The Birman-Williams theorem gives a connection between the collection of unstable periodic orbits (UPOs) contained within a chaotic attractor and the topology of that attractor, for three-dimensional systems. In certain cases, the fractal dimension of a ch ...
We introduce the SPRIG (Smart Proofs via Recursive Information Gathering) protocol. SPRIG allows agents to propose, question, and defend mathematical proofs in a decentralized fashion. A structure of stakes and bounties aims at producing debates in good fa ...
Motivated by the transfer of proofs between proof systems, and in particular from first order automated theorem provers (ATPs) to interactive theorem provers (ITPs), we specify an extension of the TPTP derivation text format to describe proofs in first-ord ...
Current cryptographic solutions will become obsolete with the arrival of large-scale universal quantum computers. As a result, the National Institute of Standards and Technology supervises a post-quantum standardization process which involves evaluating ca ...
We study the proof theory and algorithms for orthologic, a logical system based on ortholattices, which have shown practical relevance in simplification and normalization of verification conditions. Ortholattices weaken Boolean algebras while having polyno ...
Since the advent of internet and mass communication, two public-key cryptographic algorithms have shared the monopoly of data encryption and authentication: Diffie-Hellman and RSA.
However, in the last few years, progress made in quantum physics -- and mo ...
Euclidean lattices are mathematical objects of increasing interest in the fields of cryptography and error-correcting codes. This doctoral thesis is a study on high-dimensional lattices with the motivation to understand how efficient they are in terms of b ...
In this paper, we present a model for the analytical computation of the power flow sensitivity coefficients (SCs) for hybrid AC/DC networks. The SCs are defined as the partial derivates of the nodal voltages with respect to the active and reactive power in ...
We prove the non-planarity of a family of 3-regular graphs constructed from the solutions to the Markoff equation x2 + y2 + z2 = xyz modulo prime numbers greater than 7. The proof uses Euler characteristic and an enumeration of the short cycles in these gr ...
Billions of people now have conversations daily over the Internet. A large portion of this communication takes place via secure messaging protocols that offer "end-to-end encryption'" guarantees and resilience to compromise like the widely-used Double Ratc ...
We provide new explicit examples of lattice sphere packings in dimensions 54, 55, 162, 163, 486 and 487 that are the densest known so far, using Kummer families of elliptic curves over global function fields.
In some cases, these families of elliptic curve ...
Geometric properties of lattice quantum gravity in two dimensions are studied numerically via Monte Carlo on Euclidean Dynamical Triangulations. A new computational method is proposed to simulate gravity coupled with fermions, which allows the study of int ...
This paper addresses the overwhelming computational resources needed with standard numerical approaches to simulate architected materials. Those multiscale heterogeneous lattice structures gain intensive interest in conjunction with the improvement of addi ...
The Bitcoin architecture heavily relies on the ECDSA signature scheme which is broken by quantum adversaries as the secret key can be computed from the public key in quantum polynomial time. To mitigate this attack, bitcoins can be paid to the hash of a pu ...
With the looming threat of large-scale quantum computers, a fair portion of recent cryptographic research has focused on examining cryptographic primitives from the perspective of a quantum adversary. Shor's 1994 result revealed that quantum computers can ...
A hash proof system (HPS) is a form of implicit proof of membership to a language. Out of the very few existing post-quantum HPS, most are based on languages of ciphertexts of code-based or lattice-based cryptosystems and inherently suffer from a gap cause ...
The rising atmospheric level of carbon dioxide, CO2, contributes to climate change and poses urgent need to find scalable solutions both to decrease its emissions and to be able to recycle it, if the goals of Paris Agreement to limit the temperature rise a ...
We propose a 2-round blind signature protocol based on the random oracle heuristic and the hardness of standard lattice problems (Ring/Module-SIS/LWE and NTRU) with a signature size of 22 KB. The protocol is round-optimal and has a transcript size that can ...
The Supersingular Isogeny Diffie-Hellman (SIDH) protocol has been the main and most efficient isogeny-based encryption protocol, until a series of breakthroughs led to a polynomial-time key-recovery attack. While some countermeasures have been proposed, th ...
