Related papers: Constructing elliptic curve isogenies in quantum s…

We construct an oracular (i.e., black box) problem that can be solved exponentially faster on a quantum computer than on a classical computer. The quantum algorithm is based on a continuous time quantum walk, and thus employs a different…

We revisit the ordinary isogeny-graph based cryptosystems of Couveignes and Rostovtsev-Stolbunov, long dismissed as impractical. We give algorithmic improvements that accelerate key exchange in this framework, and explore the problem of…

Shor's quantum algorithm for discrete logarithms applied to elliptic curve groups forms the basis of a "quantum attack" of elliptic curve cryptosystems. To implement this algorithm on a quantum computer requires the efficient implementation…

Finding problems that allow for superpolynomial quantum speedup is one of the most important tasks in quantum computation. A key challenge is identifying problem structures that can only be exploited by quantum mechanics. In this paper, we…

We introduce the notion of isolated genus two curves. As there is no known efficient algorithm to explicitly construct isogenies between two genus two curves with large conductor gap, the discrete log problem (DLP) cannot be efficiently…

Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…

This paper contains a survey of supersingular isogeny graphs associated to supersingular elliptic curves and their various applications to cryptography. Within limitation of space, we attempt to address a broad audience and make this part…

This whitepaper seeks to elucidate implications that the capabilities of developing quantum architectures have on blockchain vulnerabilities and mitigation strategies. First, we provide new resource estimates for breaking the 256-bit…

We introduce an explicit construction for a key distribution protocol in the Quantum Computational Timelock (QCT) security model, where one assumes that computationally secure encryption may only be broken after a time much longer than the…

The Discrete Logarithm Problem is well-known among cryptographers, for its computational hardness that grants security to some of the most commonly used cryptosystems these days. Still, many of these are limited to a small number of…

Given an undirected, weighted graph, with $n$ vertices and $m$ edges, and two special vertices $s$ and $t$, the problem is to find the shortest path between them. We give two bounded-error quantum algorithms with improved runtime in the…

An elliptic curve-based signcryption scheme is introduced in this paper that effectively combines the functionalities of digital signature and encryption, and decreases the computational costs and communication overheads in comparison with…

We consider a quantum polynomial-time algorithm which solves the discrete logarithm problem for points on elliptic curves over $GF(2^m)$. We improve over earlier algorithms by constructing an efficient circuit for multiplying elements of…

Given a supersingular elliptic curve E and a non-scalar endomorphism $\alpha$ of E, we prove that the endomorphism ring of E can be computed in classical time about disc(Z[$\alpha$])^1/4 , and in quantum subexponential time, assuming the…

An important subcase of the hidden subgroup problem is equivalent to the shift problem over abelian groups. An efficient solution to the latter problem would serve as a building block of quantum hidden subgroup algorithms over solvable…

Several cryptographic protocols constructed based on less-known algorithmic problems, such as those in non-commutative groups, group rings, semigroups, etc., which claim quantum security, have been broken through classical reduction methods…

In recent years, the elliptic curve Qu-Vanstone (ECQV) implicit certificate scheme has found application in security credential management systems (SCMS) and secure vehicle-to-everything (V2X) communication to issue pseudonymous…

We show a relation between quantum learning theory and algorithmic hardness. We use the existence of efficient, local learning algorithms for energy estimation -- such as the classical shadows algorithm -- to prove that finding near-ground…

We present a new method for constructing genus 2 curves over a finite field with a given number of points on its Jacobian. This method has important applications in cryptography, where groups of prime order are used as the basis for…

We show that several problems that figure prominently in quantum computing, including Hidden Coset, Hidden Shift, and Orbit Coset, are equivalent or reducible to Hidden Subgroup for a large variety of groups. We also show that, over…