Revisiting LFSMs

Linear Finite State Machines (LFSMs) are particular primitives widely used in information theory, coding theory and cryptography. Among those linear automata, a particular case of study is Linear Feedback Shift Registers (LFSRs) used in many cryptographic applications such as design of stream ciphers or pseudo-random generation. LFSRs could be seen as particular LFSMs without inputs. In this paper, we first recall the description of LFSMs using traditional matrices representation. Then, we introduce a new matrices representation with polynomial fractional coefficients. This new representation leads to sparse representations and implementations. As direct applications, we focus our work on the Windmill LFSRs case, used for example in the E0 stream cipher and on other general applications that use this new representation. In a second part, a new design criterion called diffusion delay for LFSRs is introduced and well compared with existing related notions. This criterion represents the diffusion capacity of an LFSR. Thus, using the matrices representation, we present a new algorithm to randomly pick LFSRs with good properties (including the new one) and sparse descriptions dedicated to hardware and software designs. We present some examples of LFSRs generated using our algorithm to show the relevance of our approach.Comment: Submitted to IEEE-I

Sentencing and the Salience of Pain and Hope

What would a jurisprudence of sentencing that was induced from the experience of punishment, rather than deduced from the technocracy of criminal justice, look like? Rather than focusing narrowly on the question of quantum, such a jurisprudence would be concerned with the character and quality of punishment. A fit sentence would account for pain, loss, estrangement, alienation, and other features of the offender’s aggregate experience of suffering at the hands of the state in response to his or her wrongdoing. This would be a broader, more resolutely political conception of criminal punishment. This article shows that the jurisprudence of the Supreme Court of Canada has nudged the law in precisely this direction, calling on judges to think about sentencing in ways better attuned to the lived experience of punishment. In judgments concerning police misconduct, collateral consequences of a sentence, and delayed parole, the Court has recognized the salience of pain and hope to the task of sentencing, firmly establishing that proportionality – the guiding measure of a fit sentence – is an indelibly individualized concept that must be calibrated to the real effects of the criminal process and proposed sentence on the life lived by the offender. With this, we can begin to imagine new possibilities in our sentencing practices and must conceive of the essential legal and ethical task of the sentencing judge in new terms: an imaginative engagement with the lives of those that they punish

Judicial Discretion and the Rise of Individualization: The Canadian Sentencing Approach

“Who are courts sentencing if not the offender standing in front of them?” The epigraph to this paper points to the ethical heart of a distinctive and important development in Canadian sentencing law. It is drawn from a case in which the Supreme Court of Canada grappled with the signal societal trauma wrought by the operation of the criminal justice system – the travesty of Indigenous over-representation in Canadian prisons. This development involves an approach that has already disrupted certain elements of contemporary sentencing practice in Canada, and it is one that, depending on how sentencing judges embrace it, may open up new futures in Canadian sentencing. This development is the emergence of individualized proportionality as the fundamental principle of sentencing in Canada. One object of this paper is to explain and explore the rise, shape, and implications of this deep commitment to individualization as the defining feature of contemporary Canadian sentencing law

The Rule in Hodge\u27s Case: Rumours of its Death are Greatly Exaggerated

Certain academic commentators and Canadian courts have announced the death of the rule in Hodge\u27s Case. The author challenges this proclamation of death, observing that Hodge\u27s rule is a particular manifestation of the epistemology that informs our law of evidence. He argues not only that the rule is doctrinally intact, but that the principles and spirit that animate Hodge\u27s rule have broad influence in our law of evidence and have utility in the appellate review of unreasonable verdicts. Hodge\u27s rule, Hodge-like reasoning, and the associated epistemology, are alive and well in Canada

Emotions and the Veil of Voluntarism: The Loss of Judgment in Canadian Criminal Defences

In this perspective piece, the author attacks the notion of moral involuntariness in the Supreme Court of Canada\u27s judgment in R. v. Ruzic. He asserts that the voluntarist account of criminal liability is purely descriptive. Through the embrace of a mechanistic understanding of human agency, it forestalls judgment and veils the normative foundation of criminal law. The author asserts the need for a more normative approach, one which seeks to evaluate the moral blameworthiness of an act. In the case of duress, the author suggests that it is not enough to simply state that a person\u27s will is constrained because he or she is acting under the influence of emotion. An evaluative account of emotions would suggest that emotions involve thought on the part of the actor, and that emotions can be mistaken. Therefore, the moral bases of emotions can and should be evaluated. The law could have considerable conservative inertia under a legal regime which allowed certain attitudes to go unexamined. For instance, the sources of a particular emotional reaction might be rooted in a subordinating, retrograde vision of society that placed a low value on certain classes of persons. Hence, the voluntarist account may allow morally suspect social norms and their regressive effects to persist in the criminal law. Through these and other lines of inquiry, the author leads us to question some of the underpinnings of criminal law thinking, and calls for the reintroduction of meaningful and open judgment into the law of criminal defences

Key Theoretical Issues in the Interaction of Law and Religion: A Guide for the Perplexed

There is perhaps no more important access point into the key issues of modern political and legal theory than the questions raised by the interaction of law and religion in contemporary constitutional democracies. Of course, much classical political and moral theory was forged on the issue of the relationship between religious difference and state authority. John Locke’s work was directly influenced by this issue, writing as he did about the just configuration of state authority and moral difference in the wake of the Thirty Years’ War. Yet debates about the appropriate role of religion in public life and the challenges posed by religious difference also cut an important figure, in a variety of ways, in the writings of Hobbes, Rousseau, Spinoza, Hegel, and much of the work that we now view as being at the centre of the development of modern political philosophy

The Cultural Limits of Legal Tolerance

This article presents the argument that our understanding of the nature of the relationship between modern constitutionalism and religious difference has suffered with the success of the story of legal tolerance and multiculturalism. Taking up the Canadian case, in which the conventional narrative of legal multiculturalism has such purchase, this piece asks how the interaction of law and religion - and, in particular, the practices of legal tolerance - would look if we sought in earnest to understand law as a component, rather than a curator, of cultural diversity in modern liberal societies. Understanding the law as itself a cultural form forces us to think about the interaction of law and religion as an instance of cross-cultural encounter. Drawing from theoretical accounts of cross-cultural encounter and philosophical literature about the nature of toleration, and paying close attention to the shape of Canadian constitutional doctrine on religious freedom (law\u27s rules of cross-cultural engagement), this paper suggests that legal toleration is far less accommodative and far more assimilative than the conventional narrative lets on. Influential alternative theoretical accounts ultimately reproduce this dynamic because they similarly obscure the role of culture on both sides of the encounter of law and religion. Indeed, owing to the particular features of the culture of law\u27s rule, even the more thickly cultural solutions proposed in dialogic theory ultimately fail. In the end, this article exposes the very real cultural limits of legal tolerance