# The Odyssey of Entropy: Cryptography
## 3 Entropy and Encryption
### Modeling, Design and Implementation
#### 3.1.3 Cryptographic Primitives  
Several researchers have used entropy in their research works focusing on the design and implementation of cryptographic primitives, such as random number generations and hashing. Some of these works are studied below.  
* **Random Number Generation Algorithm:** Entropy has been considered by researchers as a measure for randomness for decades [91]. One well-known issue with pseudo-random number generators is that the entropy of their output dependson the entropy of the seed. This issue was reported by [PERSON] et al. [92] to exist in entropy sources of random number generators used in real-world cryptographic protocols, such as SSL (secure socket layer). Several research works have proposed methods for increasing the entropy of the seed via harvesting entropy from execution times of programs [93] or chaotic functions [94]. In recent years, entropy has been used as an objective for improving different chaos-based random number generators [95; 96] as well as randomness tests for image encryption [97; 98]. The criticality of entropy in research on true random number generators is due to the fact that their susceptibility to process variations as well as intrusion attacks, degrades the generated entropy. This makes it necessary to include an on-the-fly mechanism for the detection and correction of bias variations [99].
* **Hashing Functions and Algorithms:** A hash function with maximized conditional entropy was used by [PERSON] et al. [100] as part of the solution to the ANN (approximate nearest neighbor) problem. Later on, [PERSON] et al. [101] suggested LSH (locality sensitive hashing) as a promising solution to the ANN problem. However, they argued that in LSH, points are often mapped to poor distributions. They proposed a number of novel hash map functions based on entropy to alleviate this problem. Maximum-entropy hash functions were used in some other applications, such as packet classification [102]. The role of graph entropy in perfect hashing was studied by [PERSON] et al. [103]. Later on, a graph entropy bound was calculated by [PERSON] [104] for the size of perfect hash function families. A fuzzy hash method based on quantum entropy distribution was used to construct a biometric authentication algorithm by [PERSON] and [PERSON] [105]. Entropy measurement and improvement techniques were used by [PERSON] et al. [106] along with perceptual hashing for key frame extraction in content-based video retrieval. Moreover, entropy reduction on layout data combined with lossless compression and cryptographic hashing was used by [PERSON] et al. [107] to manage IP (intellectual property) via tracking geometrical layout from design through manufacturing and into production. Inaccessible entropy was used in the design of one-way hash functions by [PERSON] et al. [108]. A generator \(G\) is said to have inaccessible entropy if the total accessible entropy (calculated over all blocks blocks) is considerably smaller than the real entropy of \(G\)'s output. The possibility of designing a hash function with a hash-bit-rate equal to the conditional entropy was investigated by [PERSON] et al. [109].