Invariance: a Theoretical Approach for Coding Sets of Words Modulo Literal (Anti)Morphisms

Let $A$ be a finite or countable alphabet and let $\theta$ be literal (anti)morphism onto $A^*$ (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under $\theta$ ($\theta$-invariant for short).We establish an extension of the famous defect theorem. Moreover, we prove that for the so-called thin $\theta$-invariant codes, maximality and completeness are two equivalent notions. We prove that a similar property holds in the framework of some special families of $\theta$-invariant codes such as prefix (bifix) codes, codes with a finite deciphering delay, uniformly synchronized codes and circular codes. For a special class of involutive antimorphisms, we prove that any regular $\theta$-invariant code may be embedded into a complete one.Comment: To appear in Acts of WORDS 201

Completing circular codes in regular submonoids

AbstractLet M be an arbitrary submonoid of the free monoid A∗, and let X⊆M be a variable length code (for short a code). X is weakly M-complete iff any word in M is a factor of some word in X∗ [J. Néraud, C. Selmi, Free monoid theory: Maximality and completeness in arbitrary submonoids, Internat. J. Algebra Comput. 13 (5) (2003) 507–516]. Given a regular submonoid M, and given an arbitrary code X⊆M, we are interested in the existence of a weakly M-complete code Xˆ that contains X. Actually, in [J. Néraud, Completing a code in a regular submonoid, in: Acts of MCU’2004, Lect. Notes Comput. Sci. 3354 (2005) 281–291; J. Néraud, Completing a code in a submonoid of finite rank, Fund. Inform. 74 (2006) 549–562], by presenting a general formula, we have established that, in any case, such a code Xˆ exists. In the present paper, we prove that any regular circular code X⊆M may be embedded into a weakly M-complete one iff the minimal automaton with behavior M has a synchronizing word. As a consequence of our result an extension of the famous theorem of Schützenberger is stated for regular circular codes in the framework of regular submonoids. We study also the behaviour of the subclass of uniformly synchronous codes in connection with these questions

Embedding a θ\theta-invariant code into a complete one

Let A be a finite or countable alphabet and let $\theta$ be a literal (anti-)automorphism onto A * (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under $\theta$ ($\theta$-invariant for short) that is, languages L such that $\theta$ (L) is a subset of L.We establish an extension of the famous defect theorem. With regards to the so-called notion of completeness, we provide a series of examples of finite complete $\theta$-invariant codes. Moreover, we establish a formula which allows to embed any non-complete $\theta$-invariant code into a complete one. As a consequence, in the family of the so-called thin $\theta$--invariant codes, maximality and completeness are two equivalent notions.Comment: arXiv admin note: text overlap with arXiv:1705.0556

Topologies for Error-Detecting Variable-Length Codes

Given a finite alphabet $A$, a quasi-metric $d$ over $A^*$, and a non-negative integer $k$, we introduce the relation $\tau_{d,k}\subseteq A^*\times A^*$ such that $(x,y)\in\tau_{d,k}$ holds whenever $d(x,y)\le k$. The error detection capability of variable-length codes is expressed in term of conditions over $\tau_{d,k}$. With respect to the prefix metric, the factor one, and any quasi-metric associated with some free monoid (anti-)automorphism, we prove that one can decide whether a given regular variable-length code satisfies any of those error detection constraints.Comment: arXiv admin note: text overlap with arXiv:2208.1468

Methods for minimizing performance degradation caused by branch delays

The presence of branch instructions in an instruction stream may adversely affect the performance of a processor by introducing significant delays in the execution process. As processors become more pipelined, the impact these delays have upon performance increases. This thesis investigates why delays occur when branch instructions are encountered. It also summarizes various hardware methodologies which can alleviate the performance degradation due to these delays. Simulation results show that these hardware methodologies can improve branch performance by up to 45 percent. Some branches are inherently necessary in order to implement programming decisions. However, the use of branches within programs can inadvertently cause significant performance degradation. This thesis analyzes several methods to implement a programming decision and the performance of each method, thus providing insight into programming guidelines which can be followed to improve branch performance. Measurements of these software techniques show performance improvements of up to 178 percent

Coding “What” and “When” in the Archer Fish Retina

Traditionally, the information content of the neural response is quantified using statistics of the responses relative to stimulus onset time with the assumption that the brain uses onset time to infer stimulus identity. However, stimulus onset time must also be estimated by the brain, making the utility of such an approach questionable. How can stimulus onset be estimated from the neural responses with sufficient accuracy to ensure reliable stimulus identification? We address this question using the framework of colour coding by the archer fish retinal ganglion cell. We found that stimulus identity, “what”, can be estimated from the responses of best single cells with an accuracy comparable to that of the animal's psychophysical estimation. However, to extract this information, an accurate estimation of stimulus onset is essential. We show that stimulus onset time, “when”, can be estimated using a linear-nonlinear readout mechanism that requires the response of a population of 100 cells. Thus, stimulus onset time can be estimated using a relatively simple readout. However, large nerve cell populations are required to achieve sufficient accuracy

