Recursive double-size fixed precision arithmetic

International audienceThis work is a part of the SHIVA (Secured Hardware Immune Versatile Architecture) project whose purpose is to provide a programmable and reconfigurable hardware module with high level of security. We propose a recursive double-size fixed precision arithmetic called RecInt. Our work can be split in two parts. First we developped a C++ software library with performances comparable to GMP ones. Secondly our simple representation of the integers allows an implementation on FPGA. Our idea is to consider sizes that are a power of 2 and to apply doubling techniques to implement them efficiently: we design a recursive data structure where integers of size 2^k, for k>k0 can be stored as two integers of size 2^{k-1}. Obviously for k<=k0 we use machine arithmetic instead (k0 depending on the architecture)

Métodos numérico-simbólicos para calcular soluciones liouvillianas de ecuaciones diferenciales lineales

El objetivo de esta tesis es dar un algoritmo para decidir si un sistema explicitable de ecuaciones diferenciales kJiferenciales de orden superior sobre las funciones racionales complejas, dado simbólicamente,admite !Soluciones liouvillianas no nulas, calculando una (de laforma dada por un teorema de Singer) en caso !afirmativo. mediante métodos numérico-simbólicos del tipo Introducido por van der Hoeven.donde el uso de álculo numérico no compromete la corrección simbólica. Para ello se Introduce untipo de grupos algebraicos lineales, los grupos euriméricos, y se calcula el cierre eurimérico del grupo de Galois diferencial,mediante una modificación del algoritmo de Derksen y van der Hoeven, dado por los generadores de Ramis.Departamento de Algebra, Análisis Matemático, Geometría y Topologí

Computer Aided Verification

This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications

Side-Channel Analysis: Countermeasures and Application to Embedded Systems Debugging

Side-Channel Analysis plays an important role in cryptology, as it represents an important class of attacks against cryptographic implementations, especially in the context of embedded systems such as hand-held mobile devices, smart cards, RFID tags, etc. These types of attacks bypass any intrinsic mathematical security of the cryptographic algorithm or protocol by exploiting observable side-effects of the execution of the cryptographic operation that may exhibit some relationship with the internal (secret) parameters in the device. Two of the main types of side-channel attacks are timing attacks or timing analysis, where the relationship between the execution time and secret parameters is exploited; and power analysis, which exploits the relationship between power consumption and the operations being executed by a processor as well as the data that these operations work with. For power analysis, two main types have been proposed: simple power analysis (SPA) which relies on direct observation on a single measurement, and differential power analysis (DPA), which uses multiple measurements combined with statistical processing to extract information from the small variations in power consumption correlated to the data. In this thesis, we propose several countermeasures to these types of attacks, with the main themes being timing analysis and SPA. In addition to these themes, one of our contributions expands upon the ideas behind SPA to present a constructive use of these techniques in the context of embedded systems debugging. In our first contribution, we present a countermeasure against timing attacks where an optimized form of idle-wait is proposed with the goal of making the observable decryption time constant for most operations while maintaining the overhead to a minimum. We show that not only we reduce the overhead in terms of execution speed, but also the computational cost of the countermeasure, which represents a considerable advantage in the context of devices relying on battery power, where reduced computations translates into lower power consumption and thus increased battery life. This is indeed one of the important themes for all of the contributions related to countermeasures to side- channel attacks. Our second and third contributions focus on power analysis; specifically, SPA. We address the issue of straightforward implementations of binary exponentiation algorithms (or scalar multiplication, in the context of elliptic curve cryptography) making a cryptographic system vulnerable to SPA. Solutions previously proposed introduce a considerable performance penalty. We propose a new method, namely Square-and-Buffered- Multiplications (SABM), that implements an SPA-resistant binary exponentiation exhibiting optimal execution time at the cost of a small amount of storage --- O(\sqrt(\ell)), where \ell is the bit length of the exponent. The technique is optimal in the sense that it adds SPA-resistance to an underlying binary exponentiation algorithm while introducing zero computational overhead. We then present several new SPA-resistant algorithms that result from a novel way of combining the SABM method with an alternative binary exponentiation algorithm where the exponent is split in two halves for simultaneous processing, showing that by combining the two techniques, we can make use of signed-digit representations of the exponent to further improve performance while maintaining SPA-resistance. We also discuss the possibility of our method being implemented in a way that a certain level of resistance against DPA may be obtained. In a related contribution, we extend these ideas used in SPA and propose a technique to non-intrusively monitor a device and trace program execution, with the intended application of assisting in the difficult task of debugging embedded systems at deployment or production stage, when standard debugging tools or auxiliary components to facilitate debugging are no longer enabled in the device. One of the important highlights of this contribution is the fact that the system works on a standard PC, capturing the power traces through the recording input of the sound card

Making up Numbers

"Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.

Making up Numbers

"Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.