A novel information entropy based randomness test for image encryption

Abstract

The quality of image encryption is commonly measured by the Shannon entropy over the ciphertext image. However, this measurement does not consider to the randomness of local image blocks and is inappropriate for scrambling based image encryption methods. In this paper, a new information entropy-based randomness measurement for image encryption is introduced which, for the first time, answers the question of whether a given ciphertext image is sufficiently random-like. It measures the randomness over the ciphertext in a fairer way by calculating the averaged entropy of a series of small image blocks within the entire test image. In order to fulfill both quantitative and qualitative measurement, the expectation and the variance of this averaged block entropy for a true-random image are strictly derived and corresponding numerical reference tables are also provided. Moreover, a hypothesis test at significance α-level is given to help accept or reject the hypothesis that the test image is ideally encrypted/random-like. Simulation results show that the proposed test is able to give both effectively quantitative and qualitative results for image encryption. The same idea can also be applied to measure other digital data, like audio and video./ Information Sciences 00 (2018) 1-23 2 Since then, research on the sequence cipher published many excellent ciphers, including Blowfish [8] in 1993, Twofish [28] in 1998 and advanced encryption standard (AES) [3] in 1998. Nowadays, these encryption algorithms still prevail and are used by thousands of people, organizations and companies.As the other side of the coin, cryptography analysis developed at the same time as data encryption.Many ciphers are considered to be insecure due to some undesired properties that are weak to some cryptography analysis. For example, DES is believed to be insecure as it is weak to the differential attack and the bruteforce attack [34]. Many of these attacks, such as the frequency attack, ciphertext-only attack and known ciphertext attack are designed directly for weak ciphertext, which is not random-like. Therefore, the ability of generating random-like ciphertext is one of most crucial criteria for a secure cipher.A main focus of testing the randomness of a ciphertext is its distribution. Ideally, this distribution of ciphertext is uniform, because a uniform distribution implies that the each symbol in ciphertext is equally important. As a result, the cipher is invulnerable to statistical attacks. Moreover, both the relationship between ciphertext and plaintext and the relationship between ciphertext and encryption key are very complicated and involved. These two properties, namely confusion and diffusion, were identified by Claude Shannon in his 1949 masterpiece paper [30]. Conventionally, randomness tests are designed for binary sequences, for example the Kolmogorov test [32], poker test [32], gap test [32], autocorrelation test [32], Shannon entropy [29], diffusion randomness test [16], etc. Moreover, the standard randomness tests FIPS 140-1[...

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