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Arithmetic and geometric structures in cryptography

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On the Security of Two-Round Multi-Signatures

Bryan Alexander Ford, Manu Drijvers

A multi-signature scheme allows a group of signers to collaboratively sign a message, creating a single signature that convinces a verifier that every individual signer approved the message. The increased interest in technologies to decentralize trust has ...

IEEE COMPUTER SOC2019

Tits Buildings And K-Stability

Giulio Codogni

A polarized variety is K-stable if, for any test configuration, the Donaldson-Futaki invariant is positive. In this paper, inspired by classical geometric invariant theory, we describe the space of test configurations as a limit of a direct system of Tits ...

CAMBRIDGE UNIV PRESS2019

On the Size of K-Cross-Free Families

János Pach, Andrei Kupavskii, Istvan Tomon

Two subsets A,B of an n-element ground set X are said to be crossing, if none of the four sets AB, A\B, B\A and X(AB) are empty. It was conjectured by Karzanov and Lomonosov forty years ago that if a family F of subsets of X does not contain k pairwise cr ...

SPRINGER HEIDELBERG2019

Indiscreet logarithms in finite fields of small characteristic

Robert Granger, Thorsten Kleinjung, Jens Markus Zumbrägel

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 ...

2018

On subadditivity of Kodaira dimension in positive characteristic over a general type base

Zsolt Patakfalvi

We show that for a surjective, separable morphism f of smooth projective varieties over a field of positive characteristic such that f(*) OX congruent to O-Y subadditivity of Kodaira dimension holds, provided the base is of general type and the Hasse-Witt ...

2018

Practical and Scalable Synthesis of 7-Azetidin-1-yl-4-(hydroxymethyl)coumarin: An Improved Photoremovable Group

Pablo Rivera Fuentes

A robust and scalable route to prep. the 7-azetidinylated alc., a useful precursor for the photoprotection of a variety of leaving groups, and its use in the prepn. of model phosphate, sulfonate, and carbamate derivs. is presented. ...

2018

Isogeny graphs of ordinary abelian varieties

Dimitar Petkov Jetchev, Benjamin Pierre Charles Wesolowski, Ernest Hunter Brooks

Fix a prime number l. Graphs of isogenies of degree a power of l are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ordinary abelian varieties over a finite field. We analyse gr ...

Springer Heidelberg2017

Mirror symmetry for moduli spaces of Higgs bundles via $p$-adic integration

Dimitri Stelio Wyss, Michael Gröchenig

We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type

SL_n

and

PGL_n

. More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generica ...

2017

Short Stickelberger Class Relations and Application to Ideal-SVP

Benjamin Pierre Charles Wesolowski

The worst-case hardness of finding short vectors in ideals of cyclotomic number fields (Ideal-SVP) is a central matter in lattice based cryptography. Assuming the worst-case hardness of Ideal-SVP allows to prove the Ring-LWE and Ring-SIS assumptions, and t ...

Springer International Publishing Ag2017

LPN in Cryptography

Sonia Mihaela Bogos

The security of public-key cryptography relies on well-studied hard problems, problems for which we do not have efficient algorithms. Factorization and discrete logarithm are the two most known and used hard problems. Unfortunately, they can be easily solv ...

EPFL2017

Mirror symmetry for moduli spaces of Higgs bundles via $p$-adic integration

Dimitri Stelio Wyss, Michael Gröchenig

We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type

SL_n

and

PGL_n

. More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generica ...

2017