This paper analyzes and optimizes quantum circuits for computing discrete logarithms on binary elliptic curves, including reversible circuits for fixed-base-point scalar multiplication and the full stack of relevant subroutines. The main optimization …

Often clients (e.g., sensors, organizations) need to outsource joint computations that are based on some joint inputs to external untrusted servers. These computations often rely on the aggregation of data collected from multiple clients, while the …

We introduce a new class of irreducible pentanomials over $F_2$ of the form $f(x) = x^{2b+c} + x^{b+c} + x^b + x^c + 1$. Let $m=2b+c$ and use $f$ to define the finite field extension of degree $m$. We give the exact number of operations required for …

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