2 citations · 4 across the 12 of their papers we have counts for
12 papers
An Infinite Family of Real Quadratic Fields with Three Classes of Perfect Unary Forms
Christian Porter
In this paper, we revisit the theory of perfect unary forms over real quadratic fields. Specifically, we deduce an infinite family of real quadratic fields w…
Unit Reducible Cyclotomic Fields
Christian Porter, Piero Sarti, Cong Ling +1
In this paper, we continue the study of unit reducible fields as introduced in \cite{LPL23} for the special case of cyclotomic fields. Specifically, we deduce that the cyclotomic f…
Strongly Reduced Lattice Bases
Christian Porter
In this paper, we show that for each lattice basis, there exists an equivalent basis which we describe as ``strongly reduced''. We show that bases reduced in this manner exhibit ra…
Quantum algorithmic solutions to the shortest vector problem on simulated coherent Ising machines
Edmund Dable-Heath, Laura Casas, Victor Hertz +3
Quantum computing poses a threat to contemporary cryptosystems, with advances to a state in which it will cause problems predicted for the next few decades. Many of the proposed cr…
On Pisot Units and the Fundamental Domain of Galois Extensions of
Christian Porter, Alexandre Bali, Alar Leibak
In this paper, we present two main results. Let be a number field that is Galois over with degree , where is the number of real embeddings and is the…
A New Bound for the Orthogonality Defect of HKZ Reduced Lattices
Christian Porter, Edmund Dable-Heath, Cong Ling
In this work, we determine a sharp upper bound on the orthogonality defect of HKZ reduced bases up to dimension . Using this result, we determine a general upper bound for the o…
An Upper Bound on the Number of Classes of Perfect Unary Forms in Totally Real Number Fields
Christian Porter, Andrew Mendelsohn
Let be a totally real number field of degree over , with discriminant and regulator respectively. In this paper, using a similar method to van Woerde…
Unit Reducible Fields and Perfect Unary Forms
Alar Leibak, Christian Porter, Cong Ling
In this paper, we introduce the notion of unit reducibility for number fields, that is, number fields in which all positive unary forms attain their nonzero minimum at a unit. Furt…
Reduction Theory of Algebraic Modules and their Successive Minima
Christian Porter, Cong Ling
Lattices defined as modules over algebraic rings or orders have garnered interest recently, particularly in the fields of cryptography and coding theory. Whilst there exist many at…
Subfield Algorithms for Ideal- and Module-SVP Based on the Decomposition Group
Christian Porter, Andrew Mendelsohn, Cong Ling
Whilst lattice-based cryptosystems are believed to be resistant to quantum attack, they are often forced to pay for that security with inefficiencies in implementation. This proble…
On the Optimality of Gauss's Algorithm over Euclidean Imaginary Quadratic Fields
Christian Porter, Shanxiang Lyu, Cong Ling
In this paper, we continue our previous work on the reduction of algebraic lattices over imaginary quadratic fields for the special case when the lattice is spanned over a two dime…
Lattice Reduction over Imaginary Quadratic Fields
Shanxiang Lyu, Christian Porter, Cong Ling
Complex bases, along with direct-sums defined by rings of imaginary quadratic integers, induce algebraic lattices. In this work, we study such lattices and their reduction algorith…