# Parallel and Distributed Implementations of the Wiedemann and the Block-Wiedemann Methods over GF(2)

### Rahul Roy, Abhijit Das, Dipanwita Roy Chowdhury

#### 2022

#### Abstract

Finding the prime factors of large composite integers is the fundamental computational problem in number theory. Currently, the fastest known integer-factoring algorithm is the General Number Field Sieve method (GNFSM) which has been used by the research community to factor RSA moduli of sizes 500–800 bits. One of the steps of this method involves finding non-zero solutions of the linear system available from the sieving stage. Since the linear systems involved in GNFSM are necessarily sparse, special iterative system solvers are used. One such solver is called the Wiedemann method. This paper reports our efficient implementation of the Wiedemann method, and its block version. We start with a single-core sequential implementation, and then make efforts to parallelize the implementation to run on multiple cores of a single machine. Special load-balancing techniques are designed to reduce synchronization overheads after each iteration. Finally, we distribute the computation across multiple computing nodes. Our load-balancing ideas are refined, and computation-communication overlapping techniques are explored in order to absorb the communication overheads. Speed-up figures achieved by the different improvements incorporated in our implementations are reported. To the best of our knowledge, we are the first to report distributed implementations of the Wiedemann method.

Download#### Paper Citation

#### in Harvard Style

Roy R., Das A. and Roy Chowdhury D. (2022). **Parallel and Distributed Implementations of the Wiedemann and the Block-Wiedemann Methods over GF(2)**. In *Proceedings of the 19th International Conference on Security and Cryptography - Volume 1: SECRYPT,* ISBN 978-989-758-590-6, pages 540-547. DOI: 10.5220/0011267700003283

#### in Bibtex Style

@conference{secrypt22,

author={Rahul Roy and Abhijit Das and Dipanwita Roy Chowdhury},

title={Parallel and Distributed Implementations of the Wiedemann and the Block-Wiedemann Methods over GF(2)},

booktitle={Proceedings of the 19th International Conference on Security and Cryptography - Volume 1: SECRYPT,},

year={2022},

pages={540-547},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0011267700003283},

isbn={978-989-758-590-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 19th International Conference on Security and Cryptography - Volume 1: SECRYPT,

TI - Parallel and Distributed Implementations of the Wiedemann and the Block-Wiedemann Methods over GF(2)

SN - 978-989-758-590-6

AU - Roy R.

AU - Das A.

AU - Roy Chowdhury D.

PY - 2022

SP - 540

EP - 547

DO - 10.5220/0011267700003283