# Best Fit DNA-Based Cryptographic Keys: The Genetic Algorithm Approach

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{7}

^{*}

## Abstract

**:**

## 1. Introduction

- Inculcate the benefits of Genetic Algorithms in DNA cryptography instead of Traditional Cryptography.
- Categorize the initial population of keys as strong or weak. The strong keys are used as it is for encryption. The weak keys instead of getting dropped are strengthened by the Genetic Algorithm. This step reduces the key generation time by only applying the scheme to weak keys. It also reduces key wastage.
- Propose suitable fitness functions by checking the frequency and gap of occurrence of the four nitrogenous bases to convert the weak keys into their fitter counterparts. It also reduces key wastage and enhances their efficiency for effective DNA-based cryptographic schemes.

## 2. Related Work

- The majority of the existing schemes are based on traditional binary keys and much less emphasis has been made on DNA-based keys.
- Most existing algorithms discussed are applying their proposed methodology to the initial key population which makes the key generation process lengthy and difficult.
- Based on the suitability of their proposal, each algorithm has defined its fitness test and selection, crossover, and mutation are the predominant genetic operators used.

- To choose the appropriate fitness test to be used as four different nitrogenous bases are involved in DNA cryptosystems.
- To decide whether the methodology is to be applied to the initial key population or not. For this, the fitness test is applied, and keys are categorized as strong or weak. If found strong, they are directly used for encryption. Only the weak keys are acted upon and thus the number of keys to be acted upon is reduced and the time complexity will reduce.
- To reduce key wastage by strengthening the weak keys and removing visible patterns instead of completely discarding them.

## 3. Proposed Methodology

#### 3.1. Generating the Initial Population

#### 3.2. Applying Fitness Tests

#### 3.3. Defining Fitness Functions for Weak Keys

_{1}and λ

_{2}are defined based on the Frequency Test and the Gap Test, respectively. Next λ is calculated by summing the obtained values of λ

_{1}and λ

_{2}. Finally, the Fitness function F is obtained. All steps are illustrated next.

_{1}let the total number of weak keys be n. The frequency or number of occurrences of A, T, C, and G are stored in four variables A, T, C, and G, respectively. The ideal value of frequency which is approximately 25% of the length of keys is stored in the variable i. Next, the concept of standard deviation is applied to find the deviation of obtained frequency from the ideal frequency for each of the four nucleotides and stored in σ

_{A}, σ

_{T}, σ

_{C}and σ

_{G}. Finally, λ

_{1}is calculated as the average of σ

_{A}, σ

_{T}, σ

_{C}and σ

_{G}. Equations (1)–(5) give the necessary formulas to calculate λ

_{1.}

_{1}= (σ

_{A}+ σ

_{T}+ σ

_{C}+ σ

_{G})/4

_{2}be a flag to show which DNA string has more than three repetitive occurrences for any of the four nucleotides. Each of the 14 weak keys is scrutinized. If such a scenario for any of the A, T, C or G is obtained, λ

_{2}is made 1 else 0.

_{1}and λ

_{2}as given in Equation (6). Table 2 showcases the calculation of λ for each of the 14 weak keys of the initial 25 × 25 population.

#### 3.4. Arranging in Decreasing Order of Fitness Function

#### 3.5. Perform Crossover Operation

#### 3.6. Perform Mutation Operation

#### 3.7. Generate the New Population

#### 3.8. Reapply Fitness Test and Repeat the Entire Process

## 4. Results and Calculations

#### 4.1. Generating the Initial Population

#### 4.2. Applying Fitness Tests

#### 4.3. Defining Fitness Functions for Weak Keys

_{A}, σ

_{T}, σ

_{C}, σ

_{G}and λ

_{1}are calculated using Equations (1)–(5). Table 2 illustrates the entire calculation of λ

_{1}.

_{2}is made 1 else 0. The process is demonstrated in Table 3.

