Speeding up wheel factoring method

Bahig, Hazem M.; Nassr, Dieaa I.; Mahdi, Mohammed A.; Hazber, Mohamed A. G.; Al-Utaibi, Khaled A.

doi:10.1007/s11227-022-04470-y

Cited by 3 publications

(7 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this paper, we focus on the challenge of factoring odd composite integers n. We investigate a new way to enhance the recent wheel factoring technique [33]. We expand the wheel method by using a greater number of prime integers as a basis rather than a limited number of prime integers.…”

Section: Of 11mentioning

confidence: 99%

“…In this section, we will go over the three most important algorithms related to our research: Wheel Factorization Method (WFM), Forward Wheel Factorization Method (FWFM), and Backward Wheel Factorization Method (BWFM) [33].…”

Section: Related Workmentioning

confidence: 99%

“…The value of inc [8] is used to establish the following turn ′ s start. With the FWFM, complete the while−loop in a single iteration rather than Algorithm 2: FactorBasis [33] 1 Input: A composite integer m.…”

Section: Forward Wfm (Fwfm)mentioning

confidence: 99%

“…Algorithms 3 and 4 present the complete pseudocodes for the FWFM and TurnTest algorithms, respectively. Algorithm 3: Forward Wheel Factoring Method (FWFM) [33] 1 Input: A composite integer m.…”

Section: Forward Wfm (Fwfm)mentioning

confidence: 99%

“…Algorithm 5 provides the whole pseudocode for the backward wheel factoring method (BWFM). Algorithm 5: Backward Wheel Factoring Method (BWFM) [33] 1 Input: A composite integer m.…”

Section: Backward Wfm (Bwfm)mentioning

confidence: 99%

See 4 more Smart Citations

Accelerating the Wheel Factoring Techniques

Zaki¹,

Bakr²,

Alsahangiti³

et al. 2023

Preprint

View full text Add to dashboard Cite

The efficiency with which an integer may be factored into its prime factors determines several public key cryptosystems′ security in use today. Although there is a quantum-based technique with a polynomial time for integer factoring, on a traditional computer, there is no polynomial time algorithm. We investigate how to enhance the wheel factoring technique in this paper. Current wheel factorization algorithms rely on a very restricted set of prime integers as a base. In this study, we intend to adapt this notion to rely on a greater number of prime integers, resulting in a considerable improvement in the execution time. The experiments on composite numbers n reveal that the proposed algorithm improves on the existing wheel factoring algorithm by about 75%

show abstract

Section: Of 11mentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Forward Wfm (Fwfm)mentioning

confidence: 99%

Section: Forward Wfm (Fwfm)mentioning

confidence: 99%

“…Algorithm 5 provides the whole pseudocode for the backward wheel factoring method (BWFM). Algorithm 5: Backward Wheel Factoring Method (BWFM) [33] 1 Input: A composite integer m.…”

Section: Backward Wfm (Bwfm)mentioning

confidence: 99%

See 3 more Smart Citations

Accelerating the Wheel Factoring Techniques

Zaki¹,

Bakr²,

Alsahangiti³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

A survey of fermat factorization algorithms for factoring RSA composite numbers

Balasubramanian,

Pitchai

2023

Multidiscip. Sci. J.

View full text Add to dashboard Cite

In this research, we delve into the challenges associated with factorization in the context of the RSA cryptosystem. The RSA cryptosystem's security relies on the computational complexity of breaking down its modulus, which is essentially a product of two prime numbers denoted as 'p' and 'q.' Notably, the RSA modulus differs from the typical factorization problem, as it involves exceptionally large prime numbers, each roughly half the size of the modulus itself. If one manages to determine the factors of this modulus, it compromises the security of the entire RSA cryptosystem, as these factors can be exploited to derive the private key.Within this article, we provide an overview of the advancements made in the realm of factoring RSA moduli. Recent efforts in RSA factorization have successfully tackled 250-digit decimal RSA moduli. We also explore the common algorithms employed in factorization and delve into approaches based on the Fermat factorization method. Additionally, we discuss the various programming tools utilized to handle the challenge of factoring large numbers. Furthermore, we delve into the enhancement of the simple Fermat Primality test as a means to expedite the Primality Testing algorithm. Lastly, we offer a concise summary outlining the steps involved in the Number Field Sieve algorithm.

show abstract

Acceleration of Wheel Factoring Techniques

et al. 2023

View full text Add to dashboard Cite

The efficiency with which an integer may be factored into its prime factors determines several public key cryptosystems’ security in use today. Although there is a quantum-based technique with a polynomial time for integer factoring, on a traditional computer, there is no polynomial time algorithm. We investigate how to enhance the wheel factoring technique in this paper. Current wheel factorization algorithms rely on a very restricted set of prime integers as a base. In this study, we intend to adapt this notion to rely on a greater number of prime integers, resulting in a considerable improvement in the execution time. The experiments on composite numbers n reveal that the proposed algorithm improves on the existing wheel factoring algorithm by about 75%.

show abstract

Speeding up wheel factoring method

Cited by 3 publications

References 25 publications

Accelerating the Wheel Factoring Techniques

Accelerating the Wheel Factoring Techniques

A survey of fermat factorization algorithms for factoring RSA composite numbers

Acceleration of Wheel Factoring Techniques

Contact Info

Product

Resources

About