Developing an Automatic Generation Tool for Cryptographic Pairing Functions

Pairing-Based Cryptography is receiving steadily more attention from industry, mainly because of the increasing interest in Identity-Based protocols. Although there are plenty of applications, efficiently implementing the pairing functions is often difficult as it requires more knowledge than previous cryptographic primitives. The author presents a tool for automatically generating optimized code for the pairing functions which can be used in the construction of such cryptographic protocols. In the following pages I present my work done on the construction of pairing function code, its optimizations and how their construction can be automated to ease the work of the protocol implementer. Based on the user requirements and the security level, the created cryptographic compiler chooses and constructs the appropriate elliptic curve. It identifies the supported pairing function: the Tate, ate, R-ate or pairing lattice/optimal pairing, and its optimized parameters. Using artificial intelligence algorithms, it generates optimized code for the final exponentiation and for hashing a point to the required group using the parametrisation of the chosen family of curves. Support for several multi-precision libraries has been incorporated: Magma, MIRACL and RELIC are already included, but more are possible

Cryptographic Pairings: Efficiency and DLP security

This thesis studies two important aspects of the use of pairings in cryptography, efficient algorithms and security. Pairings are very useful tools in cryptography, originally used for the cryptanalysis of elliptic curve cryptography, they are now used in key exchange protocols, signature schemes and Identity-based cryptography. This thesis comprises of two parts: Security and Efficient Algorithms. In Part I: Security, the security of pairing-based protocols is considered, with a thorough examination of the Discrete Logarithm Problem (DLP) as it occurs in PBC. Results on the relationship between the two instances of the DLP will be presented along with a discussion about the appropriate selection of parameters to ensure particular security level. In Part II: Efficient Algorithms, some of the computational issues which arise when using pairings in cryptography are addressed. Pairings can be computationally expensive, so the Pairing-Based Cryptography (PBC) research community is constantly striving to find computational improvements for all aspects of protocols using pairings. The improvements given in this section contribute towards more efficient methods for the computation of pairings, and increase the efficiency of operations necessary in some pairing-based protocol

On the Alpha Value of Polynomials in the Tower Number Field Sieve Algorithm

International audienceIn this paper, we provide a notable step towards filling the gap between theory (estimates of running-time) and practice (a discrete logarithm record computation) for the Tower Number Field Sieve (TNFS) algorithm. We propose a generalisation of ranking formula for selecting the polynomials used in the very first step of TNFS algorithm. For this we provide a definition and an exact implementation (Magma and SageMath) of the alpha function. This function measures the bias in the smoothness probability of norms in number fields compared to random integers of the same size. We use it to estimate the yield of polynomials, that is the expected number of relations, as a generalisation of Murphy's E function, and finally the total amount of operations needed to compute a discrete logarithm with TNFS algorithm in the targeted fields. This is an improvement of the earlier work of Barbulescu and Duquesne on estimating the running-time of the algorithm. We apply our estimates to a wide size range of finite fields GF(pn), for small composite n = 12, 16, 18, 24, that are target fields of pairing-friendly curves

An Improvement of Optimal Ate Pairing on KSS curve with Pseudo 12-sparse Multiplication

International audienc

An Improvement of Optimal Ate Pairing on KSS curve with Pseudo 12-sparse Multiplication

International audienc

Metodi Matriciali per l'Acquisizione Efficiente e la Crittografia di Segnali in Forma Compressa

The idea of balancing the resources spent in the acquisition and encoding of natural signals strictly to their intrinsic information content has interested nearly a decade of research under the name of compressed sensing. In this doctoral dissertation we develop some extensions and improvements upon this technique's foundations, by modifying the random sensing matrices on which the signals of interest are projected to achieve different objectives. Firstly, we propose two methods for the adaptation of sensing matrix ensembles to the second-order moments of natural signals. These techniques leverage the maximisation of different proxies for the quantity of information acquired by compressed sensing, and are efficiently applied in the encoding of electrocardiographic tracks with minimum-complexity digital hardware. Secondly, we focus on the possibility of using compressed sensing as a method to provide a partial, yet cryptanalysis-resistant form of encryption; in this context, we show how a random matrix generation strategy with a controlled amount of perturbations can be used to distinguish between multiple user classes with different quality of access to the encrypted information content. Finally, we explore the application of compressed sensing in the design of a multispectral imager, by implementing an optical scheme that entails a coded aperture array and Fabry-Pérot spectral filters. The signal recoveries obtained by processing real-world measurements show promising results, that leave room for an improvement of the sensing matrix calibration problem in the devised imager

AutoGraff: towards a computational understanding of graffiti writing and related art forms.

The aim of this thesis is to develop a system that generates letters and pictures with a style that is immediately recognizable as graffiti art or calligraphy. The proposed system can be used similarly to, and in tight integration with, conventional computer-aided geometric design tools and can be used to generate synthetic graffiti content for urban environments in games and in movies, and to guide robotic or fabrication systems that can materialise the output of the system with physical drawing media. The thesis is divided into two main parts. The first part describes a set of stroke primitives, building blocks that can be combined to generate different designs that resemble graffiti or calligraphy. These primitives mimic the process typically used to design graffiti letters and exploit well known principles of motor control to model the way in which an artist moves when incrementally tracing stylised letter forms. The second part demonstrates how these stroke primitives can be automatically recovered from input geometry defined in vector form, such as the digitised traces of writing made by a user, or the glyph outlines in a font. This procedure converts the input geometry into a seed that can be transformed into a variety of calligraphic and graffiti stylisations, which depend on parametric variations of the strokes