#### 4.4. Arranging in Decreasing Order of Fitness Function

#### 4.5. Perform Crossover Operation

#### 4.6. Perform Mutation Operation

#### 4.7. Generate the New Population

#### 4.8. Reapply Fitness Test and Repeat the Entire Process

## 5. Analysis of Proposed Methodology

#### 5.1. Number of Crossover and Mutation

#### 5.2. Effect of Different Values of N and M on the Number of Weak Keys Achieved

#### 5.3. The Comparison of Number of Populations Generated to Strengthen Weak Keys Using Proposed Algorithm

#### 5.4. Immunity to Security Attacks

^{4}× M × N. Thus, the exponential power is 4. Therefore, each DNA key component is 8 times stronger than its binary counterpart. Figure 11 illustrates that the size of the key space is increasing exponentially, thus making the keys less vulnerable to intrusions.

#### 5.5. Complexity Analysis

#### 5.6. Practical Application of Proposed Scheme

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Gehani, A.; LaBean, T.; Reif, J. DNA-Based Cryptography. In Aspects of Molecular Computing; Springer: Berlin/Heidelberg, Germany, 2003; pp. 167–188. [Google Scholar]
- Xiao, G.; Lu, M.; Qin, L.; Lai, X. New field of cryptography: DNA cryptography. Chin. Sci. Bull.
**2006**, 51, 1413–1420. [Google Scholar] [CrossRef] - Borda, M.; Tornea, O. DNA secret writing techniques. In Proceedings of the 2010 8th International Conference on Communications, Bucharest, Romania, 10–12 June 2010; IEEE: Piscataway, NJ, USA, 2010; pp. 451–456. [Google Scholar]
- Nandy, N.; Banerjee, D.; Pradhan, C. Color image encryption using DNA based cryptography. Int. J. Inf. Technol.
**2018**, 13, 533–540. [Google Scholar] [CrossRef] - Cherian, A.; Raj, S.R.; Abraham, A. A survey on different DNA cryptographic methods. Int. J. Sci. Res.
**2013**, 2, 167–169. [Google Scholar] - Pramanik, S.; Setua, S.K. DNA cryptography. In Proceedings of the 2012 7th International Conference on Electrical and Computer Engineering, Dhaka, Bangladesh, 20–22 December 2012; IEEE: Piscataway, NJ, USA, 2012; pp. 551–554. [Google Scholar]
- Katoch, S.; Chauhan, S.S.; Kumar, V. A review on genetic algorithm: Past, present, and future. Multimed. Tools Appl.
**2021**, 80, 8091–8126. [Google Scholar] [CrossRef] - Mirjalili, S. Genetic algorithm. In Evolutionary Algorithms and Neural Networks; Springer: Cham, Switzerland, 2019; pp. 43–55. [Google Scholar]
- Bottaci, L. A genetic algorithm fitness function for mutation testing. In Proceedings of the SEMINALL-Workshop at the 23rd International Conference on Software Engineering, Toronto, ON, Canada, 12–19 May 2001. [Google Scholar]
- Poon, P.W.; Carter, J.N. Genetic algorithm crossover operators for ordering applications. Comput. Oper. Res.
**1995**, 22, 135–147. [Google Scholar] [CrossRef] - Razali, N.M.; Geraghty, J. Genetic algorithm performance with different selection strategies in solving TSP. In Proceedings of the World Congress on Engineering, London, UK, 6–8 July 2011; International Association of Engineers: Hong Kong, China, 2011; Volume 2, pp. 1–6. [Google Scholar]
- Syswerda, G. Simulated crossover in genetic algorithms. In Foundations of Genetic Algorithms; Elsevier: Amsterdam, The Netherlands, 1993; Volume 2, pp. 239–255. [Google Scholar]
- De Falco, I.; Della Cioppa, A.; Tarantino, E. Mutation-based genetic algorithm: Performance evaluation. Appl. Soft Comput.
**2002**, 1, 285–299. [Google Scholar] [CrossRef] - Soni, A.; Agrawal, S. Using genetic algorithm for symmetric key generation in image encryption. Int. J. Adv. Res. Comput. Eng. Technol. IJARCET
**2012**, 1, 137–140. [Google Scholar] - Singh, D.; Rani, P.; Kumar, R. To design a genetic algorithm for cryptography to enhance the security. Int. J. Innov. Eng. Technol.
**2013**, 2, 380–385. [Google Scholar] - Mishra, S.; Bali, S. Public key cryptography using genetic algorithm. Int. J. RecentTechnol. Eng.
**2013**, 2, 150–154. [Google Scholar] - Jhingran, R.; Thada, V.; Dhaka, S. A study on cryptography using genetic algorithm. Int. J. Comput. Appl.
**2015**, 118, 10–14. [Google Scholar] [CrossRef] - Malhotra, N.; Nagpal, G. Genetic Symmetric Key Generation for IDEA. JIPS
**2015**, 11, 239–247. [Google Scholar] - Jain, A.; Chaudhari, N.S. An improved genetic algorithm for developing deterministic OTP key generator. Complexity
**2017**, 2017, 1–17. [Google Scholar] [CrossRef] - Chunka, C.; Goswami, R.S.; Banerjee, S. An efficient mechanism to generate dynamic keys based on genetic algorithm. Secur. Priv.
