Aljabar Semiprima Mendasar dan Aplikasinya pada Protokol Autentikasi

Khurul Wardati; Muhammad Zaki Riyanto

doi:10.21831/pythagoras.v17i1.48982

Aljabar Semiprima Mendasar dan Aplikasinya pada Protokol Autentikasi

Khurul Wardati, Departemen Matematika, UIN Sunan Kalijaga Yogyakarta, Indonesia
Muhammad Zaki Riyanto, Departemen Matematika, UIN Sunan Kalijaga Yogyakarta, Indonesia

10.21831/pythagoras.v17i1.48982

Abstract

Library research dengan pendekatan deduksi-induksi ini bertujuan untuk mengkaji kesemiprimaan mendasar aljabar tak bebas yang dibangun secara hingga atas ring komutatif unital. Tujuan secara praktis penelitian ini adalah mengaplikasikan suatu contoh aljabar semiprima mendasar yang non-komutatif pada protokol autentikasi berdasarkan masalah dekomposisi. Di samping itu, aljabar semiprima mendasar lebih umum dari aljabar semiprima, hal ini ditunjukkan dengan suatu contoh penyangkal. Hasil utama dari penelitian ini adalah suatu aljabar yang dibangun secara hingga bersifat semiprima mendasar jika dan hanya jika ideal dasar nol merupakan irisan dari semua ideal dasar prima. Lebih lanjut ideal dasar nol merupakan satu-satunya ideal dasar nilpoten. Syarat perlu dan cukup ini serupa dengan sifat aljabar semiprima, dan pembuktian sifat-sifat ini pada keduanya memerlukan konsep annihilator.

The basically semiprime algebra and its application on authentication protocol

Abstract

This library research is conducted with a deductive-inductive approach. The aim of this study is to explore the basically semiprimeness of the finitely generated non-free algebra over a commutative unital ring. The basically semiprime algebra is more general than a semiprime algebra, which is proven by a counterexample. In theory, Theorem 12 is the main result of the study. The finitely generated algebra over a commutative unital ring is basically semiprime, if and only if, the zero basic ideal is the intersection of all prime basic ideals, if and only if, the zero basic ideal is the only nilpotent basic ideal. These necessary and sufficient conditions are analogous to the properties of a semiprime algebra, and proving these properties in both requires a concept of annihilator. The practical aim of this research is to apply an example of non-commutative basically semiprime algebra in an authentication protocol based on the decomposition problem.

Keywords

Aljabar semiprima mendasar; annihilator; ideal dasar nilpotent; protokol autentikasi

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DOI: https://doi.org/10.21831/pythagoras.v17i1.48982