Pairings have found a range of applications in many areas of cryptography. As such, to utilize the enormous potential of pairing-based protocols one needs to efficiently compute pairings across various computing platforms. In this thesis, we give an introduction to pairing-based cryptography and describe the Tate pairing and its variants. We then describe some recent work to realize efficient computation of pairings. We further extend these optimizations and implement the O-Ate pairing on BN-curves on ARM and x86-64 platforms. Specifically, we extend the idea of lazy reduction to field inversion, optimize curve arithmetic, and construct efficient tower extensions to optimize field arithmetic. We also analyze the use of affine coordinates for pairing computation leading us to the conclusion that they are a competitive choice for fast pairing computation on ARM processors, especially at high security level. Our resulting implementation is more than three times faster than any previously reported implementation on ARM processors.

No description available.

Náklady na posádky v aerolinkách jsou po nákladech na palivo druhé největší. Cílem aerolinky je zajistit bezpečný provoz s minimálním počtem posádek a tím optimalizovat náklady. Práce popisuje metodiku odhadu počtu posádek na roční období. Používá přiřazení, ve kterém je každému dnu člena posádky přiřazena činnost, kterou vykonává. V práci je popsán nelineární model, který využívá přiřazení a následně agreguje dny pro získání celkového počtu posádek. Model je řešen v programu Premium Solver Platform a Lingu 7.

The present study investigated the use of stimulus-stimulus pairing (SSP) as the first step to build an echoic repertoire with children with no vocal communication skills. We began with echoic probes to establish the child did not have the target sound in their echoic repertoire, then implemented SSP to increase the rate of the target vocalization, and systematically added direct reinforcement, and a delay, until the participant responded in 80% of trials; we then implemented echoic training. We conducted this procedure with 3 young children with autism. This procedure was effective for one of three participants, and her echoic learning history immediately generalized to other sounds. For the other two participants, SSP increased the rate of vocalizations; however, they did not respond in enough trials to move to echoic training before withdrawing from the study. This study provides preliminary evidence for the use of SSP as part of echoic training for children with limited functional communication.

La compréhension usuelle de l'appariement proton-neutron, dont les traces sont actuellement étudiées en noyaux N = Z, s'appuie sur le mécanisme de paires de Cooper et modèles BCS type. Dans cette thèse, nous présentons une approche alternative qui, contrairement aux modèles BCS, conserve exactement le nombre de particules et l'isospin. Dans cette approche, l'état fondamental de noyaux N = Z est décrit comme un condensé de quartets alpha-similaires faits de deux neutrons et deux protons couplés à l'isospin total T = 0 et de spin J total = 0. La comparaison avec des calculs exacts du modèle en couches montre que le modèle de condensation quartet (QCM) donne une description très précise de l'appariement des corrélations à noyaux N = Z, bien mieux que les modèles BCS. Il est également montré que l'appariement proton-neutron et alpha de type condensation sont importantes non seulement pour les noyaux N = Z, mais aussi pour les noyaux avec des neutrons excédentaires. Dans ce dernier cas, le condensat de quartets d'alpha coexiste avec le condensat des paires de neutrons en excès par rapport au isotopes N = Z. En utilisant le cadre de QCM, nous avons également étudié la compétition entre l’appariement proton-neutron isovectoriel et isoscalaire dans les noyaux N = Z. Nos résultats indiquent que la contribution de l'appariement isoscalaire aux corrélations d'appariement du fondamental est très faible par rapport à l'appariement isovectoriel. / The common understanding of proton-neutron pairing, whose fingerprints are currently investigated in N = Z nuclei, relies on Cooper pair mechanism and BCS-type models. In the present thesis we present an alternative approach which, contrary to BCS models, conserves exactly the particle number and the isospin. In this approach the ground state of N=Z nuclei is described as a condensate of alpha-like quartets built by two neutrons and two protons coupled to the total isospin T=0 and total spin J=0. The comparison with exact shell model calculations shows that the quartet condensation model (QCM) gives a very accurate description of pairing correlations in N=Z nuclei, much better than the BCS models. It is also shown that proton-neutron pairing and alpha-type condensation are important not only for N=Z nuclei but also for nuclei with excess neutrons. In the latter case the condensate of alpha-like quartets coexist with the condensate of the neutron pairs in excess relative to the N=Z isotope. Using the framework of QCM we have also studied the competition between the isovector and the isoscalar proton-neutron pairing in nuclei with N=Z. Our results indicate that the contribution of isoscalar pairing to the ground state pairing correlations is very small compared to the isovector pairing.

The most efficient algorithm for solving the elliptic curve discrete logarithm problem can only be done in exponential time. Hence, we can use it in many cryptographic applications. Weil pairing is a mapping which maps a pair of points on elliptic curves to a multiplicative group of a finite field with nondegeneracy and bilinearity. Pairing was found to reduce the elliptic curve discrete logarithm problem into the discrete logarithm problem of a finite field, and became an important issue since then. In 1986, Miller proposed an efficient algorithm for computing Weil pairings. Many researchers focus on the improvement of this algorithm. In 2006, Blake et al. proposed the reduction of total number of lines based on the conjugate of a line. Liu et al. expanded their concept and proposed two improved methods. In this paper, we use both NAF and segmentation algorithm to implement the Weil pairing and analyse its complexity.

Not available / text

No description available.

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Ph.D. (Physics) / Please refer to full text to view abstract