**2018**, 4, e37. [Google Scholar] [CrossRef] - Nazeer, M.I.; Mallah, G.A.; Shaikh, N.A.; Bhatra, R.; Memon, R.A.; Mangrio, M.I. Implication of genetic algorithm in cryptography to enhance security. Int. J. Adv. Comput. Sci. Appl.
**2018**, 9, 375–379. [Google Scholar] [CrossRef] - Kalsi, S.; Kaur, H.; Chang, V. DNA cryptography and deep learning using genetic algorithm with NW algorithm for key generation. J. Med. Syst.
**2018**, 42, 17. [Google Scholar] [CrossRef] [Green Version] - Turčaník, M.; Javurek, M. Cryptographic Key Generation by Genetic Algorithms. Inf. Secur.
**2019**, 43, 54–61. [Google Scholar] [CrossRef] - Vidhya, E.; Rathipriya, R. Key Generation for DNA Cryptography Using Genetic Operators and Diffie-Hellman Key Exchange Algorithm. Comput. Sci.
**2020**, 15, 1109–1115. [Google Scholar] - Tahir, M.; Sardaraz, M.; Mehmood, Z.; Muhammad, S. CryptoGA: A cryptosystem based on genetic algorithm for cloud data security. Clust. Comput.
**2021**, 24, 739–752. [Google Scholar] [CrossRef] - Abduljabbar, R.B.; Hamid, O.K.; Alhyani, N.J. Features of genetic algorithm for plain text encryption. Int. J. Electr. Comput. Eng.
**2021**, 11, 434. [Google Scholar] [CrossRef] - Alhassan, S. Audio Cryptography via Enhanced Genetic Algorithm. Int. J. Multimed. Appl. IJMA
**2021**, 13, 37–45. [Google Scholar] [CrossRef] - Garg, D.; Bhatia, K.K.; Gupta, S. A novel Genetic Algorithm based Encryption Technique for Securing Data on Fog Network Using DNA Cryptography. In Proceedings of the 2022 2nd International Conference on Innovative Practices in Technology and Management (ICIPTM), Pradesh, India, 23–25 February 2022; IEEE: Piscataway, NJ, USA, 2022; Volume 2, pp. 362–368. [Google Scholar]
- Hussein, A.A.; Ayoob, N.K. Key Generation for Vigenere Ciphering Based on Genetic Algorithm. J. Univ. Babylon Pure Appl. Sci.
**2022**, 30, 200–208. [Google Scholar] [CrossRef] - Shivani, S.; Patel, S.C.; Arora, V.; Sharma, B.; Jolfaei, A.; Srivastava, G. Real-time cheating immune secret sharing for remote sensing images. J. Real-Time Image Process.
**2021**, 18, 1493–1508. [Google Scholar] [CrossRef] - Garg, H.; Sharma, B.; Shekhar, S.; Agarwal, R. Spoofing detection system for e-health digital twin using EfficientNet Convolution Neural Network. Multimed. Tools Appl.
**2022**, 81, 26873–26888. [Google Scholar] [CrossRef] - Shekhar, S.; Garg, H.; Agrawal, R.; Shivani, S.; Sharma, B. Hatred and trolling detection transliteration framework using hierarchical LSTM in code-mixed social media text. Complex Intell. Syst.
**2021**, 1–14. [Google Scholar] [CrossRef] - Gupta, M.; Patel, R.B.; Jain, S.; Garg, H.; Sharma, B. Lightweight branched blockchain security framework for Internet of Vehicles. Trans. Emerg. Telecommun. Technol.
**2022**, e4520. [Google Scholar] [CrossRef] - Gupta, M.; Kumar, R.; Shekhar, S.; Sharma, B.; Patel, R.B.; Jain, S.; Dhaou, I.B.; Iwendi, C. Game Theory-Based Authentication Framework to Secure Internet of Vehicles with Blockchain. Sensors
**2022**, 22, 5119. [Google Scholar] [CrossRef] - Agarwal, R.; Jalal, A.S.; Arya, K.V. Enhanced Binary Hexagonal Extrema Pattern (EBHXEP) Descriptor for Iris Liveness Detection. Wirel. Pers. Commun.
**2020**, 115, 2627–2643. [Google Scholar] [CrossRef] - Agarwal, R.; Jalal, A.S.; Arya, K.V. Local binary hexagonal extrema pattern (LBHXEP): A new feature descriptor for fake iris detection. Vis. Comput.
**2021**, 37, 1357–1368. [Google Scholar] [CrossRef] - Agarwal, R.; Jalal, A.S.; Arya, K.V. A review on presentation attack detection system for fake fingerprint. Mod. Phys. Lett. B
**2020**, 34, 2030001. [Google Scholar] [CrossRef] - Pavithran, P.; Mathew, S.; Namasudra, S.; Srivastava, G. A novel cryptosystem based on DNA cryptography, hyperchaotic systems and a randomly generated Moore machine for cyber physical systems. Comput. Commun.
**2022**, 188, 1–12. [Google Scholar] [CrossRef] - Rupa, C.; Harshita, M.; Srivastava, G.; Gadekallu, T.R.; Maddikunta, P.K. Securing Multimedia using a Deep Learning based Chaotic Logistic Map. IEEEJ. Biomed. HealthInform.
**2022**. [Google Scholar] [CrossRef] [PubMed]

