Information Theory Based Evaluation of the RC4 Stream Cipher Outputs
Abstract
:1. Introduction
2. Preliminaries
2.1. Description of the RC4 Stream Encryption Algorithm
Algorithm 1 RC4 keyscheduling. 

Algorithm 2 RC4 pseudorandom generator. 

2.2. Iterative Probabilistic Attacks
2.3. Entropy As a Measure of Uncertainty
3. Definition of the Proposed Test Statistic
3.1. Basis of the Evaluation Criterion
3.2. Definition of the Test Statistic
3.3. Decision Criteria Using the QStatistic
4. PreComputing of Probabilities and Estimation of Entropies
4.1. Frequency PreCalculation
4.2. Estimation of Joint, Marginal, and Conditional Probabilities
4.3. Entropy Estimation
5. Experimental Evaluation
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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J/Z  0  1  …  255  

0  f(0,0)  f(0,1)  …  f(0,255)  ${f}_{({j}_{t}=0)}$ 
1  f(1,0)  f(1,1)  …  f(1,255)  ${f}_{({j}_{t}=1)}$ 
⋮  ⋮  ⋮  …  ⋮  ⋮ 
255  f(255,0)  f(255,1)  …  f(255,255)  ${f}_{({j}_{t}=255)}$ 
${f}_{({z}_{t}=0)}$  ${f}_{({z}_{t}=1)}$  …  ${f}_{({z}_{t}=255)}$  M 
J/Z  0  …  ${\mathit{z}}_{\mathit{t}}$  …  255 

0  ⋮  
⋮  ⋮  ⋮  
${j}_{t}$  $\widehat{P}({j}_{t}/{z}_{t})$  
⋮  ⋮  ⋮  …  ⋮  
255 
Z/T  1  2  …  512 

0  ${\widehat{H}}_{0}^{1}$  ${\widehat{H}}_{0}^{2}$  …  ${\widehat{H}}_{0}^{512}$ 
1  ${\widehat{H}}_{1}^{1}$  ${\widehat{H}}_{1}^{2}$  …  ${\widehat{H}}_{1}^{512}$ 
⋮  ⋮  ⋮  …  ⋮ 
255  ${\widehat{H}}_{255}^{1}$  ${\widehat{H}}_{255}^{2}$  …  ${\widehat{H}}_{255}^{512}$ 
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MadarroCapó , E.J.; LegónPérez , C.M.; Rojas, O.; SosaGómez, G. Information Theory Based Evaluation of the RC4 Stream Cipher Outputs. Entropy 2021, 23, 896. https://doi.org/10.3390/e23070896
MadarroCapó EJ, LegónPérez CM, Rojas O, SosaGómez G. Information Theory Based Evaluation of the RC4 Stream Cipher Outputs. Entropy. 2021; 23(7):896. https://doi.org/10.3390/e23070896
Chicago/Turabian StyleMadarroCapó , Evaristo José, Carlos Miguel LegónPérez , Omar Rojas, and Guillermo SosaGómez. 2021. "Information Theory Based Evaluation of the RC4 Stream Cipher Outputs" Entropy 23, no. 7: 896. https://doi.org/10.3390/e23070896