Random Number Generators in Image Encryption: A Comparative Analysis of RANLUX, MIXMAX, and Lehmer Methods

Öz

This study offers a comparative evaluation of three prominent random number generators frequently employed in image encryption: RANLUX, MIXMAX, and Lehmer. The level of randomness in encryption directly affects its performance and is closely linked to the structure of the generator used. RANLUX is a variant of the linear congruential generator (LCG) that enhances randomness through a decimation mechanism. MIXMAX offers strong chaotic behavior based on its Lyapunov exponent, while Lehmer stands out for its low computational cost. The mentioned algorithms are evaluated using metrics such as correlation coefficient, NPCR, PSNR, entropy, and histogram analysis. RANLUX effectively eliminates inter-pixel correlation with a correlation value of –0.0025. MIXMAX demonstrates high resistance against differential attacks with an NPCR value of 99.63%. PSNR results show that RANLUX causes the highest distortion. Entropy analysis reveals that all algorithms provide high randomness; however, RANLUX achieves the best performance with a value of 7.9992, which is closest to the theoretical maximum. The study also includes a discussion and conclusions based on scientific findings.

Anahtar Kelimeler

• Image Encryption
• Random Number Generator
• Chaotic Systems

Görüntü Şifrelemede Rastgele Sayı Üreteçleri: RANLUX, MIXMAX ve Lehmer Yöntemlerinin Karşılaştırmalı Bir Analizi

Öz

Bu çalışma, görüntü şifreleme alanında sıkça kullanılan üç farklı rastgele sayı üreteci olan RANLUX, MIXMAX ve Lehmer algoritmalarını karşılaştırmalı olarak incelemektedir. Şifrelemedeki rastgelelik düzeyi kullanılan üretecin yapısı şifreleme başarımını doğrudan etkilemektedir. RANLUX, azaltma mekanizmasıyla rastgeleliği artıran bir doğrusal artan rastgele sayı üreteci türevidir. MIXMAX, Lyapunov üs katsayısı ile güçlü kaotik özellikler sunarken, Lehmer algoritması düşük hesaplama maliyetiyle öne çıkmaktadır. Bahsi geçen algoritmalar korelasyon katsayısı, NPCR, PSNR, entropi ve histogram analizi gibi ölçütlerle değerlendirilmiştir. RANLUX, -0,0025’lik korelasyon değeriyle pikseller arası ilişkiyi en etkin şekilde ortadan kaldırmıştır. MIXMAX, %99,63’lük NPCR değeriyle diferansiyel saldırılara karşı yüksek direnç göstermiştir. PSNR sonuçları da RANLUX’un en yüksek bozulmayı sağladığını göstermektedir. Entropi sonuçları, tüm algoritmaların yüksek rastgelelik sunduğunu, ancak RANLUX’un 7.9992 değeriyle teorik maksimuma en yakın sonucu vererek en güçlü şifreleme performansını sergilediğini göstermektedir. Çalışmamızda bilimsel bulgulara dayanan tartışma ve sonuçlara da yer verilmektedir.

Anahtar Kelimeler

• Görüntü Şifreleme
• Rastgele Sayı Üretici
• Kaotik Sistemler

Kaynakça

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