Titlebook: Arithmetic of Finite Fields; 7th International Wo Lilya Budaghyan,Francisco Rodríguez-Henríquez Conference proceedings 2018 Springer Nature

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Vector-Valued Modular Forms on Finite Upper Half PlanesFinite upper half planes are finite field analogs of the Poincaré upper half plane. Vector-valued modular forms on finite upper half planes are introduced, and then equivariant functions on these planes are defined. The existence of these functions is an application of vector-valued modular forms.

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https://doi.org/10.1007/978-1-4302-1842-5e critical when we use Diffie–Hellman as a basic component in more complicated constructions. In this survey we compare and contrast pre- and post-quantum Diffie–Hellman algorithms, highlighting some important subtleties.

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Testing Variables and Assigning Defaults finding a point on an elliptic curve of a prescribed prime power order or equivalently finding preimages under the Lang map on elliptic curves over finite fields. We formulate this as an open problem whose resolution would solve the finite field isomorphism problem with run time nearly linear in ..

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Pre- and Post-quantum Diffie–Hellman from Groups, Actions, and Isogeniese critical when we use Diffie–Hellman as a basic component in more complicated constructions. In this survey we compare and contrast pre- and post-quantum Diffie–Hellman algorithms, highlighting some important subtleties.