A Unified Method for Private Exponent Attacks on RSA Using Lattices

Bahig, Hatem M.; Nassr, Dieaa I.; Bhery, Ashraf; Nitaj, Abderrahmane

doi:10.1142/s0129054120500045

Cited by 7 publications

(3 citation statements)

References 23 publications

(54 reference statements)

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“…There are more factoring techniques, but they require more knowledge of cryptosystems or specific requirements for the prime factors (see [1,3,4,19]). Utilizing highperformance-Computing systems such as multicore systems [6,7,13,15], cloud computing systems [28], and graphics processing units [2,8] is one method for accelerating factoring algorithms.…”

Section: Of 11mentioning

confidence: 99%

Accelerating the Wheel Factoring Techniques

Zaki¹,

Bakr²,

Alsahangiti³

et al. 2023

Preprint

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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%

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Section: Of 11mentioning

confidence: 99%

Accelerating the Wheel Factoring Techniques

Zaki¹,

Bakr²,

Alsahangiti³

et al. 2023

Preprint

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show abstract

“…Therefore, solving this problem in an efficient timeframe leads to breaking the RSA. In other side, the difficulty in finding a polynomial time for the factorization leads to difficulty in breaking the RSA cryptosystem [6,7,8,9]. Moreover, the integer factorization problem is important from the point of view of complexity theory.…”

Section: = Modmentioning

confidence: 99%

Performance Analysis of Fermat Factorization Algorithms

Bahig¹,

Mohammed²,

Khaled³

et al. 2020

IJACSA

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“…In order to unify small private exponent attacks on RSA and to determine a universal attack using continued fractions or lattices, the authors in [14,15] proposed concepts of the Wiener and Coppersmith intervals using continued fractions and lattices, respectively. An integer interval I is called Wiener's interval if each m ∈ I satisfies Wiener's attack, i.e.,…”

mentioning

confidence: 99%

Small Private Exponent Attacks on RSA Using Continued Fractions and Multicore Systems

et al. 2022

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The RSA (Rivest–Shamir–Adleman) asymmetric-key cryptosystem is widely used for encryptions and digital signatures. Let (n,e) be the RSA public key and d be the corresponding private key (or private exponent). One of the attacks on RSA is to find the private key d using continued fractions when d is small. In this paper, we present a new technique to improve a small private exponent attack on RSA using continued fractions and multicore systems. The idea of the proposed technique is to find an interval that contains ϕ(n), and then propose a method to generate different points in the interval that can be used by continued fraction and multicore systems to recover the private key, where ϕ is Euler’s totient function. The practical results of three small private exponent attacks on RSA show that we extended the previous bound of the private key that is discovered by continued fractions. When n is 1024 bits, we used 20 cores to extend the bound of d by 0.016 for de Weger, Maitra-Sarkar, and Nassr et al. attacks in average times 7.67 h, 2.7 h, and 44 min, respectively.

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A Unified Method for Private Exponent Attacks on RSA Using Lattices

Cited by 7 publications

References 23 publications

Accelerating the Wheel Factoring Techniques

Accelerating the Wheel Factoring Techniques

Performance Analysis of Fermat Factorization Algorithms

Small Private Exponent Attacks on RSA Using Continued Fractions and Multicore Systems

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