19 citations · 28 across the 7 of their papers we have counts for
10 papers
Quantum Undergraduate Education and Scientific Training
Justin K. Perron, Charles DeLeone, Shahed Sharif +4
Currently, education and workforce training in quantum information science and technology (QIST) exists primarily at the graduate and postdoctoral levels, with few undergraduate ef…
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…
Geometry of Biquadratic and Cyclic Cubic Log-Unit Lattices
Fernando Azpeitia Tellez, Christopher Powell, Shahed Sharif
By Dirichlet's Unit Theorem, under the log embedding the units in the ring of integers of a number field form a lattice, called the log-unit lattice. We investigate the geometry of…
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…
Period and index for higher genus curves
Shahed Sharif
Given a curve over a field , the period of is the gcd of degrees of -rational divisor classes, while the index is the gcd of degrees of -rational divisors. S. Li…
Explicit arithmetic of Jacobians of generalized Legendre curves over global function fields
Lisa Berger, Chris Hall, René Pannekoek +5
We study the Jacobian of the smooth projective curve of genus with affine model over the function field , when is p…
A descent map for curves with totally degenerate semi-stable reduction
Shahed Sharif
Let be a local field of residue characteristic . Let be a curve over whose minimal proper regular model has totally degenerate semi-stable reduction. Under certain h…
Period, index and potential sha
Pete L. Clark, Shahed Sharif
In this paper we advance the theory of O'Neil's period-index obstruction map and derive consequences for the arithmetic of genus one curves over global fields. Our first result imp…
Period and index of genus one curves over number fields
Shahed Sharif
The period of a curve is the smallest positive degree of Galois-invariant divisor classes. The index is the smallest positive degree of rational divisors. We construct examples of…