A Practical Analysis of the Fermat Factorization and Pollard Rho Method for Factoring Integers

Aminudin Aminudin,Eko Budi Cahyono

doi:10.24843/lkjiti.2021.v12.i01.p04

Aminudin Aminudin, Eko Budi Cahyono

Open Access

https://doi.org/10.24843/lkjiti.2021.v12.i01.p04

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Abstract

The development of public-key cryptography generation using the factoring method is very important in practical cryptography applications. In cryptographic applications, the urgency of factoring is very risky because factoring can crack public and private keys, even though the strength in cryptographic algorithms is determined mainly by the key strength generated by the algorithm. However, solving the composite number to find the prime factors is still very rarely done. Therefore, this study will compare the Fermat factorization algorithm and Pollard rho by finding the key generator public key algorithm's prime factor value. Based on the series of test and analysis factoring integer algorithm using Fermat's Factorization and Pollards' Rho methods, it could be concluded that both methods could be used to factorize the public key which specifically aimed to identify the prime factors. During the public key factorizing process within 16 bytes – 64 bytes, Pollards' Rho's average duration was significantly faster than Fermat's Factorization.

Highlights

Information security is a major challenge in an era of information flood like today
Based on the series of test and analysis factoring integer algorithm using Fermat's Factorization and Pollards' Rho methods, it could be concluded that both methods could be used to factorize the public key which aimed to identify the prime factors
During the public key factorizing process within 16 bytes – 64 bytes, Pollards' Rho's average duration was significantly faster than Fermat's Factorization

Summary

Introduction

The cryptology method can be one of the solutions used to secure this information [1]. The main task of cryptography is to hide data using specific algorithms, while cryptanalyst is a method for investigating the security of a cryptographic system by finding weaknesses in codes, ciphers, protocols, or key management schemes.[2]. Cryptanalysts are needed to test the robustness of the encryption algorithm. There are several mathematical approaches in testing the robustness of cryptographic algorithms, including discrete logarithms and factorization. The factorization method is used to break numbers into smaller numbers [3]. This factorization method is used for the RSA algorithm to generate public and private keys

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