# The Odyssey of Entropy: Cryptography
## 3 Entropy and Encryption
### Modeling, Design and Implementation
#### 3.1.2 Cryptosystem Elements  
The security of a cryptosystem depends on the security of three main elements: the encryption and decryption algorithms, the key generation and management module, and the key agreement or exchange protocol [71]. In the following, we review the role of entropy and related concepts in the design and implementation of each of the aforementioned elements.  
* **Encryption and Decryption Algorithms:** Entropy has played a role in several research reports focusing on the design of encryption and decryption algorithms. Some of these research works are discussed below.  
* **Encryption:** The role of image block entropy in image encryption was studied by researchers [72] just like the case of image steganography (reviewed in Section 4.3.1). A multimedia encryption scheme based on entropy coding with low computational overhead was proposed by [PERSON] and [PERSON] [73]. A method for encrypting entropy-coded compressed video streams without the need for decoding was introduced by [PERSON] et al. [74]. Moreover, the encryption of entropy-coded videos was studied in some other research works. To mention a few, one may refer to Refs. [75; 76; 77; 78]. The impact of key entropy on the security of an image encryption scheme was studied by [PERSON] et al. [79]. [PERSON] [80] investigated the security of high-entropy volumes, where the most typical sources are entropy-encoded multimedia files or compressed text sequences. Min entropy was used by [PERSON] [81] to reduce the size of the key search space of an encryption scheme to a value lower than that of a brute-force or birthday attack. A chaotic encryption scheme for low-entropy images was proposed by [PERSON] et al. [82]. This method uses confusion and diffusion techniques to make it difficult for the adversary to perform statistical analysis on adjacent pixels, which are likely to have close values.
* **Decryption:** There are few works focusing on the security of the encryption algorithm. For example, the multiple decryption problem was introduced by [PERSON] and [PERSON] [83] as a generalization of the problem of source coding subject to a fidelity criterion. They used entropy to evaluate the security of a multiple-channel system in this scenario.
* **Key Generation and Management Module:** Several research works have focused on the role of entropy in key generation and management. Some of these works are briefly reviewed in the following. The entropy of the key has been of interest to researchers as a measure of security for decades [84]. [PERSON] and [PERSON] [85] used Shannon entropy analysis to evaluate the security of their proposed biometric key generation scheme. [PERSON] et al. [86] tried to alleviate the quantization discrepancy problem in quantization-based key generation methods using an ECQS (entropy-constrained-like quantization scheme). It was highlighted by [PERSON] [87] that the existing bounds on the key entropy for retaining information-theoretical security are not tight enough. The reason is that existing random number generators do not create truly random sequences. More realistic bounds for the key entropy were derived in this research. \"Personal Entropy\" was introduced by [PERSON] et al. [88] as a means for remembering personal passphrases based on which secret keys are generated. Personal entropy is created via asking the user several personal questions.
* **Key Agreement and Exchange Protocol:** There are a few research works focusing on the applications of entropy in key exchange protocols. Among these works, we can refer to a framework designed by [PERSON] et al. [89] for fingerprinting key exchange protocols using their impact on high-entropy data blocks. Another example is the key transmission method presented by [PERSON] and [PERSON] [90] for MISO (multiple-input single-output) flat-fading channels. This method tries to increase relative entropy using an artificial noise in order to minimize the BER (bit error rate) for the key receiver, while keeping it close to unity (maximum) for the eavesdropper.