Encuentro en Criptografía pós-cuántica y temas afines.
El encuentro se realizará en la Facultad de Ingeniería, miércoles
3/12 de 10:00 a 12:40 y el viernes 5/12 de 9:00 a 12:30.
Debajo podrán encontrar información sobre las charlas.
En caso que les interese alguna charla y no puedan venir, vamos a
transmitir las mismas por
Zoom: https://salavirtual-udel
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Miércoles 3 de diciembre (salón 703-rojo, Fing)·
10:00-10:40: Lattices and LWE in Cryptography (Nicolas Thériault)·
10:50-11:30: Introduction to Coding Theory and open problems (Claudio
Qureshi)·
11:30-12:00: Coffee break.
12:00-12:40: Speeding up the computation of group order of genus 2
curves over finite fields (Nicolas Thériault)
Viernes 5 de diciembre (salón 502-azul, Fing)·
9:00-9:40: An Introduction to Code-Based
Cryptography (Valerie Gauthier
9:50–10:30: Code Equivalence Problem and Application to the Design of
Digital Signature (Ayub Otmani)·
10:30–11:00: Coffee break.
11:00–11:40: Exponentially large Superfluous set of Edges of De Bruijn
and Kautz graphs (Eduardo Canale)·
11:50-12:30 Paley-like graphs from vector spaces (Lucas Reis)
Charlas del día miércoles 3/12:
1. Lattices and LWE in Cryptography (10:00 a 10:40)
Nicolas Thériault, Universidad de Santiago de Chile (USACH), Chile.
In this talk we introduce the ideas used in lattice-based cryptography
to provide secure communications via the LWE problem, allowing key
encapsulation, signatures and homomorphic encryption. We explain how
these techniques could be adapted to give advantages in situations like
electronic votations and give examples of parameters that could provide
the desired security with more efficiency. We finish with some upcoming
issues on lattice-based cryptography.
2. Introduction to Coding Theory and open problems
Claudio Qureshi, UdelaR
This will be an introductory talk on coding theory. We will review the
fundamental concepts, motivations, and some classical families of
error-correcting codes. The talk is intended as preparation for
Valerie’s lecture on Friday on code-based cryptography, so we will
emphasize the ideas that are most relevant for cryptographic
applications. I will also briefly discuss a few open problems in coding
theory.
3. Speeding up the computation of group order of genus 2 curves over
finite fields
Nicolas Thériault, Universidad de Santiago de Chile (USACH), Chile.
In 2012, Gaudry and Schost obtained the first known randomly selected
cryptographically interesting hyperelliptic curve of genus 2 over a
field of 127 bits. Producing this curve required a very significant
computation, in the order of one million CPU-hours, in which computing
the order of a specific curve (after a comparatively fast selection
process) would take on average close to 1000 CPU-hours. Furthermore, the
curves considered had full 2-torsion groups, i.e. the curve had group
order 16*prime.We present new developments in the computation of the
group order of specific curves which allow us to significantly reduce
the cost of several of the sub-algorithms used by Gaudry and Schost,
specifically: improved division-by-L algorithms, specialized
factorization algorithms and the use of special towers of field
extensions, which allow us to compute the group order of each
hyperelliptic curve in less than 100 CPU-hour. Furthermore, our
algorithm applies to more general curves and we are able to obtain
examples of curves with prime order (giving slightly stronger curves)
over fields of 127 bits
Charlas del día viernes 5/12:
1. An Introduction to Code-Based Cryptography
Valerie Gauthier, Universidad de los Andes, Colombia.
Code-based cryptography is among the most attractive post-quantum
cryptographic techniques. In tis talk we will introduce the main
code-based cryptographic primitives, namely the McEliece and the
Niederreiter public key encryption schemes.
2. Code Equivalence Problem and Application to the Design of Digital
Signature
Ayub Otmani, Université de Rouen Normandie, Francia.
This talk introduces the problem of deciding if two finite-dimensional
linear subspaces over an arbitrary field—known as linear codes—are
equivalent up to a linear isometry for the Hamming metric. A famous
example is when the linear transformation is a permutation of the
coordinates. The latter specific case is referred to as the Permutation
Code Equivalence (PCE) problem.
A state-of-the-art review of different results concerning the complexity
of this problem will be provided. In particular, I will focus on a
reduction showing that when the linear codes have trivial hulls, the
decision of code equivalence can be achieved by using any subroutine
that decides if two weighted undirected graphs are isomorphic. This
reduction is efficient because it boils down to computing the inverse of
a square matrix whose order is the length of the codes.
The talk will also introduce some cryptographic protocols whose security
relies on the hardness of the code equivalence problem. I will then
conclude with some possible generalizations and open questions.
3. Exponentially large Superfluous set of Edges of De Bruijn and Kautz
graphs
Eduardo Canale, UdelaR
A new lower bound for the cardinality of a superfluous sets of edges
(i.e. those whose removal does not increase the diameter) of Bruijn and
Kautz graphs is presented. The bound is exponentially larger than the
one known so far. A generalization for any underlying graph of a
directed graph is also presented.
4. Paley-like graphs from vector spaces
Lucas Reis, Universidade Federal de Minas Gerais, Brasil
Motivated by the well-known Paley graphs over finite fields and their
generalizations, in this talk we explore a multiplicative-additive
analogue of such graphs over finite fields. Namely, if U is an Fq-vector
space in the unique n-degree extension F (of Fq), we study the graph G_U
with vertex set F and edges (a, b) with a*b in U.
Our main goal is to estimate the clique number w(G_U) of the
corresponding graph. We provide some results in this direction, along
with some problems.
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Encuentro de Criptografía Pós-cuántica y temas afines
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