On the discrete logarithm problem in finite fields of fixed characteristic

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A classical result of Hasse states that the norm principle holds for finite cyclic extensions of global fields, in other words local norms are global norms. We investigate the norm principle for finite dimensional commutative kale algebras over global fiel ...

We explore a few algebraic and geometric structures, through certain questions posed by modern cryptography. We focus on the cases of discrete logarithms in finite fields of small characteristic, the structure of isogeny graphs of ordinary abelian varietie ...

Recently, several striking advances have taken place regarding the discrete logarithm problem (DLP) in finite fields of small characteristic, despite progress having remained essentially static for nearly thirty years, with the best known algorithms being ...

Let F-p be a prime field of order p > 2, and let A be a set in F-p with very small size in terms of p. In this note, we show that the number of distinct cubic distances determined by points in A x A satisfies vertical bar(A - A)(3) + (A - A)(3 vertical bar ...

On the discrete logarithm problem in finite fields of fixed characteristic

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Ising Model and Field Theory: Lattice Local Fields and Massive Scaling Limit

Modeling spatially dependent functional data via regression with differential regularization

On the Security of Two-Round Multi-Signatures

Generalized Norm-compatible Systems on Unitary Shimura Varieties

Coupling non-conforming discretizations of PDEs by spectral approximation of the Lagrange multiplier space

Minimal Polynomials Of Unipotent Elements Of Non-Prime Order In Irreducible Representations Of The Exceptional Algebraic Groups In Some Good Characteristics

Hasse principles for multinorm equations

Arithmetic and geometric structures in cryptography

Indiscreet logarithms in finite fields of small characteristic

Four-Variable Expanders Over The Prime Fields