# An Intelligent and Fast Chaotic Encryption Using Digital Logic Circuits for Ad-Hoc and Ubiquitous Computing

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Proposed Methodology/Scheme

_{i}= Cipher text; $E({P}_{i})$ = Encryption of the plain text ${P}_{i}$; $D({C}_{i})$ = Decryption of the cipher text ${C}_{i}$.

#### 3.1. Scheme for Key Generation

_{n+}

_{1}so keys are random and independent with each other.

#### 3.2. Scheme for Encryption Process

#### 3.3. Scheme for Decryption Process

#### 3.4. Key Generation Algorithm

#### 3.5. Encryption Algorithm

#### 3.6. Decryption Algorithm

## 4. Example

Letter | ASCII | Binary Number |

P | 80 | 01010000 |

I | 73 | 01001001 |

Y | 89 | 01011001 |

U | 85 | 01010101 |

S | 83 | 01010011 |

H | 72 | 01001000 |

S | 83 | 01010011 |

#### 4.1. Key Generation

- ${X}_{n+1}$ = {6 × 4 × (4 − 1)} MOD 256
- ${X}_{n+1}$ = 72

- ${X}_{n+1}$ = {6 × 72 × (72 − 1)} MOD 256
- ${X}_{n+1}$ = 208

- ${X}_{n+1}$ = {6 × 208 × (208 − 1)} MOD 256
- ${X}_{n+1}$ = 32

- ${X}_{n+1}$ = {6 × 32 × (32 − 1)} MOD 256
- ${X}_{n+1}$ = 64

- ${X}_{n+1}$ = {6 × 64 × (64 − 1)} MOD 256
- ${X}_{n+1}$ = 128
- ${X}_{n+1}$ = 72, 208, 32, 64, 128.

72 = 01001000 | 2’s compliment | = | 10111000 | = | 184 |

208 = 11010000 | 2’s compliment | = | 00110000 | = | 48 |

32 = 00100000 | 2’s compliment | = | 11100000 | = | 224 |

64 = 01000000 | 2’s compliment | = | 11000000 | = | 192 |

128 = 10000000 | 2’s compliment | = | 10000000 | = | 128 |

_{1}= 184, K

_{2}= 48, K

_{3}= 224, K

_{4}= 192, K

_{5}= 128).

#### 4.2. Encryption Algorithm

Cipher Text– | ||

Plaintext | XNOR | Key |

P | XNOR | 184 |

80 | XNOR | 184 |

01010000 | XNOR | 10111000 |

0 | XNOR | 1 | = | 0 |

1 | XNOR | 0 | = | 0 |

0 | XNOR | 1 | = | 0 |

1 | XNOR | 1 | = | 1 |

0 | XNOR | 1 | = | 0 |

0 | XNOR | 0 | = | 1 |

0 | XNOR | 0 | = | 1 |

0 | XNOR | 0 | = | 1 |

Cipher Text–00010111 = 23 = ↨ |

#### 4.3. Decryption Algorithm

Plain Text: | ||

Cipher Text | XNOR | Key |

↨ | XNOR | 184 |

23 | XNOR | 184 |

00010111 | XNOR | 10111000 |

0 | XNOR | 1 | = | 0 |

0 | XNOR | 0 | = | 1 |

0 | XNOR | 1 | = | 0 |

1 | XNOR | 1 | = | 1 |

0 | XNOR | 1 | = | 0 |

1 | XNOR | 0 | = | 0 |

1 | XNOR | 0 | = | 0 |

1 | XNOR | 0 | = | 0 |

Plain Text–01010000 = 80 = P |

## 5. Analysis of Key Security

#### 5.1. Sensitivity of Number of Keys J

#### 5.2. Sensitivity of Constant A

#### 5.3. Sensitivity of Initial Condition X_{n}

_{n}produces fully different keys, so cipher texts are completely different. This is known as confusion. In Table 6 it has been shown that little difference in values of initial variable ${X}_{n}$ produced fully different cipher text.

## 6. Cryptanalysis

#### 6.1. Cipher Text Only Attacks

${P}_{1}$ = Q then | ${C}_{1}={E}_{{k}_{1}}({P}_{1})={E}_{184}$ | (Q) = ▬ |

${P}_{2}$ = QQ then | ${C}_{2}={E}_{{k}_{1,2}}({P}_{2})={E}_{184,48}$ | (QQ) = ▬₧ |

${P}_{3}$ = QQQ then | ${C}_{3}={E}_{{k}_{1,2,3}}({P}_{3})={E}_{184,48,224}$ | (QQQ) = ▬₧N |

${P}_{4}$ = QQQQ then | ${C}_{4}={E}_{{k}_{1,2,3,4}}({P}_{4})={E}_{184,48,224,192}$ | (QQQQ) = ▬₧Nn |