**Figure 2.**(

**a**). Randomly Generated Initial 25 × 25. (

**b**) Categorization of Keys among initial 25 × 25 Keys based on Fitness Tests.

**Figure 5.**(

**a**) First New Population after Crossover and Mutation. (

**b**) Weak Keys in the First New Population based on Fitness Tests.

**Figure 6.**(

**a**) Child Population from First New Population. (

**b**) Mutation of Child Population from First New Population. (

**c**) Second New Population after Crossover and Mutation. (

**d**) Weak Keys in the Second New Population based on Fitness Tests.

**Figure 7.**(

**a**) Child Population from Second New Population (

**b**) Mutation of Child Population from Second New Population. (

**c**) Third New Population after Crossover and Mutation. (

**d**) Weak Keys in the Third New Population based on Fitness Tests.

**Figure 9.**(

**a**) Third New Population after Crossover and Mutation. (

**b**) Weak Keys in the Third New Population based on Fitness Tests.

**Figure 11.**Size of Key Space to be searched for Brute Force Attacks for different values of M and N.

Author Name | Type of Cryptosystem | Genetic Operators Used | Fitness Test Applied | Whether GA-Applied on Complete Initial Key Population |
---|---|---|---|---|

Soni et al. (2012) | Traditional | Selection Crossover Mutation | Nil | Yes |

Singh et al. (2013) | Traditional | Crossover | Nil | Yes |

Mishra et al. (2013) | Traditional | Selection Crossover Mutation | Pearson’s Coefficient of auto-correlation | Yes |

