Analisis Performa Algoritma Modifikasi RSA Standar dengan Montgomery Modular Multiplication

Antonie, Aurellia (2025) Analisis Performa Algoritma Modifikasi RSA Standar dengan Montgomery Modular Multiplication. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Perkembangan teknologi informasi di Indonesia memberikan banyak manfaat, tetapi juga meningkatkan risiko keamanan, seperti kebocoran data. Salah satu upaya untuk meningkatkan keamanan sistem data adalah melalui penerapan kriptografi, yang prosesnya didasarkan pada konsep matematika seperti teori bilangan, aljabar, analisis kompleksitas, dan verifikasi formal. RSA merupakan salah satu algoritma kriptografi asimetris. Nama RSA diambil dari inisial nama ketiga peneliti yang memperkenalkan algoritma ini, yaitu Ron Rivest, Len Adleman, dan Adi Shamir. Sistem keamanan RSA didasarkan pada kesulitan memfaktorkan bilangan prima besar. Meskipun tingkat keamanannya tinggi, RSA standar memiliki kelemahan dalam kecepatan proses penyandian yang relatif lebih lambat dibandingkan algoritma lain. Sehingga dilakukan modifikasi terhadap RSA dengan menerapkan Montgomery Modular Multiplication untuk meningkatkan performa kecepatan waktu eksekusi. Selain itu, efisiensi penggunaan memori juga perlu diperhatikan dalam sistem kriptografi. Penelitian ini bertujuan untuk menganalisis performa RSA standar dan RSA yang dimodifikasi menggunakan Montgomery Modular Multiplication, dengan fokus pada peningkatan waktu eksekusi dan penggunaan memori. Hasil penelitian menunjukkan bahwa RSA dengan modifikasi Montgomery Modular Multiplication memiliki kecepatan proses enkripsi hingga 4.30 kali lebih cepat dibandingkan RSA standar. Dan pada proses dekripsi, algoritma RSA modifikasi ini juga menunjukkan keunggulan dengan kecepatan hingga 4,50 kali lebih cepat daripada RSA standar. Sementara itu, pada aspek penggunaan memori, proses enkripsi RSA modifikasi Montgomery Modular Multiplication menggunakan memori 1.014 kali lebih banyak dibanding RSA standar. Pada proses dekripsi, RSA modifikasi ini menggunakan memori 1.014 kali lebih efisien daripada RSA standar. Hal ini menunjukkan bahwa RSA modifikasi Montgomery Modular Multiplication berusaha mempertahankan penggunaan memori yang stabil dan tetap berada dalam kisaran yang sebanding dengan RSA standar.
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The development of information technology in Indonesia provides many benefits, but also increases security risks, such as data leakage. One of the efforts to improve data system security is through the application of cryptography, whose process is based on mathematical concepts such as number theory, algebra, complexity analysis, and formal verification. RSA is one of the asymmetric cryptography algorithms. RSA is named after the initials of the three researchers who introduced the algorithm, Ron Rivest, Len Adleman, and Adi Shamir. RSA’s security is based on the difficulty of factoring large prime numbers. Despite its high level of security, standard RSA has a weakness in the speed of the encoding process which is relatively slower than other algorithms. Therefore, modifications are made to RSA by applying Montgomery Modular Multiplication to improve the performance of execution time speed. In addition, the efficiency of memory usage also needs to be considered in cryptographic systems. This research aims to analyze the performance of standard RSA and modified RSA using Montgomery Modular Multiplication, with a focus on improving execution time and memory usage. The results show that RSA with Montgomery Modular Multiplication modification has an encryption process speed up to 4.30 times faster than standard RSA. And in the decryption process, this modified RSA algorithm also shows superiority with speeds up to 4.50 times faster than standard RSA. Meanwhile, in the aspect of memory usage, the encryption process of Montgomery Modular Multiplication modified RSA uses 1.014 times more memory than standard RSA. In the decryption process, this modified RSA uses 1,014 times more efficient memory than the standard RSA. This shows that the Montgomery Modular Multiplication modified RSA tries to maintain a stable memory usage and remains in a comparable range to the standard RSA.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Montgomery Modular Multiplication, Kriptografi, Running Time, Memori, RSA, Montgomery Modular Multiplication, Cryptography, Running Time, Memory, RSA
Subjects:	Q Science Q Science > QA Mathematics Q Science > QA Mathematics > QA76.9.A25 Computer security. Digital forensic. Data encryption (Computer science)
Divisions:	Faculty of Mathematics and Science > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	Aurellia Antonie
Date Deposited:	01 Aug 2025 06:37
Last Modified:	01 Aug 2025 06:37
URI:	http://repository.its.ac.id/id/eprint/124463

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