${P}_{5}$ = QQQQQ then | ${C}_{5}={E}_{{k}_{1,2,3,4,5}}({P}_{5})={E}_{184,48,224,192,128}$ | (QQQQQ) = ▬₧Nn. |

${P}_{6}$ = QQQQQQ then | ${C}_{6}={E}_{{k}_{1,2,3,4,5,1}}({P}_{6})={E}_{184,48,224,192,128,184}$ | (QQQQQQ) = ▬₧Nn.▬ |

#### 6.2. Known Plain Text Attack

${P}_{1}$ = R then | ${C}_{1}={E}_{{k}_{1}}({P}_{1})={E}_{184}$ | (R) = § |

${P}_{2}$ = RR then | ${C}_{2}={E}_{{k}_{1,2}}({P}_{2})={E}_{184,48}$ | (RR)= §¥ |

${P}_{3}$ = RRR then | ${C}_{3}={E}_{{k}_{1,2,3}}({P}_{3})={E}_{184,48,224}$ | (RRR) = §¥M |

${P}_{4}$ = RRRR then | ${C}_{4}={E}_{{k}_{1,2,3,4}}({P}_{4})={E}_{184,48,224,192}$ | (RRRR) = §¥Mm |

${P}_{5}$ = RRRRR then | ${C}_{5}={E}_{{k}_{1,2,3,4,5}}({P}_{5})={E}_{184,48,224,192,128}$ | (RRRRR) = §¥Mm- |

${P}_{6}$ = RRRRRR then | ${C}_{6}={E}_{{k}_{1,2,3,4,5,1}}({P}_{6})={E}_{184,48,224,192,128,184}$ | (RRRRRR) = §¥Mm-§ |

#### 6.3. Chosen Plaintext Attacks

- ${P}_{1}$ = DE then cipher text ${C}_{1}={E}_{{k}_{1,2}}({P}_{1})={E}_{184,48}$ (DE) = ♥è
- ${P}_{2}$ = ED then cipher text ${C}_{2}={E}_{{k}_{1,2}}({P}_{2})={E}_{184,48}$ (ED) = ☻ï

#### 6.4. Chosen Cipher Text Attack

- ${C}_{1}$ = ♥è then plaintext ${P}_{1}={D}_{{k}_{1,2}}({C}_{1})={D}_{184,48}$ (♥è) = DE
- ${C}_{2}$ = ☻ï then plain text ${P}_{2}={D}_{{k}_{1,2}}({C}_{2})={D}_{184,48}$ (☻ï) = ED

## 7. Performance Analysis

#### Metrics and Performance

#### Encryption Time

#### Encryption Throughput, X_{e}

#### Power Consumption

#### CPU Time

#### Cipher Size

## 8. Comparison with AES and Chaotic Algorithms [3]

#### 8.1. Encryption Time

#### 8.2. Encryption Throughput

#### 8.3. Encryption Power Consumption

## 9. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 6.**Encryption time of compared Algorithm [12] and CET-2C.

**Figure 7.**Encryption times of compared Algorithms 1 and 2 [17] and CET-2C.

Features | Alem Haddush Fitwi et al. [3] | Amir Akhavan1 et al. [12] | Amit Pande et al. [20] | Ashraf Zaher et al. [1] | Ayman Mousa et al. [4] | Bassem Bakhache et al. [6] | Bhavana Agrawal et al. [9] |
---|---|---|---|---|---|---|---|

Security | Secure enough | High | Comparatively high | Secure Enough | High | High | Medium |

Cryptanalysis Attack Prevention | Brute Force | Forgery and Birthday Attack | Except Known plaintext | - | - | Linear and Differential | All Four |

Cipher type | Stream | Stream | Stream | Stream | Block | Stream | Stream |

Application Area | Multimedia System | Real Time Applications | Real Time Embedded Systems | Communication System | - | Industrial Control | Communication System |

Space Complexity | High | Medium | High | Medium | Enough High | Low | High |

Implementation of algorithm | Complex | Complex | Hard | Hard | Complex Enough | Highly Complex | Complex |

Used technique | Hysteresis Switched System | High Dimensional Chaotic Map | MLM based PRNG | Chaos Shift Keying | - | PWLCM | Chaos based RSA and AES |

Efficiency/Reliability | Medium | High | Medium | Medium | Medium | High | High |

Methodology/Environment | NIST and Monte Carlo Test | SP800-22 and DIEHARD Test Suits | XilinxVirtex-6 FPGA | Duffing Oscillator | Microsoft SQL | NIST Environment | - |