Jhingran et al. (2015) | Traditional | Selection Crossover Mutation | Nil | Yes |

Malhotra et al. (2015) | Traditional | Selection Crossover Mutation | Comparing with parents | No |

Jain et al. (2017) | Traditional | Selection Crossover Mutation | Frequency Test. Serial Test, Autocorrelation Test, Poker Test | Yes |

Chunka et al. (2018) | Traditional | Selection Crossover Mutation | Frequency test, Block frequency, Runs test, Cumulative sums forward, Cumulative sums backward | Yes |

Nazeer et al. (2018) | Traditional | Selection Crossover Mutation | Shannon Key Entropy | Yes |

Kalsi et al. (2018) | DNA | Selection Crossover Mutation | Run Test and Needleman- Wunsch Algorithm | Yes |

Turčaník et al. (2019) | Traditional | Selection Crossover Mutation | Frequency Test | Yes |

Vidhya et al. (2020) | DNA | Selection Crossover Mutation | Shanon Key Entropy | Yes |

Tahir et al. (2021) | Traditional | Selection Crossover Mutation | Shanon key Entropy | Yes |

Abduljabbar et al. (2021) | Traditional | Selection Crossover Mutation | Nil | Yes |

Salamudeen et al. (2021) | Audio | Bits fission Switching Mutation Fusion Deconditioning | Fission-Fusion Scheme | Yes |

Garg et al. (2022) | DNA | Crossover Mutation | NA | Yes |

Hussein et al. (2022) | Traditional | Crossover Mutation | Entropy Test | Yes |

Weak Key | a | t | c | g | σ_{A} | σ_{T} | σ_{C} | σ_{G} | λ_{1} |
---|---|---|---|---|---|---|---|---|---|

