spostrzeżenie - Computer Security and Privacy - # Correcting Subverted Random Oracles

Correcting Subverted Random Oracles to Achieve Indifferentiability

Q: How can the proposed construction be extended to handle subversion of other types of cryptographic primitives beyond random oracles

The proposed construction can be extended to handle subversion of other types of cryptographic primitives by adapting the concept of crooked indifferentiability to suit the specific characteristics of those primitives. For example, if we consider a subverted cryptographic hash function, similar to the random oracle scenario, we can define a correction function that transforms the subverted hash function into a corrected version that behaves like a random function. This correction process would involve using public randomness to modify the subverted hash function in a way that makes it indistinguishable from a truly random hash function. For other cryptographic primitives like encryption schemes or digital signature algorithms, the extension would involve defining how the subversion of these primitives can be corrected using a similar approach. The correction function would need to ensure that the subverted primitive is transformed into a version that maintains the desired security properties, even in the presence of adversarial subversion. In essence, the extension of the construction to handle subversion of other cryptographic primitives would involve customizing the correction process to address the specific vulnerabilities and challenges posed by each type of primitive while maintaining the overall goal of achieving crooked indifferentiability.

Q: What are the potential applications of the corrected random oracle construction in emerging areas of cryptography, such as blockchain, secure multi-party computation, or post-quantum cryptography

The corrected random oracle construction has several potential applications in emerging areas of cryptography, including: Blockchain Technology: In blockchain systems, where the integrity and security of cryptographic hash functions are crucial, the corrected random oracle construction can be used to protect against subversion attacks on hash functions. By ensuring that the hash functions used in blockchain protocols are corrected and behave like random functions, the construction can enhance the security and trustworthiness of blockchain networks. Secure Multi-Party Computation: In secure multi-party computation protocols, where multiple parties collaborate to perform computations while preserving data privacy, the corrected random oracle construction can be employed to safeguard the cryptographic primitives used in these protocols. By correcting subverted primitives, the construction can help maintain the confidentiality and integrity of the computations. Post-Quantum Cryptography: With the rise of quantum computing and its potential to break traditional cryptographic schemes, post-quantum cryptography aims to develop new cryptographic algorithms that are secure against quantum attacks. The corrected random oracle construction can play a role in ensuring the security of these new cryptographic primitives by correcting any subverted components and maintaining their integrity in a quantum-resistant manner. By applying the corrected random oracle construction in these emerging areas of cryptography, researchers and practitioners can enhance the resilience and security of cryptographic systems in the face of evolving threats and challenges.

Główne pojęcia

A simple construction can transform a "subverted" random oracle, which disagrees with the original one at a small fraction of inputs, into an object that is indifferentiable from a random function, even if the adversary is made aware of all randomness used in the transformation.

Streszczenie

The paper focuses on the problem of correcting faulty or adversarially corrupted random oracles, so that they can be confidently applied for cryptographic purposes.
The authors prove that a simple construction can transform a "subverted" random oracle, which disagrees with the original one at a small fraction of inputs, into an object that is indifferentiable from a random function, even if the adversary is made aware of all randomness used in the transformation.
The key contributions are:

The authors illustrate the security failures that can arise from the use of hash functions that are subverted at only a negligible fraction of inputs, using two concrete examples: a chain take-over attack on blockchain and a system sneak-in attack on password authentication.
The authors introduce a new notion called "crooked" indifferentiability to reflect the challenges in the setting with subversion. This adapts the successful framework of indifferentiability to the setting where the construction uses only a subverted implementation and the construction aims to be indifferentiable from a clean random oracle.
The authors present a simple construction that can transform a subverted random oracle into an object that is indifferentiable from a random function, even if the adversary is made aware of all randomness used in the transformation. The analysis of this construction is non-trivial and involves overcoming several technical challenges.
The authors discuss how their correction function can be easily applied to save the faulty hash implementation in several important application scenarios, including blockchain, password authentication, and digital signatures.

Statystyki

The construction depends on a parameter ℓ = poly(n) and public randomness R = (r1, ..., rℓ), where each ri is an independent and uniform element of {0, 1}^n.

Cytaty

"The random oracle methodology has proven to be a powerful tool for designing and reasoning about cryptographic schemes."
"We prove that a simple construction can transform a "subverted" random oracle—which disagrees with the original one at a small fraction of inputs—into an object that is indifferentiable from a random function, even if the adversary is made aware of all randomness used in the transformation."

