Quantum Algorithms for the Approximate k-List Problem and Their Application to Lattice Sieving

Elena Kirshanova,Eamonn W Postlethwaite,Subhayan Roy Moulik,Erik Mårtensson

doi:10.1007/978-3-030-34578-5_19

Quantum Algorithms for the Approximate k-List Problem and Their Application to Lattice Sieving

Elena Kirshanova, Eamonn W Postlethwaite + Show 2 more

https://doi.org/10.1007/978-3-030-34578-5_19

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Publication Date: Jan 1, 2019

Citations: 13

Affiliation: Immanuel Kant Baltic Federal University, Royal Holloway University of London, University of Oxford, Lund University, Informa (Sweden)

#Shortest Vector Problem #Lattice Sieving + Show 8 more

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Abstract

The Shortest Vector Problem (SVP) is one of the mathematical foundations of lattice based cryptography. Lattice sieve algorithms are amongst the foremost methods of solving SVP. The asymptotically fastest known classical and quantum sieves solve SVP in a d-dimensional lattice in \(2^{\mathsf {c}d + o(d)}\) time steps with \(2^{\mathsf {c}' d + o(d)}\) memory for constants \(c, c'\). In this work, we give various quantum sieving algorithms that trade computational steps for memory.

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