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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Journal of Mathematical and Fundamental Sciences Jurnal Ilmiah Soulmath : Jurnal Edukasi Pendidikan Matematika Journal of Fundamental Mathematics and Applications (JFMA) Indonesian Journal of Physics (IJP) International Journal of Computing Science and Applied Mathematics-IJCSAM
Yunus, Mahmud
Departemen Matematika, Institut Teknologi Sepuluh Nopember
Astronomy Chemistry Computer Science & IT Decision Sciences, Operations Research & Management Earth & Planetary Sciences Education Electrical & Electronics Engineering Energy Engineering Mathematics Physics

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Pengembangan Algoritma Kriptografi Citra Digital Berbasis Transformasi Wavelet Haar-q Dzaky Muhammad; Kistosil Fahim; Mahmud Yunus
Jurnal Ilmiah Soulmath : Jurnal Edukasi Pendidikan Matematika Vol 14 No 3 (2026)
Publisher : Universitas Dr. Soetomo

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Abstract

Abstract This article presents the development of the first digital image cryptography algorithm based on -calculus. The focus of this research lies on the implementation aspects and the evaluation of the fundamental security criteria of the encryption system. The proposed cryptographic scheme integrates domain transformation using the -Haar wavelet transform and chaotic maps. The application of this -analog concept provides a wider range of variations in the encryption procedure compared to the classical Haar transform. Furthermore, the -parameter integrated into the key space is proven to significantly enhance the security of the encryption system. Experimental results demonstrate excellent performance; the encryption algorithm successfully generates cipher images that are visually random and significantly different from their original counterparts. Meanwhile, the decryption process is capable of identically reconstructing the visual information of the original image, despite involving complex floating-point operations. Keywords: chaotic map; cryptography; -calculus; -Haar wavelet transform   Abstrak Artikel ini menyajikan pengembangan algoritma kriptografi citra digital pertama yang berbasis pada kalkulus- . Fokus penelitian ini terletak pada aspek implementasi dan pengujian kriteria dasar keamanan sistem enkripsi. Skema kriptografi yang diusulkan mengintegrasikan transformasi domain menggunakan transformasi wavelet Haar-  ( -Haar wavelet transform) dan peta chaos. Penerapan konsep analog-  ini memberikan ruang variasi yang lebih luas dalam prosedur enkripsi dibandingkan dengan transformasi Haar klasik. Selain itu, parameter  yang diintegrasikan ke dalam ruang kunci terbukti mampu meningkatkan keamanan sistem enkripsi secara signifikan. Hasil eksperimen menunjukkan performa yang sangat baik; algoritma enkripsi mampu menghasilkan citra sandi yang acak secara visual dan berbeda secara signifikan dari citra aslinya. Sementara itu, proses dekripsi mampu merekonstruksi kembali informasi visual citra asal secara identik, meskipun melibatkan operasi bilangan floating-point yang kompleks. Kata Kunci: kalkulus- ; kriptografi; peta chaos; transformasi wavelet Haar-
Co-Authors Adam Adam Ahmat Rif’an Maulana Annisa Rahmita Soemarsono Auda Nuril Zazilah Bandung Arry Sanjoyo Chairul Imron, Chairul Dwi Ratna Sulistyaningrum Dzaky Muhammad Erna Apriliani Fahim, Kistosil Gusti Yuni Shinta Lestari Gusti Yuni Shinta Lestari Hariyanto Hariyanto Hariyanto Hariyanto Hendra Gunawan Laksono Trisnantoro Lukman Hanafi Lukman Zicky Mohamad Ilham Dwi Firmansyah Nurul Hidayat Sadjidon Sadjidon Sadjidon Sadjidon Sie, Evan Setiawan Silviana Maya P Subiono - Sunarsini Sunarsini