Redefining “No Evidence of a Breach” in Election Security

For legal purposes, we rightly understand the lack of evidence to mean a lack of existence. For example, many candidates in the 2022 elections baselessly claimed that the 2020 presidential election was stolen. But, absent evidence of systemic fraud, the law correctly determines that President Biden was duly elected. If the law entertained any outlandish assertion regardless of evidentiary support, accusers could peddle whatever claims they please, forcing the accused to disprove them. Similar to the legal understanding of “no evidence,” many appear to believe that no evidence of a security breach in our voting equipment indicates no breach. For example, in the run-up to the 2022 elections, Georgia’s Secretary of State Brad Raffensperger “spent months voicing skepticism that . . . a security breach ever occurred” in Coffee County’s voting machines, arguing that “[t]here’s no evidence of any of that” and therefore that “[i]t didn’t happen.” A lack of evidence is rightly equivalent to a lack of existence, for legal purposes. But, for security purposes, no evidence of a breach does not necessarily mean no breach because security breaches can occur without the target’s knowledge. Indeed, the more competent the infiltrators are, the more likely they are to commit breaches undetected. The Allies taught the world this lesson in World War II, when they infiltrated the encrypted communications of the Axis powers without being exposed. To this day, it remains an axiomatic rule of cyber security practice that one should never interpret the lack of evidence of a security breach to mean no breach. Shortly after Raffensperger claimed that a breach did not happen because there was no evidence, it was revealed that voting machines in Coffee County had been breached. This Article calls for a bifurcated understanding of “no evidence of a breach” in the context of elections. For election fraud claims, we should continue to take no evidence to mean no fraud. But for evaluating the security of our election infrastructure, officials and legal scholars must understand that a breach can still occur despite the lack of evidence of a breach. I argue that the widespread conflation of no evidence of a breach and no breach is a frequently overlooked obstacle to election security reform. If one interprets no evidence of a breach as no breach, both the public and the politicians who represent them can rationalize not spending money on updating voting equipment as long as there is no definitive evidence that it was breached. Persuading the public of the fact that security breaches can occur despite the lack of evidence, while also showing why no evidence must still be interpreted as no existence for legal purposes, is a critical challenge that scholars must meet in order to effect meaningful election security reform

Analyse et Conception d'Algorithmes de Chiffrement Légers

The work presented in this thesis has been completed as part of the FUI Paclido project, whose aim is to provide new security protocols and algorithms for the Internet of Things, and more specifically wireless sensor networks. As a result, this thesis investigates so-called lightweight authenticated encryption algorithms, which are designed to fit into the limited resources of constrained environments. The first main contribution focuses on the design of a lightweight cipher called Lilliput-AE, which is based on the extended generalized Feistel network (EGFN) structure and was submitted to the Lightweight Cryptography (LWC) standardization project initiated by NIST (National Institute of Standards and Technology). Another part of the work concerns theoretical attacks against existing solutions, including some candidates of the nist lwc standardization process. Therefore, some specific analyses of the Skinny and Spook algorithms are presented, along with a more general study of boomerang attacks against ciphers following a Feistel construction.Les travaux présentés dans cette thèse s’inscrivent dans le cadre du projet FUI Paclido, qui a pour but de définir de nouveaux protocoles et algorithmes de sécurité pour l’Internet des Objets, et plus particulièrement les réseaux de capteurs sans fil. Cette thèse s’intéresse donc aux algorithmes de chiffrements authentifiés dits à bas coût ou également, légers, pouvant être implémentés sur des systèmes très limités en ressources. Une première partie des contributions porte sur la conception de l’algorithme léger Lilliput-AE, basé sur un schéma de Feistel généralisé étendu (EGFN) et soumis au projet de standardisation international Lightweight Cryptography (LWC) organisé par le NIST (National Institute of Standards and Technology). Une autre partie des travaux se concentre sur des attaques théoriques menées contre des solutions déjà existantes, notamment un certain nombre de candidats à la compétition LWC du NIST. Elle présente donc des analyses spécifiques des algorithmes Skinny et Spook ainsi qu’une étude plus générale des attaques de type boomerang contre les schémas de Feistel