In this discourse, I introduce the reader to the concept of Chosen-Plaintext Attacks, by first defining them and then introducing to some of the properties of encryption schemes secure against Chosen-Plaintext attacks. I then introduce the concept of pseudorandom functions and try to show, how pseudorandom functions or permutations help understanding CPA-security.
The discourse ends with constructing a CPA-secure encryption scheme based on pseudorandom permutations and a proposition that proves its correctness.
Inhaltsverzeichnis (Table of Contents)
- Flashback
- Chosen-Plaintext Attacks
- Pseudorandom Functions
- Pseudorandom Permutations
Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)
The objective of this discourse is to introduce a stronger security definition in cryptography, moving beyond passive eavesdropping to encompass chosen-plaintext attacks (CPA). It aims to explain the necessity of considering CPA security and to demonstrate how to construct encryption schemes that are secure against such attacks.
- Security definitions in cryptography
- Chosen-plaintext attacks (CPA) and their real-world implications
- Formal definition of CPA security
- Pseudorandom functions and their role in CPA-secure encryption
- Pseudorandom permutations and their relationship to pseudorandom functions
Zusammenfassung der Kapitel (Chapter Summaries)
Flashback: This introductory chapter sets the stage by revisiting the passive eavesdropping model of security, where an adversary only observes encrypted communication. It introduces the concept of a stronger security definition where the adversary can influence the messages being encrypted, leading to the need for considering chosen-plaintext attacks.
Chosen-Plaintext Attacks: This chapter formally defines chosen-plaintext attacks (CPA). It presents real-world examples, such as a scenario involving a computer terminal and a famous World War II example where the US used a chosen-plaintext attack to decipher Japanese communication about the attack on Midway Island, illustrating how an adversary could influence what messages are encrypted and the potential consequences of vulnerabilities to CPA. The chapter then introduces a formal experiment to define CPA security, culminating in a definition of when an encryption scheme is considered CPA-secure.
Pseudorandom Functions: This chapter introduces pseudorandom functions as a generalization of pseudorandom generators. It formally defines keyed functions and length-preserving functions, providing a detailed analysis of their properties and establishing the necessary criteria for a function to be considered pseudorandom. The chapter uses a combinatorial approach to analyze the cardinality of the set of all functions and to formally define pseudorandom functions. An example of an insecure function is given, highlighting the importance of the conditions established earlier.
Pseudorandom Permutations: Building upon the concept of pseudorandom functions, this chapter introduces pseudorandom permutations, where the function must be a bijection. It defines keyed permutations and length-preserving permutations, and shows how the definition of pseudorandom permutations closely mirrors that of pseudorandom functions. The main result of this chapter is a proof demonstrating that if a function is a pseudorandom permutation, and its block length is sufficiently large, then it's also a pseudorandom function. The proof involves a careful analysis of the probability that a randomly chosen function is not a permutation and shows how this probability is negligible for sufficiently large block lengths.
Schlüsselwörter (Keywords)
Chosen-plaintext attacks (CPA), CPA security, encryption schemes, pseudorandom functions, pseudorandom permutations, security definitions, cryptography, indistinguishability, private-key encryption, negligible function, polynomial-time algorithm, Midway Island, World War II.
Frequently Asked Questions: A Comprehensive Language Preview on Chosen-Plaintext Attacks and Pseudorandom Functions
What topics are covered in this language preview?
This preview comprehensively covers chosen-plaintext attacks (CPA) and their implications for cryptographic security. It delves into the formal definitions of CPA security, pseudorandom functions, and pseudorandom permutations. The preview also includes a historical overview, chapter summaries, and key terms.
What is the objective of this language preview?
The main objective is to introduce a stronger security definition in cryptography that goes beyond passive eavesdropping to account for active attacks like chosen-plaintext attacks. It aims to explain how to build encryption schemes secure against such attacks.
What are chosen-plaintext attacks (CPA)?
Chosen-plaintext attacks are a type of cryptanalytic attack where the adversary can choose the plaintexts to be encrypted and obtain the corresponding ciphertexts. This allows the attacker to gain insights into the encryption algorithm and potentially break the encryption.
What are the real-world implications of CPA?
The preview uses real-world examples, including a historical example involving the attack on Midway Island during World War II, to illustrate the serious consequences of vulnerabilities to CPAs. These attacks can lead to the compromise of sensitive information and systems.
How is CPA security formally defined?
The preview provides a formal definition of CPA security using a specific experiment. An encryption scheme is considered CPA-secure if an adversary cannot distinguish between the encryption of a chosen plaintext and the encryption of a randomly chosen plaintext.
What are pseudorandom functions, and what is their role in CPA-secure encryption?
Pseudorandom functions are keyed functions that are computationally indistinguishable from truly random functions. They play a crucial role in constructing CPA-secure encryption schemes because their unpredictable nature makes it difficult for adversaries to gain information about the plaintext even when they can choose the plaintexts to be encrypted.
What are pseudorandom permutations, and how do they relate to pseudorandom functions?
Pseudorandom permutations are a special type of pseudorandom function where the function is a bijection (one-to-one and onto). The preview demonstrates that under certain conditions, a pseudorandom permutation is also a pseudorandom function.
What is the significance of the Midway Island example?
The Midway Island example illustrates a historical instance where a chosen-plaintext attack was successfully used to decipher enemy communications. This highlights the practical importance and effectiveness of chosen-plaintext attacks in real-world scenarios.
What are the key terms and concepts discussed in this preview?
Key terms include chosen-plaintext attacks (CPA), CPA security, encryption schemes, pseudorandom functions, pseudorandom permutations, security definitions, cryptography, indistinguishability, private-key encryption, negligible function, polynomial-time algorithm.
What chapters are included in this preview?
The preview includes a flashback chapter reviewing passive eavesdropping, a chapter formally defining chosen-plaintext attacks, a chapter on pseudorandom functions, and a chapter on pseudorandom permutations.
- Quote paper
- Matthias Himmelmann (Author), 2016, Security against Chosen-Plaintext Attacks, Munich, GRIN Verlag, https://www.hausarbeiten.de/document/351992