Accelerating lattice reduction with FPGAs

International audienceWe describe an FPGA accelerator for the Kannan­–Fincke­–Pohst enumeration algorithm (KFP) solving the Shortest Lattice Vector Problem (SVP). This is the first FPGA implementation of KFP specifically targeting cryptographically relevant dimensions. In order to optimize this implementation, we theoretically and experimentally study several facets of KFP, including its efficient parallelization and its underlying arithmetic. Our FPGA accelerator can be used for both solving stand-alone instances of SVP (within a hybrid CPU­–FPGA compound) or myriads of smaller dimensional SVP instances arising in a BKZ-type algorithm. For devices of comparable costs, our FPGA implementation is faster than a multi-core CPU implementation by a factor around 2.12

Cryptographic extensions for custom and GPU-like architectures

The PhD thesis work deals with the exploration of hardware architectures dedicated to cryptographic applications, in particular, solutions based on reconfigurable hardware, such as FPGA. The thesis presents the results achieved for the acceleration of operations essential to homomorphic cryptography, specifically, the integer multiplication of very long operands, based on the Schonhage-Strassen algorithm and implemented with an ad-hoc FPGA hardware. Then, the thesis reports the exploration of novelty approaches for cryptographic acceleration, based on vectorial dedicated architectures, software programmable, with the corresponding implementation of symmetric and public key operations (namely, AES encryption and Montgomery multiplication) with improved performances

On the Cryptanalysis of Public-Key Cryptography

Nowadays, the most popular public-key cryptosystems are based on either the integer factorization or the discrete logarithm problem. The feasibility of solving these mathematical problems in practice is studied and techniques are presented to speed-up the underlying arithmetic on parallel architectures. The fastest known approach to solve the discrete logarithm problem in groups of elliptic curves over finite fields is the Pollard rho method. The negation map can be used to speed up this calculation by a factor √2. It is well known that the random walks used by Pollard rho when combined with the negation map get trapped in fruitless cycles. We show that previously published approaches to deal with this problem are plagued by recurring cycles, and we propose effective alternative countermeasures. Furthermore, fast modular arithmetic is introduced which can take advantage of prime moduli of a special form using efficient "sloppy reduction." The effectiveness of these techniques is demonstrated by solving a 112-bit elliptic curve discrete logarithm problem using a cluster of PlayStation 3 game consoles: breaking a public-key standard and setting a new world record. The elliptic curve method (ECM) for integer factorization is the asymptotically fastest method to find relatively small factors of large integers. From a cryptanalytic point of view the performance of ECM gives information about secure parameter choices of some cryptographic protocols. We optimize ECM by proposing carry-free arithmetic modulo Mersenne numbers (numbers of the form 2M – 1) especially suitable for parallel architectures. Our implementation of these techniques on a cluster of PlayStation 3 game consoles set a new record by finding a 241-bit prime factor of 21181 – 1. A normal form for elliptic curves introduced by Edwards results in the fastest elliptic curve arithmetic in practice. Techniques to reduce the temporary storage and enhance the performance even further in the setting of ECM are presented. Our results enable one to run ECM efficiently on resource-constrained platforms such as graphics processing units

Covert timing channels, caching, and cryptography

Side-channel analysis is a cryptanalytic technique that targets not the formal description of a cryptographic primitive but the implementation of it. Examples of side-channels include power consumption or timing measurements. This is a young but very active field within applied cryptography. Modern processors are equipped with numerous mechanisms to improve the average performance of a program, including but not limited to caches. These mechanisms can often be used as side-channels to attack software implementations of cryptosystems. This area within side-channel analysis is called microarchitecture attacks, and those dealing with caching mechanisms cache-timing attacks. This dissertation presents a number of contributions to the field of side-channel analysis. The introductory portion consists of a review of common cache architectures, a literature survey of covert channels focusing mostly on covert timing channels, and a literature survey of cache-timing attacks, including selective related results that are more generally categorized as side-channel attacks such as traditional timing attacks. This dissertation includes eight publications relating to this field. They contain contributions in areas such as side-channel analysis, data cache-timing attacks, instruction cache-timing attacks, traditional timing attacks, and fault attacks. Fundamental themes also include attack mitigations and efficient yet secure software implementation of cryptosystems. Concrete results include, but are not limited to, four practical side-channel attacks against OpenSSL, each implemented and leading to full key recovery

Understanding Quantum Technologies 2022

Understanding Quantum Technologies 2022 is a creative-commons ebook that provides a unique 360 degrees overview of quantum technologies from science and technology to geopolitical and societal issues. It covers quantum physics history, quantum physics 101, gate-based quantum computing, quantum computing engineering (including quantum error corrections and quantum computing energetics), quantum computing hardware (all qubit types, including quantum annealing and quantum simulation paradigms, history, science, research, implementation and vendors), quantum enabling technologies (cryogenics, control electronics, photonics, components fabs, raw materials), quantum computing algorithms, software development tools and use cases, unconventional computing (potential alternatives to quantum and classical computing), quantum telecommunications and cryptography, quantum sensing, quantum technologies around the world, quantum technologies societal impact and even quantum fake sciences. The main audience are computer science engineers, developers and IT specialists as well as quantum scientists and students who want to acquire a global view of how quantum technologies work, and particularly quantum computing. This version is an extensive update to the 2021 edition published in October 2021.Comment: 1132 pages, 920 figures, Letter forma