base graph $G$ on $n$ vertices from oracle access to an obfuscated version of it, rather than traversing it. From $G$ we build the spired…