Speed (Processing) | Low | High | Enough | Medium | High | High | Medium |

Prediction Possibility | No | No | No | Yes | No | Slightly | Yes |

Feasible | At Some Condition | Yes | No | Yes | Yes | No | Yes |

Accuracy | Medium | High | Medium | High | Medium | Medium | Medium |

Key length | Large | Large Enough | High | Large Enough | Large | Slightly Large | Large |

Cost | High | High | High | Medium | Medium | Low | High |

Quality Assurance | High | High | Applicable | High | Reasonable | Resemblance | Applicable |

Plain Text (ASCII) | XNOR | Key ${\mathit{K}}_{\mathit{j}}$ | Cipher Text |
---|---|---|---|

P | 184 | 00010111 | |

80 | 23 | ||

01010000 | XNOR | 10111000 | ↨ |

I | 48 | 10000110 | |

73 | 134 | ||

01001001 | XNOR | 00110000 | Å |

Y | 224 | 01000110 | |

89 | 70 | ||

01011001 | XNOR | 11100000 | F |

U | 192 | 01101010 | |

85 | 106 | ||

01010101 | XNOR | 11000000 | j |

S | 128 | 00101100 | |

83 | 44 | ||

01010011 | XNOR | 10000000 | , |

H | 184 | 00001111 | |

72 | 15 | ||

01001000 | XNOR | 10111000 | ☼ |

S | 48 | 10011100 | |

83 | 156 | ||

01010011 | XNOR | 00110000 | £ |

Cipher Text | XNOR | Key ${\mathit{K}}_{\mathit{j}}$ | Plain Text (ASCII) |
---|---|---|---|

↨ | 184 | 01010000 | |

23 | 80 | ||

00010111 | XNOR | 10111000 | P |

Å | 48 | 01001001 | |

134 | 73 | ||

10000110 | XNOR | 00110000 | I |

F | 224 | 01011001 | |

70 | 89 | ||

01000110 | XNOR | 11100000 | Y |

j | 192 | 01010101 | |

106 | 85 | ||

01101010 | XNOR | 11000000 | U |

, | 128 | 01010011 | |

44 | 83 | ||

00101100 | XNOR | 10000000 | S |

☼ | 184 | 01001000 | |

15 | 72 | ||

00001111 | XNOR | 10111000 | H |

£ | 48 | 01010011 | |

156 | 83 | ||

10011100 | XNOR | 00110000 | S |

j | A | ${\mathit{X}}_{\mathit{n}}$ | ${\mathit{X}}_{\mathit{n}+\mathbf{1}}$ | Keys (${\mathit{K}}_{\mathit{j}}$) | Cipher Text |
---|---|---|---|---|---|

2 | 6 | 4 | 72,208 | 184,48,184,48,184,48,184 | ↨Å▲Üç |

3 | 6 | 4 | 72,208,32 | 184,48,224,184,48,224,184 | ↨ÅF↕£W |

4 | 6 | 4 | 72,208,32,64 | 184,48,224,192,184,48,224 | ↨ÅFjçL |

5 | 6 | 4 | 72,208,32,64,128 | 184,48,224,192,128,184,48 | ↨ÅFj,☼£ |

j | A | ${\mathit{X}}_{\mathit{n}}$ | ${\mathit{X}}_{\mathit{n}+\mathbf{1}}$ | Keys (${\mathit{K}}_{\mathit{j}}$) | Cipher Text |
---|---|---|---|---|---|

5 | 2 | 4 | 24,80,96,64,128 | 232,176,160,192,128,232,176 | G♠♠j,_∟ |

5 | 3 | 4 | 36,196,228,132,164 | 220,60,28,124,92,220,60 | sè║╓≡kÉ |

5 | 5 | 4 | 60,80,192,0,0 | 196,176,64,1,1,196,176 | k♠µ½¡s∟ |

5 | 6 | 4 | 72,208,32,64,128 | 184,48,224,192,128,184,48 | ↨ÅFj,☼£ |

j | A | ${\mathit{X}}_{\mathit{n}}$ | ${\mathit{X}}_{\mathit{n}+\mathbf{1}}$ | Keys (${\mathit{K}}_{\mathit{j}}$) | Cipher Text |
---|---|---|---|---|---|

5 | 6 | 2 | 12,24,240,96,192 | 244,232,16,160,64,244,232 | [^╢LF∞CD |

5 | 6 | 3 | 36,136,80,32,64 | 220,120,176,224,192,220,120 | s╬▬Jlk╘ |

5 | 6 | 4 | 72,208,32,64,128 | 184,48,224,192,128,184,48 | ↨ÅFj,☼£ |

5 | 6 | 5 | 120,176,224,192,128 | 136,80,32,64,128,136,80 | 'µÅΩ,?ⁿ |

Message Sizes in KB | Encryption Time in Seconds | ||
---|---|---|---|

Chaotic Algorithm [3] | AES [3] | CET-2C | |

200 | 1.65 | 1 | 0.0698 |

250 | 2.05 | 1 | 0.076 |

300 | 2.48 | 1 | 0.082 |

350 | 2.83 | 1 | 0.0891 |

400 | 3.35 | 1 | 0.0976 |

450 | 3.75 | 1 | 0.1054 |

Message Sizes in KB | Overall % Gain for Encryption Time of CET-2C | |
---|---|---|

