21 citations · 79 across the 29 of their papers we have counts for
32 papers
Realizing orders as group rings
H. W. Lenstra, A. Silverberg, D. M. H. van Gent
An order is a commutative ring that as an abelian group is finitely generated and free. A commutative ring is reduced if it has no non-zero nilpotent elements. In this paper we use…
Quantum Money from Quaternion Algebras
Daniel M. Kane, Shahed Sharif, Alice Silverberg
We propose a new idea for public key quantum money. In the abstract sense, our bills are encoded as a joint eigenstate of a fixed system of commuting unitary operators. We perform…
Algebraic maps constant on isomorphism classes of unpolarized abelian varieties are constant
Eric Rains, Karl Rubin, Travis Scholl +2
We show that if a rational map is constant on each isomorphism class of unpolarized abelian varieties of a given dimension, then it is a constant map. Our results are motivated by…
Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves
Dan Boneh, Darren Glass, Daniel Krashen +5
We describe a framework for constructing an efficient non-interactive key exchange (NIKE) protocol for n parties for any n >= 2. Our approach is based on the problem of computing i…
Testing isomorphism of lattices over CM-orders
Hendrik W. Lenstra, Alice Silverberg
A CM-order is a reduced order equipped with an involution that mimics complex conjugation. The Witt-Picard group of such an order is a certain group of ideal classes that is closel…
Universal gradings of orders
H. W. Lenstra, A. Silverberg
For commutative rings, we introduce the notion of a {\em universal grading}, which can be viewed as the "largest possible grading". While not every commutative ring (or order) has…