AGGTTCACTGGGCCCCTCTGCTTTT | 2 | 9 | 8 | 6 | 1.069 | 0.802 | 0.535 | 0 | 0.6015 |

TGCTACGGGAAACAGACACGGTTAA | 9 | 4 | 5 | 7 | 0.802 | 0.535 | 0.266 | 0.266 | 0.4673 |

TACTGGGGGGAGTTGTCCGCGGGAC | 3 | 5 | 5 | 12 | 0.802 | 0.266 | 0.266 | 1.603 | 0.7342 |

ACATCTCTGTAACGACTAGATCCCT | 7 | 7 | 8 | 3 | 0.266 | 0.266 | 0.535 | 0.802 | 0.4673 |

ACAACGCCACGATAGCCGTCACGTC | 7 | 3 | 10 | 5 | 0.266 | 0.802 | 1.069 | 0.266 | 0.6008 |

ACAGGCCAGTGTCTTCACCAGACGA | 7 | 4 | 8 | 6 | 0.266 | 0.535 | 0.535 | 0 | 0.3340 |

ATATTGTGACTTCTGGTCGAGGTAT | 5 | 10 | 3 | 6 | 0.266 | 1.069 | 0.802 | 0 | 0.5343 |

TTTCTTCCTGGATGAGTTTGGTATC | 3 | 12 | 4 | 6 | 0.802 | 1.603 | 0.535 | 0 | 0.7350 |

CGGGAGGGTACGTAGGAACGCCTAC | 6 | 3 | 6 | 9 | 0 | 0.802 | 0 | 0.802 | 0.4010 |

TAGAGGCGAGCGCATGTAGCAAGGC | 7 | 3 | 5 | 9 | 0.266 | 0.802 | 0.266 | 0.802 | 0.5340 |

GGAAACAGGTCGGGCGACGGGCCGC | 5 | 1 | 7 | 12 | 0.266 | 1.336 | 0.266 | 1.603 | 0.8677 |

GTCCATATTGCAGTTAGAGATTCTG | 6 | 9 | 4 | 6 | 0 | 0.802 | 0.535 | 0 | 0.3343 |

CGCGTTCGGAAGGGGGCACCATCTC | 4 | 4 | 8 | 9 | 0.535 | 0.535 | 0.535 | 0.802 | 0.6018 |

CGAATCGGGAGGAAAATTTGTCTCT | 7 | 7 | 4 | 7 | 0.266 | 0.266 | 0.535 | 0.266 | 0.3332 |

Weak Key | λ_{2} |
---|---|

AGGTTCACTGGGCCCCTCTGCTTTT | 1 |

TGCTACGGGAAACAGACACGGTTAA | 0 |

TACTGGGGGGAGTTGTCCGCGGGAC | 1 |

ACATCTCTGTAACGACTAGATCCCT | 0 |

ACAACGCCACGATAGCCGTCACGTC | 0 |

ACAGGCCAGTGTCTTCACCAGACGA | 0 |

ATATTGTGACTTCTGGTCGAGGTAT | 0 |

TTTCTTCCTGGATGAGTTTGGTATC | 0 |

CGGGAGGGTACGTAGGAACGCCTAC | 0 |

TAGAGGCGAGCGCATGTAGCAAGGC | 0 |

GGAAACAGGTCGGGCGACGGGCCGC | 0 |

GTCCATATTGCAGTTAGAGATTCTG | 0 |

CGCGTTCGGAAGGGGGCACCATCTC | 1 |

CGAATCGGGAGGAAAATTTGTCTCT | 1 |

**Table 4.**Calculation of Sum of Fitness Functions of Frequency and Gap Test (λ) and Final Fitness Function (

**F**).

Weak Key | λ_{1} | λ_{2} | λ | F |
---|---|---|---|---|

AGGTTCACTGGGCCCCTCTGCTTTT | 0.6015 | 1 | 1.6015 | 0.1868 |

TGCTACGGGAAACAGACACGGTTAA | 0.4673 | 0 | 0.4673 | 0.3852 |

TACTGGGGGGAGTTGTCCGCGGGAC | 0.7342 | 1 | 1.7342 | 0.1500 |

ACATCTCTGTAACGACTAGATCCCT | 0.4673 | 0 | 0.4673 | 0.3852 |

