Speeding Up Multi- Exponentiation Algorithm on a Multicore System

Fathy, Khaled; Bahig, Hazem M.; Farag, Mohamed

doi:10.21608/joems.2018.2540.1008

Cited by 6 publications

(4 citation statements)

References 20 publications

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“…The increase in the values of two parameters leads to a slight increase in the running time. (4) The running time for SAAS algorithm is faster than the exact algorithm, and the difference between the two algorithms in running time increases with increase in e and k. (5) The last column of Table 2 shows the percentage improvement for the SAAS algorithm compared to the exact algorithm.…”

Section: Resultsmentioning

confidence: 99%

“…The first reason is that one of the fundamental operations that play an important role in the efficiency of many public key cryptosystems and protocols is group exponentiation (sometimes it is called multi-modular exponentiation [2,5]), i.e., computing 𝑔 ,𝑔 ,…,𝑔 simultaneously with a minimal number of operations, where g is an element in a group. Designing a fast algorithm for generating a shortest (or short) ASeq increases the efficiency of such public key cryptosystems and protocols since evaluating 𝑔 ,𝑔 ,…,𝑔 with a minimal number of multiplications is equivalent to finding a shortest ASeq(N).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An Efficient Simulated Annealing Algorithm for Short Addition Sequence

Bahig,

Hazber,

Bahig

2023

Preprint

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An addition sequence is an important operation in many applications of computer science, such as multi-modular exponentiation and outsourcing protocols. Finding an addition sequence for a set of positive integers with the shortest length is challenging due to the high computational time required to find the solution. In this paper, a new metaheuristic algorithm is designed based on the simulated annealing strategy to generate a short addition sequence. The efficiency of the proposed algorithm was proved experimentally by comparing it with the previous exact and heuristic algorithms in terms of running time and the length of the addition sequence.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Efficient Simulated Annealing Algorithm for Short Addition Sequence

Bahig,

Hazber,

Bahig

2023

Preprint

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“…The complexity of the integer factorization issue affects the security of several public key cryptosystems such as [11,20,23,25,36], while the exponentiation problem determines the effectiveness of such cryptosystems [9,10,34].…”

Section: Introductionmentioning

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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“…Many problems in number theory and computer arithmetic play important roles in cryptography. Examples of such problems are the generation of prime numbers [1][2][3], primality testing [4,5], modular exponentiation [6], addition chains and sequences [7,8] and integer factorization [9][10][11][12]. Developing fast algorithms that address these problems is one of the main challenges of algorithm complexity and leads to significant improvements in various applications.…”

Section: Introductionmentioning

confidence: 99%

Efficient Sequential and Parallel Prime Sieve Algorithms

et al. 2022

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Generating prime numbers less than or equal to an integer number m plays an important role in many asymmetric key cryptosystems. Recently, a new sequential prime sieve algorithm was proposed based on set theory. The main drawback of this algorithm is that the running time and storage are high when the size of m is large. This paper introduces three new algorithms for a prime sieve based on two approaches. The first approach develops a fast sequential prime sieve algorithm based on set theory and some structural improvements to the recent prime sieve algorithm. The second approach introduces two new parallel algorithms in the shared memory parallel model based on static and dynamic strategies. The analysis of the experimental studies shows the following results. (1) The proposed sequential algorithm outperforms the recent prime sieve algorithm in terms of running time by 98% and memory consumption by 80%, on average. (2) The two proposed parallel algorithms outperform the proposed sequential algorithm by 72% and 67%, respectively, on average. (3) The maximum speedups achieved by the dynamic and static parallel algorithms using 16 threads are 7 and 4.5, respectively. As a result, the proposed algorithms are more effective than the recent algorithm in terms of running time, storage and scalability in generating primes.

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Speeding Up Multi- Exponentiation Algorithm on a Multicore System

Cited by 6 publications

References 20 publications

An Efficient Simulated Annealing Algorithm for Short Addition Sequence

An Efficient Simulated Annealing Algorithm for Short Addition Sequence

Accelerating the Wheel Factoring Techniques

Efficient Sequential and Parallel Prime Sieve Algorithms

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