Results 1 to 10 of about 33 (33)
Graph isomorphism and Gaussian boson sampling
Special Matrices, 2021 We introduce a connection between a near-term quantum computing device, specifically a Gaussian boson sampler, and the graph isomorphism problem. We propose a scheme where graphs are encoded into quantum states of light, whose properties are then probed ...
Brádler Kamil +4 more
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Quantum algorithms for computing general discrete logarithms and orders with tradeoffs
Journal of Mathematical Cryptology, 2021 We generalize our earlier works on computing short discrete logarithms with tradeoffs, and bridge them with Seifert's work on computing orders with tradeoffs, and with Shor's groundbreaking works on computing orders and general discrete logarithms.
Ekerå Martin
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Journal of Mathematical Cryptology, 2020 In this paper we provide a framework for applying classical search and preprocessing to quantum oracles for use with Grover’s quantum search algorithm in order to lower the quantum circuit-complexity of Grover’s algorithm for single-target search ...
Biasse Jean-François, Pring Benjamin
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A subexponential-time, polynomial quantum space algorithm for inverting the CM group action
Journal of Mathematical Cryptology, 2020 We present a quantum algorithm which computes group action inverses of the complex multiplication group action on isogenous ordinary elliptic curves, using subexponential time, but only polynomial quantum space.
Jao David +3 more
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A trade-off between classical and quantum circuit size for an attack against CSIDH
Journal of Mathematical Cryptology, 2020 We propose a heuristic algorithm to solve the underlying hard problem of the CSIDH cryptosystem (and other isogeny-based cryptosystems using elliptic curves with endomorphism ring isomorphic to an imaginary quadratic order 𝒪).
Biasse Jean-François +4 more
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Quantum computation of discrete logarithms in semigroups
Journal of Mathematical Cryptology, 2014 We describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor's algorithms for period finding and the discrete logarithm problem as subroutines.
Childs Andrew M., Ivanyos Gábor
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Constructing elliptic curve isogenies in quantum subexponential time
Journal of Mathematical Cryptology, 2014 Given two ordinary elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit a nonzero isogeny between them, but finding such an isogeny is believed to be computationally difficult.
Childs Andrew +2 more
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EXPONENTIAL IMPROVEMENT IN PRECISION FOR SIMULATING SPARSE HAMILTONIANS
Forum of Mathematics, Sigma, 2017 We provide a quantum algorithm for simulating the dynamics of sparse Hamiltonians with complexity sublogarithmic in the inverse error, an exponential improvement over previous methods. Specifically, we show that a
DOMINIC W. BERRY +4 more
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A Comprehensive Review of Matrix Equations in Dynamical Systems and Control Theory
Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.Matrix equations are of foundational importance in the modeling, investigation, and control of dynamical systems. This review discusses various classes of matrix equations, their solutions, and their relevance in control theory and dynamical systems.
Chacha Stephen Chacha, Arpan Hazra
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A small serving of mash: (Quantum) algorithms for SPDH-Sign with small parameters
Journal of Mathematical CryptologyWe find an efficient method to solve the semidirect discrete logarithm problem (SDLP) over finite nonabelian groups of order p3{p}^{3} and exponent p2{p}^{2} for certain exponentially large parameters. This implies an attack on SPDH-Sign,Pronounced “SPUD-
Mendelsohn Andrew +2 more
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