ACAACGCCACGATAGCCGTCACGTC | 0.6008 | 0 | 0.6008 | 0.3541 |

ACAGGCCAGTGTCTTCACCAGACGA | 0.3340 | 0 | 0.3340 | 0.4181 |

ATATTGTGACTTCTGGTCGAGGTAT | 0.5343 | 0 | 0.5343 | 0.3695 |

TTTCTTCCTGGATGAGTTTGGTATC | 0.7350 | 0 | 0.7350 | 0.3241 |

CGGGAGGGTACGTAGGAACGCCTAC | 0.4010 | 0 | 0.4010 | 0.4011 |

TAGAGGCGAGCGCATGTAGCAAGGC | 0.5340 | 0 | 0.5340 | 0.3695 |

GGAAACAGGTCGGGCGACGGGCCGC | 0.8677 | 0 | 0.8677 | 0.2958 |

GTCCATATTGCAGTTAGAGATTCTG | 0.3343 | 0 | 0.3343 | 0.4171 |

CGCGTTCGGAAGGGGGCACCATCTC | 0.6018 | 1 | 1.6018 | 0.1677 |

CGAATCGGGAGGAAAATTTGTCTCT | 0.3332 | 1 | 1.3332 | 0.2113 |

Weak Key | F |
---|---|

ACAGGCCAGTGTCTTCACCAGACGA | 0.4181 |

GTCCATATTGCAGTTAGAGATTCTG | 0.4171 |

CGGGAGGGTACGTAGGAACGCCTAC | 0.4011 |

TGCTACGGGAAACAGACACGGTTAA | 0.3852 |

ACATCTCTGTAACGACTAGATCCCT | 0.3852 |

ATATTGTGACTTCTGGTCGAGGTAT | 0.3695 |

TAGAGGCGAGCGCATGTAGCAAGGC | 0.3695 |

ACAACGCCACGATAGCCGTCACGTC | 0.3541 |

TTTCTTCCTGGATGAGTTTGGTATC | 0.3241 |

AGGTTCACTGGGCCCCTCTGCTTTT | 0.1868 |

GGAAACAGGTCGGGCGACGGGCCGC | 0.2958 |

CGAATCGGGAGGAAAATTTGTCTCT | 0.2113 |

CGCGTTCGGAAGGGGGCACCATCTC | 0.1677 |

TACTGGGGGGAGTTGTCCGCGGGAC | 0.1500 |

Child String | a | t | c | g | i | m |
---|---|---|---|---|---|---|

ACAGGCCAGTGTGTTAGAGATTCTG | 6 | 7 | 4 | 8 | 6 | 2 |

GTCCATATTGCACTTCACCAGACGA | 7 | 6 | 8 | 4 | 6 | 2 |

CGGGAGGGTACGCAGACACGGTTAA | 7 | 3 | 5 | 10 | 6 | 3 |

TGCTACGGGAAATAGGAACGCCTAC | 8 | 4 | 6 | 7 | 6 | 2 |

ACATCTCTGTAACTGGTCGAGGTAT | 6 | 8 | 5 | 6 | 6 | 1 |

ATATTGTGACTTCGACTAGATCCCT | 6 | 9 | 6 | 4 | 6 | 2 |

TAGAGGCGAGCGTAGCCGTCACGTC | 5 | 4 | 7 | 9 | 6 | 2 |

ACAACGCCACGACATGTAGCAAGGC | 9 | 2 | 8 | 6 | 6 | 4 |

TTTCTTCCTGGACCCCTCTGCTTTT | 1 | 12 | 9 | 3 | 6 | 5 |

AGGTTCACTGGGTGAGTTTGGTATC | 4 | 9 | 3 | 9 | 6 | 3 |

GGAAACAGGTCGAAAATTTGTCTCT | 8 | 7 | 4 | 6 | 6 | 2 |

CGAATCGGGAGGGGCGACGGGCCGC | 4 | 1 | 7 | 13 | 6 | 5 |

CGCGTTCGGAAGTTGTCCGCGGGAC | 3 | 5 | 7 | 10 | 6 | 3 |

TACTGGGGGGAGGGGGCACCATCTC | 4 | 4 | 6 | 11 | 6 | 2 |

Weak Key | a | t | c | g | σ_{A} | σ_{T} | σ_{C} | σ_{G} | λ_{1} | λ_{2} | λ | F |
---|---|---|---|---|---|---|---|---|---|---|---|---|

