Computational linear algebra over finite fields

We present here algorithms for efficient computation of linear algebra problems over finite fields

Preparing sparse solvers for exascale computing.

Sparse solvers provide essential functionality for a wide variety of scientific applications. Highly parallel sparse solvers are essential for continuing advances in high-fidelity, multi-physics and multi-scale simulations, especially as we target exascale platforms. This paper describes the challenges, strategies and progress of the US Department of Energy Exascale Computing project towards providing sparse solvers for exascale computing platforms. We address the demands of systems with thousands of high-performance node devices where exposing concurrency, hiding latency and creating alternative algorithms become essential. The efforts described here are works in progress, highlighting current success and upcoming challenges. This article is part of a discussion meeting issue 'Numerical algorithms for high-performance computational science'

HLS-Based Methodology for Fast Iterative Development Applied to Elliptic Curve Arithmetic

International audienceHigh-Level Synthesis (HLS) is used by hardware developers to achieve higher abstraction in circuit descriptions. In order to shorten the hardware development time via HLS, we present an adjustment of the Iterative and Incremental Design (IID) methodology, frequently used in software development. In particular, our methodology is relevant for the development of applications with unusual complexity: the method was applied here to the development of large modular arithmetic, commonly used for cryptography applications (e.g., Elliptic Curves). Rapid feedback on circuit characteristics is used to evaluate deep architectural changes in short time, greatly reducing the time-to-market with respect to hand-made designs. In addition, our approach is highly flexible, since the same generic high-level description can be used to produce an entire set of circuits, each with different area/performance trade-offs. Thanks to the proposed approach, any change to the initial specification (e.g., the curve used) is also very fast, while it may require a large effort in the case of hand-made designs

Elliptical Curve Digital Signatures Algorithm

Elliptical digital signatures algorithm provides security services for resource constrained embedded devices. The ECDSA level security can be enhanced by several parameters as parameter key size and the security level of ECDSA elementary modules such as hash function, elliptic curve point multiplication on koblitz curve which is used to compute public key and a pseudo-random generator which generates key pair generation. This paper describes novel security approach on authentication schemes as a modification of ECDSA scheme. This paper provides a comprehensive survey of recent developments on elliptic curve digital signatures approaches. The survey of ECDSA involves major issues like security of cryptosystem, RFID-tag authentication, Montgomery multiplication over binary fields, Scaling techniques, Signature generation ,signature verification, point addition and point doubling of the different coordinate system and classification. DOI: 10.17762/ijritcc2321-8169.150318

High-Performance VLSI Architectures for Lattice-Based Cryptography

Lattice-based cryptography is a cryptographic primitive built upon the hard problems on point lattices. Cryptosystems relying on lattice-based cryptography have attracted huge attention in the last decade since they have post-quantum-resistant security and the remarkable construction of the algorithm. In particular, homomorphic encryption (HE) and post-quantum cryptography (PQC) are the two main applications of lattice-based cryptography. Meanwhile, the efficient hardware implementations for these advanced cryptography schemes are demanding to achieve a high-performance implementation. This dissertation aims to investigate the novel and high-performance very large-scale integration (VLSI) architectures for lattice-based cryptography, including the HE and PQC schemes. This dissertation first presents different architectures for the number-theoretic transform (NTT)-based polynomial multiplication, one of the crucial parts of the fundamental arithmetic for lattice-based HE and PQC schemes. Then a high-speed modular integer multiplier is proposed, particularly for lattice-based cryptography. In addition, a novel modular polynomial multiplier is presented to exploit the fast finite impulse response (FIR) filter architecture to reduce the computational complexity of the schoolbook modular polynomial multiplication for lattice-based PQC scheme. Afterward, an NTT and Chinese remainder theorem (CRT)-based high-speed modular polynomial multiplier is presented for HE schemes whose moduli are large integers