# The Odyssey of Entropy: Cryptography
## 3 Entropy and Encryption
### Analysis and Evaluation
#### 3.2.3 Applications in Adversarial Analysis  
In the following, we review the role of entropy in adversarial analysis procedures, including cryptanalysis, eavesdropping, encrypted data analysis, covert channels and attacks. * **Cryptanalysis:** Entropy measures have been frequently used in research works focusing on cryptanalysis [166]. In particular, chaotic image encryption methods were cryptanalyzed using entropy calculations [167]. Moreover, some researchers used different methods for the cryptanalysis of chaotic image encryption schemes that use entropy improvement techniques [168]. * **Eavesdropping:** Measures of mutual information in quantum key distribution and their applications in eavesdropping were investigated by [PERSON] [30]. * **Encrypted Data Analysis:** The analysis of encrypted data is another relevant area of application for entropy. For example, entropy analysis was used for identifying encrypted malware [169], detecting encrypted executable files [170], and correcting noisy encrypted images [171]. Moreover, some researchers focused on entropy analysis of encrypted strings [172]. * **Covert Channel:** Entropy has played role in research on adversarial analysis of cryptosystems via covert channels. For example, entropy was used by [PERSON] et al. [173] to analyze the capacity of a covert channel as well as the factors affecting it. * **Attacks:** Entropy analysis was used as part of several kinds of attack scenarios. To mention a few, we can refer to the following. * **CPA (Chosen Plaintext Attack):** [PERSON] et al. [174] used entropy measures in their analysis of instantiability of RSA and optimal asymmetric encryption padding (OAEP) under a chosen plaintext attack. OAEP is a padding scheme proposed by [PERSON] and [PERSON] [175], which is often used along with RSA encryption. In another research reported by [PERSON] [176], entropy was used in a CPA against SSL. Moreover, [PERSON] [177] tested several modes of operation for resistance against a blockwise adaptive chosen plaintext attack. * **CCA (Chosen Ciphertext Attack):** Like the case of chosen plain text attack, entropy analysis has played role in chosen ciphertext attack adversarial analysis. For example, a public-key cryptosystem featuring resistance against CCA was introduced by [PERSON] et al. [178]. Entropy assessment was used in order to prove the security of this cryptosystem against after-the-fact leakage without non-interactive zero-knowledge proof. Similarly, [PERSON] et al. [179] presented a CCA-secure identity-based encryption system and used entropy to show its resistance against key leakage attacks. Another research study on CCA-resistant and leakage-resistant cryptosystems was reported by [PERSON] et al. [180] in which entropy was used in the security proof. Side Channel Attack:Mutual information measure is frequently used in side channel attacks. The reason is that mutual information is capable of detecting any kind of statistical dependency, and many side channel analysis scenarios depend on a linear correlation coefficient as a wrong-key distinguisher [181]. Moreover, some research works have used entropy analyses to make cryptosystems more secure against side channel attacks. For example, a method for decreasing the entropy of the information leaked from side channels was introduced by [PERSON] et al. [182]. As another example, an information-theoretical model for side channel attacks was derived by [PERSON] and [PERSON] [183]. The impact of the entropy of the masks in masking-based countermeasures against side channel attacks was studied by [PERSON] et al. [184]. This study shows that while these countermeasures are usually studied with the maximal possible entropy for the masks, some particular mask subsets may leak remarkably more as the entropy increases. * **Replay Attack:** Entropy analysis has been used in the detection of replay attacks. As an example, we can mention the research reported by [PERSON] et al. [185], wherein a novel feature based on spectral entropy was introduced for detecting replay attacks.