Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 7 of 7 for “"Polynomial multiplication"”.
-
On The Parallelization Of Integer Polynomial Multiplication
… and reducing overheads in the implementations. Polynomial multiplication is at the core of many algorithms in symbolic computation such as real root isolation which will be our main application for now. In this thesis, we first investigate the multiplication of dense univariate polynomials with …
-
FPGA Implementation and Optimization of Bit Flipping Key Generation Algorithm for Post Quantum Cryptography in Embedded Systems Applications
… modular arithmetic operations, which include polynomial multiplication, inversion, and hashing. These factors limits its FPGA implementation power for embedded and IoT applications. This research work presents a resource-constrained FPGA implementation of BIKE on the Artix-7 FPGA, designed for …
-
Efficient Binary Field Multiplication on a VLIW DSP
… cryptography relies extensively on modular multiplication with long operands. We investigate the opportunities to optimize this operation in a heterogeneous multiprocessing platform such as TI OMAP3530. By migrating the long operand modular multiplication from a general-purpose ARM Cortex A8 …
-
Verifying Correctness of the Number Theoretic Transform and Fast Number Theoretic Transform in F⋆
… (NTT) is an algorithm that enables efficient polynomial multiplication and has recently gained importance in post-quantum cryptography. This thesis presents a proof of correctness of the NTT in F⋆ , a proof-oriented programming language that extracts to OCaml, and shows that we can use the NTT …
-
Putting Fürer's Algorithm into Practice with the BPAS Library
Fast algorithms for integer and polynomial multiplication play an important role in scientific computing as well as other disciplines. In 1971, Schönhage and Strassen designed an algorithm that improved the multiplication time for two integers of at most n bits to O(log n log log n). In 2007, …
-
Fast Algorithms, Modular Methods, Parallel Approaches and Software Engineering for Solving Polynomial Systems Symbolically
… We first adapt nearly optimal algorithms for polynomial arithmetic over fields to direct products of fields for polynomial multiplication, inversion and GCD compu tations. Then, by introducing the notion of equiprojectable decomposition, a sharp modular method for triangular decompositions …
-
Strings in proteomics and transcriptomics : algorithmic and combinatorial questions in mass spectrometry and EST clustering
… these algorithms encode the submasses of s in a polynomial and rely for their efficiency on Fast Fourier Transform for polynomial multiplication. The third weighted string problem we discuss is de novo peptide sequencing, i.e., recovering the amino acid sequence of a sample peptide from tandem MS …