Kluczowe wnioski z

Correcting Subverted Random Oracles

by Alexander Ru... o arxiv.org 04-16-2024

https://arxiv.org/pdf/2404.09442.pdf

Głębsze pytania

How can the proposed construction be extended to handle subversion of other types of cryptographic primitives beyond random oracles

The proposed construction can be extended to handle subversion of other types of cryptographic primitives by adapting the concept of crooked indifferentiability to suit the specific characteristics of those primitives. For example, if we consider a subverted cryptographic hash function, similar to the random oracle scenario, we can define a correction function that transforms the subverted hash function into a corrected version that behaves like a random function. This correction process would involve using public randomness to modify the subverted hash function in a way that makes it indistinguishable from a truly random hash function.
For other cryptographic primitives like encryption schemes or digital signature algorithms, the extension would involve defining how the subversion of these primitives can be corrected using a similar approach. The correction function would need to ensure that the subverted primitive is transformed into a version that maintains the desired security properties, even in the presence of adversarial subversion.
In essence, the extension of the construction to handle subversion of other cryptographic primitives would involve customizing the correction process to address the specific vulnerabilities and challenges posed by each type of primitive while maintaining the overall goal of achieving crooked indifferentiability.

What are the limitations of the crooked indifferentiability framework, and how can it be further strengthened to handle more advanced adversarial settings

The crooked indifferentiability framework, while effective in addressing the problem of correcting subverted random oracles, has certain limitations that could be further strengthened for handling more advanced adversarial settings. Some limitations of the framework include:

Limited Adversarial Models: The current framework assumes a specific type of adversary that can subvert the random oracle. Strengthening the framework would involve considering more sophisticated adversaries with different capabilities and strategies for subverting cryptographic primitives.
Complexity of Simulation: The simulation process in crooked indifferentiability can be challenging, especially when dealing with complex cryptographic primitives. Enhancements could focus on simplifying the simulation process without compromising the security guarantees.
Scalability: The framework may face scalability issues when applied to larger-scale cryptographic systems or when handling multiple subverted primitives simultaneously. Strengthening the framework would involve ensuring scalability and efficiency in correcting multiple subverted primitives.

To further strengthen the crooked indifferentiability framework, some approaches could include:

Introducing Adaptive Adversaries: Consider adversaries that can adapt their subversion strategies based on feedback from the correction process, making the framework more robust against dynamic attacks.
Formal Verification: Utilize formal verification techniques to ensure the correctness and security of the correction process, providing stronger guarantees against subversion.
Incorporating Machine Learning: Explore the use of machine learning algorithms to enhance the detection and correction of subverted primitives, improving the overall resilience of the framework.

By addressing these limitations and incorporating these enhancements, the crooked indifferentiability framework can be further strengthened to handle more advanced adversarial settings in cryptography.

What are the potential applications of the corrected random oracle construction in emerging areas of cryptography, such as blockchain, secure multi-party computation, or post-quantum cryptography

The corrected random oracle construction has several potential applications in emerging areas of cryptography, including:

Blockchain Technology: In blockchain systems, where the integrity and security of cryptographic hash functions are crucial, the corrected random oracle construction can be used to protect against subversion attacks on hash functions. By ensuring that the hash functions used in blockchain protocols are corrected and behave like random functions, the construction can enhance the security and trustworthiness of blockchain networks.
Secure Multi-Party Computation: In secure multi-party computation protocols, where multiple parties collaborate to perform computations while preserving data privacy, the corrected random oracle construction can be employed to safeguard the cryptographic primitives used in these protocols. By correcting subverted primitives, the construction can help maintain the confidentiality and integrity of the computations.
Post-Quantum Cryptography: With the rise of quantum computing and its potential to break traditional cryptographic schemes, post-quantum cryptography aims to develop new cryptographic algorithms that are secure against quantum attacks. The corrected random oracle construction can play a role in ensuring the security of these new cryptographic primitives by correcting any subverted components and maintaining their integrity in a quantum-resistant manner.

By applying the corrected random oracle construction in these emerging areas of cryptography, researchers and practitioners can enhance the resilience and security of cryptographic systems in the face of evolving threats and challenges.

Correcting Subverted Random Oracles to Achieve Indifferentiability