Large sparse matrix-vector multiplication over finite fields


Thesis Type: Doctorate

Institution Of The Thesis: Orta Doğu Teknik Üniversitesi, Institute of Applied Mathematics, Cryptography, Turkey

Approval Date: 2019

Student: CEYDA MANGIR

Supervisor: MURAT CENK

Abstract:

Cryptographic computations such as factoring integers and computing discrete logarithms require solving a large sparse system of linear equations over finite fields. When dealing with such systems iterative solvers such as Wiedemann or Lanczos algorithms are used. The computational cost of both methods is often dominated by successive matrix-vector products. In this thesis, we introduce a new algorithm for computing a large sparse matrix-vector multiplication over finite fields. The proposed algorithm is implemented and its performance is compared with a classical method. Our algorithm exhibits a significant improvements between 34% and 77%.