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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 ...
We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type SLn and PGLn. More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generica ...
Intrusion detection systems are a commonly deployed defense that examines network traffic, host operations, or both to detect attacks. However, more attacks bypass IDS defenses each year, and with the sophistication of attacks increasing as well, we must e ...
Let F-q be a finite field of q elements, where q is a large odd prime power and Q = a(1)x(1)(c1) + ..... + a(d)x(d)(cd) is an element of F-q[x(1) ,...,x(d)], where 2
We prove a Szemeredi-Trotter type theorem and a sum product estimate in the setting of finite quasifields. These estimates generalize results of the fourth author, of Garaev, and of Vu. We generalize results of Gyarmati and Sarkozy on the solvability of th ...
Academic Press Inc Elsevier Science2017
We consider two problems regarding arithmetic progressions in symmetric sets in the finite field (product space) model. First, we show that a symmetric set S subset of Z(q)(n) containing vertical bar S vertical bar = mu . q(n) elements must contain at leas ...
ELECTRONIC JOURNAL OF COMBINATORICS2020
For any positive integers n≥3,r≥1 we present formulae for the number of irreducible polynomials of degree n over the finite field F2r where the coefficients of xn−1, xn−2 and xn−3 are zero. Our proofs involve coun ...
Designing a secure permissionless distributed ledger (blockchain) that performs on par with centralized payment processors, such as Visa, is a challenging task. Most existing distributed ledgers are unable to scale-out, i.e., to grow their total processing ...
Security and reliability bugs are prevalent in systems software. Systems code is often written in low-level languages like C/C++, which offer many benefits but also delegate memory management and type safety to programmers. This invites bugs that cause cra ...
Nowadays, one area of research in cryptanalysis is solving the Discrete Logarithm Problem (DLP) in finite groups whose group representation is not yet exploited. For such groups, the best one can do is using a generic method to attack the DLP, the fastest ...