CET-2C over Chaotic Algorithm [3] | CET-2C over AES [3] | |

200 | 95.77 | 93.02 |

250 | 96.29 | 92.4 |

300 | 96.69 | 91.8 |

350 | 96.85 | 91.09 |

400 | 97.09 | 90.24 |

450 | 97.19 | 89.46 |

**Table 9.**Encryption time of compared Algorithm [12] and CET-2C.

Message Sizes in MB | Encryption Time in Milliseconds | |
---|---|---|

Compared Algorithm [12] | CET-2C | |

10 | 1500 | 1250 |

20 | 3500 | 2400 |

30 | 5300 | 4876 |

40 | 6800 | 6050 |

50 | 8500 | 8000 |

60 | 10,300 | 9700 |

70 | 12,100 | 10,800 |

80 | 13,800 | 12,000 |

**Table 10.**Overall %Gain of CET-2C over the compared Algorithm [12] for encryption time.

Message Sizes in MB | Overall % Gain for Encryption Time of CET-2C |
---|---|

CET-2C over Compared Algorithm [12] | |

10 | 16.67 |

20 | 31.43 |

30 | 8.00 |

40 | 11.03 |

50 | 5.88 |

60 | 5.83 |

70 | 10.74 |

80 | 13.04 |

**Table 11.**Encryption time of compared Algorithms 1 and 2 [17] and CET-2C.

Message Sizes in Bytes | Encryption Time in Milliseconds | ||
---|---|---|---|

Compared Algorithm1 [17] | Compared Algorithm2 [17] | CET-2C | |

100,000 | 1 | 3 | 54 |

500,000 | 4 | 5 | 75 |

600,000 | 204 | 620 | 82 |

700,000 | 410 | 1230 | 97 |

800,000 | 640 | 1930 | 120 |

**Table 12.**Overall %Gain of CET-2C over compared Algorithms 1 and 2 [17] for encryption time.

Message Sizes in Bytes | Overall % Gain for Encryption Time of CET-2C | |
---|---|---|

CET-2C over Compared Algorithm 1 [17] | CET-2C over Compared Algorithm 2 [17] | |

100,000 | −98.15 | −94.44 |

500,000 | −94.67 | −93.33 |

600,000 | 59.80 | 86.77 |

700,000 | 76.34 | 92.11 |

800,000 | 81.25 | 93.78 |

Message Sizes in Bytes | Encryption Throughput in Bytes/Second | ||
---|---|---|---|

Chaotic Algorithm [3] | AES [3] | CET-2C | |

10,000 | 20,000 | 2000 | 50,000 |

20,000 | 17,000 | 2000 | 44,847 |

30,000 | 16,700 | 2000 | 49,342 |

40,000 | 16,500 | 2000 | 57,405 |

50,000 | 16,400 | 2000 | 64,049 |

Message Sizes in Bytes | Overall % Gain for Encryption Throughput of CET-2C | |
---|---|---|

CET-2C over Chaotic Algorithm [3] | CET-2C over AES [3] | |

10,000 | 150 | 2400 |

20,000 | 164 | 2142 |

30,000 | 195 | 2367 |

40,000 | 248 | 2770 |

50,000 | 490 | 3102 |

© 2016 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Khare, A.; Shukla, P.K.; Rizvi, M.A.; Stalin, S.
An Intelligent and Fast Chaotic Encryption Using Digital Logic Circuits for Ad-Hoc and Ubiquitous Computing. *Entropy* **2016**, *18*, 201.
https://doi.org/10.3390/e18050201

**AMA Style**

Khare A, Shukla PK, Rizvi MA, Stalin S.
An Intelligent and Fast Chaotic Encryption Using Digital Logic Circuits for Ad-Hoc and Ubiquitous Computing. *Entropy*. 2016; 18(5):201.
https://doi.org/10.3390/e18050201

**Chicago/Turabian Style**

Khare, Ankur, Piyush Kumar Shukla, Murtaza Abbas Rizvi, and Shalini Stalin.
2016. "An Intelligent and Fast Chaotic Encryption Using Digital Logic Circuits for Ad-Hoc and Ubiquitous Computing" *Entropy* 18, no. 5: 201.
https://doi.org/10.3390/e18050201