TATCTACCTGGACCCCTCAGCTATA | 6 | 7 | 9 | 3 | 0 | 0.266 | 0.802 | 0.802 | 0.4675 | 1 | 1.4675 | 0.1873 |

AGGCTCACTGGGCGAGTCTGGTATC | 4 | 6 | 6 | 9 | 0.535 | 0 | 0 | 0.802 | 0.3342 | 0 | 0.3342 | 0.4172 |

CTAATCTGTAGTGGCGACGTGCCGC | 4 | 6 | 7 | 8 | 0.535 | 0 | 0.266 | 0.535 | 0.3340 | 0 | 0.3340 | 0.4172 |

TACTGGAGGGAGGAGGCACCATCTC | 6 | 4 | 6 | 9 | 0 | 0.535 | 0 | 0.802 | 0.3342 | 0 | 0.3342 | 0.4172 |

Child String | a | t | c | g | i | m |
---|---|---|---|---|---|---|

TATCTACCTGGACGAGTCTGGTATC | 5 | 8 | 6 | 6 | 6 | 1 |

AGGCTCACTGGGCCCCTCAGCTATA | 5 | 5 | 9 | 6 | 6 | 1 |

CTAATCTGTAGTGAGGCACCATCTC | 6 | 7 | 7 | 5 | 6 | 1 |

TACTGGAGGGAGGGCGACGTGCCGC | 4 | 3 | 6 | 12 | 6 | 3 |

Child String | a | t | c | g | i | m |
---|---|---|---|---|---|---|

AGGCTCACTGGGTGCGACGTGCCGC | 3 | 4 | 8 | 10 | 6 | 3 |

TACTGTAGTGAGCTCCTCAGCTATA | 6 | 8 | 6 | 5 | 6 | 1 |

Child String | a | t | c | g | i | m |
---|---|---|---|---|---|---|

AGACTCACTGAGTGCGACGTACCGC | 6 | 4 | 8 | 7 | 6 | 2 |

M = 25 | M = 50 | M = 100 | M = 150 | M = 200 | M = 250 | M = 300 | M = 350 | M = 400 | M = 450 | M = 500 | |
---|---|---|---|---|---|---|---|---|---|---|---|

N= 25 | 14 | 22 | 24 | 24 | 24 | 25 | 25 | 25 | 25 | 25 | 25 |

N= 50 | 22 | 38 | 44 | 49 | 49 | 49 | 50 | 50 | 50 | 50 | 50 |

N= 100 | 34 | 87 | 94 | 97 | 98 | 98 | 99 | 99 | 100 | 100 | 100 |

N= 150 | 60 | 89 | 95 | 112 | 139 | 146 | 147 | 148 | 149 | 150 | 150 |

N= 200 | 79 | 98 | 126 | 157 | 164 | 179 | 198 | 198 | 199 | 200 | 200 |

N= 250 | 89 | 99 | 135 | 168 | 173 | 191 | 240 | 248 | 249 | 250 | 250 |

N= 300 | 107 | 115 | 142 | 196 | 248 | 289 | 291 | 298 | 299 | 299 | 300 |

N= 350 | 137 | 141 | 156 | 198 | 249 | 324 | 335 | 340 | 350 | 350 | 350 |

N= 400 | 148 | 159 | 175 | 180 | 237 | 329 | 367 | 384 | 400 | 400 | 400 |

N= 450 | 158 | 173 | 192 | 226 | 290 | 316 | 384 | 437 | 450 | 450 | 450 |

N= 500 | 173 | 213 | 246 | 287 | 314 | 384 | 453 | 488 | 497 | 500 | 500 |

**Table 12.**Number of Populations Generated to Strengthen the Weak Keys for Different values of N and M.

M = 25 | M = 50 | M = 100 | M = 150 | M = 200 | M = 250 | M = 300 | M = 350 | M = 400 | M = 450 | M = 500 | |
---|---|---|---|---|---|---|---|---|---|---|---|

N= 25 | 4 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |

N= 50 | 5 | 5 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 |

N= 100 | 5 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 |

N= 150 | 6 | 6 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 |

N= 200 | 6 | 7 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | 8 |

N= 250 | 7 | 7 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | 8 |

N= 300 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 |

N= 350 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 |

N= 400 | 7 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | 8 | 8 |

N= 450 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 |

N= 500 | 7 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mukherjee, P.; Garg, H.; Pradhan, C.; Ghosh, S.; Chowdhury, S.; Srivastava, G.
Best Fit DNA-Based Cryptographic Keys: The Genetic Algorithm Approach. *Sensors* **2022**, *22*, 7332.
https://doi.org/10.3390/s22197332

**AMA Style**

Mukherjee P, Garg H, Pradhan C, Ghosh S, Chowdhury S, Srivastava G.
Best Fit DNA-Based Cryptographic Keys: The Genetic Algorithm Approach. *Sensors*. 2022; 22(19):7332.
https://doi.org/10.3390/s22197332

**Chicago/Turabian Style**

Mukherjee, Pratyusa, Hitendra Garg, Chittaranjan Pradhan, Soumik Ghosh, Subrata Chowdhury, and Gautam Srivastava.
2022. "Best Fit DNA-Based Cryptographic Keys: The Genetic Algorithm Approach" *Sensors* 22, no. 19: 7332.
https://doi.org/10.3390/s22197332