Your question is somewhat ambiguous. Please clarify the Strength of an encrypted image. If you are interested to see how well the plain and cipher images match, you can refer to the following article.
http://web.mit.edu/bcs/sinha/papers/sinha_russell2011.pdf
Unified Average Changing Intensity (UACI), Number of Pixels Change Rate (NPCR), correlation value, large key space to defy brute force attack, strong key sensitivity
The following measures are sufficient:
Security and Statistical Analysis
Histogram
Correlation of adjacent pixels
Differential attack
Information Entropy
Algorithm complexity
visit my paper below for details
https://www.researchgate.net/publication/260144791_Image_Cryptographic_Algorithm_Based_on_the_Haar_Wavelet_Transform
Article Image Cryptographic Algorithm Based on the Haar Wavelet Transform
I agree with the Alireza's answer that the "strength of an encrypted image" is vague. It may means two different things: the security of the encryption (i.e., how hard to deduce the key or the plain image or its approximation -- this is similar to text encryption) or a measure of leaked info after encryption (e.g., selective encryption -- this is unique to image encryption that text encryption does not have). The former is typically via case-by-case analysis. The strength against guessing keys can be measured by the size of the effective key space (Bonneau. J. 2012. The science of guessing: Analyzing an
anonymized corpus of 70 million passwords. In IEEE Symp. on Security and Privacy or B. Zhu et al. Security Analyses of Click-based Graphical Passwords via Image Point Memorability, ACM CCS 2014). The latter can be measured using typical image processing techniques (somewhat similar to measure quality of compressed images).
In fact, A secure encryption algorithm should have confusion and diffusion properties, then some tools are used to evaluate the strength of encrypted algorithm such as NPCR, UACI, Histogram, Key length, sensitivity attacks, and others, you can find details in Section V at the following paper
Conference Paper Dynamic Adjustment of the Chaos-Based Security in Real-Time ...
If u scramble pixel with random number such as chaotic map, the unauthorized user can't recover meaning of your useful information. You're algorithm is also protected using some strongest mathematical calculation. The strength of the algothim is determined by different theoretical and statistical analysis. If your npcr is around 99.6 or more, ucai 33.5 and also entropy is 7.999, then we say that algorithm is secure from different types attacks
The strength of any encryption algorithm can be measured by executing several performance analysis tests. In addition to above said tests, chi-square test, NIST test suite, and randomness test by using Matlab inbuilt function can be performed.
You are right your question has two meanings how to measure the strength of security of generated key to be secure and can't be hacked not just measuring the performance and quality of restored data
I think it need more searching, key sensitivity test focus on key size
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