13 research outputs found
Action de Groupe Supersingulières et Echange de Clés Post-quantique
Alice and Bob want to exchange information and make sure that an eavesdropper will not be able to listen to them, even with a quantum computer.To that aim they use cryptography and in particular a key-exchange protocol. These type of protocols rely on number theory and algebraic geometry. However current protocols are not quantum resistant, which is the reason why new cryptographic tools must be developed. One of these tools rely on isogenies, i.e. homomorphisms between elliptic curves. In this thesis the first contribution is an implementation of an isogeny-based key-exchange protocol resistant against side-channel attacks (timing and power consumption analysis, fault injection). We also generalize this protocol to a larger set of elliptic curves.Alice et Bob souhaitent échanger des informations sans qu’un attaquant, même muni d’un ordinateur quantique, puisse les entendre. Pour cela, ils ont recours à la cryptologie et en particulier à un protocole d’échange de clés. Ces protocoles reposent sur la théorie des nombres et la géométrie algébrique. Cependant les protocoles actuellement utilisés ne résistent pas aux attaques quantiques, c’est pourquoi il est nécessaire de développer de nouveaux outils cryptographiques. L’un de ces outils repose sur les isogénies, c’est-à -dire des homomorphismes entre des courbes elliptiques. Dans cette thèse nous proposons une implémentation d’un des protocoles d’échange de clés basé sur les isogénies qui résiste aux attaques par canaux auxiliaires (étude de la durée d’exécution, de la consommation de courant et injection de fautes). Nous généralisons également ce protocole à un plus grand ensemble de courbes elliptiques
Quantum Computing: Lecture Notes
This is a set of lecture notes suitable for a Master's course on quantum
computation and information from the perspective of theoretical computer
science. The first version was written in 2011, with many extensions and
improvements in subsequent years. The first 10 chapters cover the circuit model
and the main quantum algorithms (Deutsch-Jozsa, Simon, Shor, Hidden Subgroup
Problem, Grover, quantum walks, Hamiltonian simulation and HHL). They are
followed by 3 chapters about complexity, 4 chapters about distributed ("Alice
and Bob") settings, and a final chapter about quantum error correction.
Appendices A and B give a brief introduction to the required linear algebra and
some other mathematical and computer science background. All chapters come with
exercises, with some hints provided in Appendix C.Comment: 184 pages. Version 2: added a new chapter about QMA and local
Hamiltonian, more exercises in several chapters, and some small
corrections/clarification
Quantum Computing: Lecture Notes
This is a set of lecture notes suitable for a Master's course on quantum computation and information from the perspective of theoretical computer science. The first version was written in 2011, with many extensions and improvements in subsequent years. The first 10 chapters cover the circuit model and the main quantum algorithms (Deutsch-Jozsa, Simon, Shor, Hidden Subgroup Problem, Grover, quantum walks, Hamiltonian simulation and HHL). They are followed by 2 chapters about complexity, 4 chapters about distributed ("Alice and Bob") settings, and a final chapter about quantum error correction. Appendices A and B give a brief introduction to the required linear algebra and some other mathematical and computer science background. All chapters come with exercises, with some hints provided in Appendix C
Algorithms for Solving Linear and Polynomial Systems of Equations over Finite Fields with Applications to Cryptanalysis
This dissertation contains algorithms for solving linear and polynomial systems
of equations over GF(2). The objective is to provide fast and exact tools for algebraic
cryptanalysis and other applications. Accordingly, it is divided into two parts.
The first part deals with polynomial systems. Chapter 2 contains a successful
cryptanalysis of Keeloq, the block cipher used in nearly all luxury automobiles.
The attack is more than 16,000 times faster than brute force, but queries 0.62 Ă— 2^32
plaintexts. The polynomial systems of equations arising from that cryptanalysis
were solved via SAT-solvers. Therefore, Chapter 3 introduces a new method of
solving polynomial systems of equations by converting them into CNF-SAT problems
and using a SAT-solver. Finally, Chapter 4 contains a discussion on how SAT-solvers
work internally.
The second part deals with linear systems over GF(2), and other small fields
(and rings). These occur in cryptanalysis when using the XL algorithm, which converts polynomial systems into larger linear systems. We introduce a new complexity
model and data structures for GF(2)-matrix operations. This is discussed in Appendix B but applies to all of Part II. Chapter 5 contains an analysis of "the Method
of Four Russians" for multiplication and a variant for matrix inversion, which is
log n faster than Gaussian Elimination, and can be combined with Strassen-like algorithms. Chapter 6 contains an algorithm for accelerating matrix multiplication
over small finite fields. It is feasible but the memory cost is so high that it is mostly
of theoretical interest. Appendix A contains some discussion of GF(2)-linear algebra
and how it differs from linear algebra in R and C. Appendix C discusses algorithms
faster than Strassen's algorithm, and contains proofs that matrix multiplication,
matrix squaring, triangular matrix inversion, LUP-factorization, general matrix in-
version and the taking of determinants, are equicomplex. These proofs are already
known, but are here gathered into one place in the same notation
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Recent Application in Biometrics
In the recent years, a number of recognition and authentication systems based on biometric measurements have been proposed. Algorithms and sensors have been developed to acquire and process many different biometric traits. Moreover, the biometric technology is being used in novel ways, with potential commercial and practical implications to our daily activities. The key objective of the book is to provide a collection of comprehensive references on some recent theoretical development as well as novel applications in biometrics. The topics covered in this book reflect well both aspects of development. They include biometric sample quality, privacy preserving and cancellable biometrics, contactless biometrics, novel and unconventional biometrics, and the technical challenges in implementing the technology in portable devices. The book consists of 15 chapters. It is divided into four sections, namely, biometric applications on mobile platforms, cancelable biometrics, biometric encryption, and other applications. The book was reviewed by editors Dr. Jucheng Yang and Dr. Norman Poh. We deeply appreciate the efforts of our guest editors: Dr. Girija Chetty, Dr. Loris Nanni, Dr. Jianjiang Feng, Dr. Dongsun Park and Dr. Sook Yoon, as well as a number of anonymous reviewers
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Computer science: the hardware software and heart of IT
1st edition, 201