MANDELBROT VE LOJİSTİK KAOTİK HARİTA KULLANILARAK GÖRÜNTÜ ŞİFRELEME

Öz

Son yıllarda, görüntü şifreleme popüler ve önemli bir araştırma alanı olmuştur. İnternet ve ağlar üzerinden iletişime olan bağımlılığın gün geçtikçe artmasıyla birlikte, verilerin iletimi güvenlik ihlaline karşı açık hale geliyor. Bu güvenlik ihlallerine karşı en iyi çözümlerden biri de verinin şifrelenmesidir. Günümüzde çoğunlukla kullanılan geleneksel algoritmalar, düşük güvenlik seviyesi göstermesinden dolayı kaos tabanlı kripto sistemler son yıllarda fazlasıyla ilgi çekici hale gelmiştir. Buraya olan yoğun ilgiden sonra çeşitli kaotik haritalar kriptografi alanına kazandırılmıştır. Eski şifreleme yöntemlerinin kullanılmasıyla ortaya çıkan düşük güvenlik seviyesi problemi kaos şifrelemesi kullanılarak çözülmüştür. Bunun yanı sıra kaos şifrelemede anahtarın rastgeleliğinin ve boyutunun büyüklüğünün de görüntü şifrelemedeki önemi ortaya çıkmıştır. Bu araştırma makalesi görüntüleri işlemek için çeşitli türleri olan kaotik haritalar ile mandelbrot fraktallarını içeren yeni bir hibrit şifreleme algoritması sunmaktadır. Bunun sebebi fraktal görüntülerin rastgeleliğinin fazla olması nedeniyle, şifreleme için güçlü bir anahtar olarak kullanılabilmesidir. Araştırmacıların çalışmaları sonucu literatürde de yer alan pek çok kaotik metot ortaya çıkmıştır. Makalede de bunlardan birisi olan lojistik harita kaotik methodunda oluşturulan anahtar ile mandelbrot fraktal setlerinden elde bir başka anahtarın işleme tabi tutularak ortaya çıkan yeni bir anahtar ile görüntü şifrelemesi yapılmıştır. Ayrıca makalede bu kaotik harita ile fraktalların birlikte kullanılmasının sonucu elde edilen şifreli görüntülerin analizi ve karşılaştırılması yapılmaktadır. Bu analiz yapılırken oluşturulan şifreli görüntünün ve görüntünün orjinal halinin görsel değerleri karşılaştırılarak algoritmanın başarısı PSNR, Entropi, SSIM, MSE, Korelasyon Katsayısı, Histogram Analizi, NPCR ve UACI yöntemleri ile ölçülmüştür.

Anahtar Kelimeler

• Kaos Teorisi
• Kaotik Görüntü Şifreleme
• Lojistik Harita
• Mandelbrot Set
• Performans Analizi

IMAGE ENCRYPTION USING MANDELBROT AND LOGISTIC CHAOTIC MAP

Öz

In recent years, image encryption has been a popular and important research area. With the increasing dependence on communication over the Internet and networks, the transmission of data becomes vulnerable to security breaches. One of the best solutions against these security breaches is data encryption. Chaos-based cryptosystems have become very interesting in recent years, since traditional algorithms, which are mostly used today, show a low level of security. After the intense interest here, various chaotic maps have been brought to the field of cryptography. The low security level problem caused by using old encryption methods has been solved by using chaos encryption. In addition, the importance of the randomness and size of the key in image encryption has emerged in chaos encryption. This research paper presents a new hybrid encryption algorithm for processing images, including several types of chaotic maps and mandelbrot fractals. This is because fractal images are so random that they can be used as a strong key for encryption. As a result of the studies of the researchers, many chaotic methods have emerged in the literature. In the article, one of them, the logistic map chaotic method, and another key obtained from the mandelbrot fractal sets are processed and image encryption is made with a new key. In addition, this article analyzes and compares the encrypted images obtained as a result of using this chaotic map and fractals together. The success of the algorithm was measured by PSNR, Entropy, SSIM, MSE, Correlation Coefficient, Histogram Analysis, NPCR and UACI methods by comparing the visual values of the encrypted image and the original version of the image created during this analysis.

Anahtar Kelimeler

• Chaos Theory
• Chaotic Image Encryption
• Logistic Map
• Mandelbrot Set
• Performance Analysis

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