Unit 1 Information Theory for Cybersecurity Notes | HTCS401 Notes | Aktu Notes
Shannon’s Foundation of Information Theory
- Developed by Claude Shannon in 1948, it provides a mathematical framework for quantifying information and communication.
- Fundamental to understanding data compression, transmission, and encryption.
Key Concepts:
- Entropy: Measures the uncertainty or information content of a message.
- Mutual Information: Measures the amount of information gained about one random variable through another.
Example:
In a communication system, Shannon's theory helps determine the optimal coding scheme to minimize transmission errors and maximize data efficiency.
Random Variables
- Random variables represent outcomes of uncertain events in a probabilistic framework.
- Central to modeling unpredictable phenomena in cybersecurity contexts.
Types:
- Discrete: Finite or countably infinite outcomes (e.g., dice rolls).
- Continuous: Infinite possible outcomes within a range (e.g., measurement errors).
Example:
A random variable might represent the outcome of a firewall decision: allow or deny traffic based on predefined rules.
Probability Distribution Factors
- Describes the likelihood of different outcomes of a random variable.
- Helps assess risks and vulnerabilities in cybersecurity scenarios.
Parameters:
- Mean (Expected Value): Average outcome weighted by probabilities.
- Variance: Measure of the spread or dispersion of outcomes.
- Skewness and Kurtosis: Higher moments describing asymmetry and tail behavior.
Example:
Understanding the distribution of network traffic patterns helps in detecting anomalies or potential cyber attacks.
Uncertainty/Entropy Information Measures
- Entropy quantifies the amount of uncertainty or randomness in data.
- Key for designing secure cryptographic algorithms and protocols.
Calculation:
Shannon Entropy: \( H(X) = -\sum_{i} p_i \log_2 p_i \), where \( p_i \) is the probability of outcome \( i \).
Example:
- Assessing the entropy of password policies helps ensure they are robust against dictionary attacks and brute-force methods.
Leakage
- Unintended disclosure of sensitive information in a system.
- Can occur through side-channel attacks, insecure protocols, or poor data handling practices.
Types:
- Information Leakage: Disclosure of sensitive data.
- Timing Attacks: Exploiting variations in timing to infer secret information.
Example:
Monitoring power consumption to deduce cryptographic keys in smart cards is an example of a side-channel attack.
Quantifying Leakage and Partitions
- Methods to measure and mitigate information leakage in systems.
- Partitioning data and applying access controls limit exposure to sensitive information.
Techniques:
- Data Masking: Hiding sensitive information in datasets.
- Access Controls: Role-based access and authentication mechanisms.
Example:
Encrypting sensitive files and restricting access based on user roles ensures confidentiality and limits data leakage.
Lower Bounds on Key Size: Secrecy, Authentication, and Secret Sharing
- Theoretical limits on the size of cryptographic keys ensure adequate security.
- Key size impacts resistance against brute-force attacks and cryptographic strength.
Considerations:
- Cryptographic Strength: Larger key sizes increase security but also computational overhead.
- Key Management: Balancing security needs with operational efficiency.
Example:
RSA encryption uses key sizes ranging from 1024 to 4096 bits to ensure secure communication and data protection.
Provable Security, Computationally-Secure, Symmetric Cipher
- Concepts in cryptographic security guarantee the resilience of cryptographic systems under specified conditions.
- Differentiates between theoretical security (provable) and practical security (computationally secure).
Examples:
- Provable Security: Mathematical proofs demonstrating resistance against specific types of attacks.
- Computationally Secure: Security relies on the difficulty of computational problems, such as factoring large numbers (RSA).
Application:
AES (Advanced Encryption Standard) is widely used due to its computational security and resistance to known cryptographic attacks.
These detailed notes provide a comprehensive understanding of information theory concepts in the context of cybersecurity, essential for analyzing and designing secure systems and protocols.
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