The blog post "Entropy Attacks" argues against blindly trusting entropy sources, particularly in cryptographic contexts. It emphasizes that measuring entropy based solely on observed outputs, like those from /dev/random, is insufficient for security. An attacker might manipulate or partially control the supposedly random source, leading to predictable outputs despite seemingly high entropy. The post uses the example of an attacker influencing the timing of network packets to illustrate how seemingly unpredictable data can still be exploited. It concludes by advocating for robust key-derivation functions and avoiding reliance on potentially compromised entropy sources, suggesting deterministic random bit generators (DRBGs) seeded with a high-quality initial seed as a preferable alternative.
Daniel J. Bernstein, in his blog post "Entropy Attacks," meticulously dissects the concept of entropy estimation within the realm of cryptography, specifically focusing on its application in generating supposedly random numbers for cryptographic keys. He argues that conventional entropy estimation techniques are fundamentally flawed and can lead to significant security vulnerabilities, leaving systems susceptible to attack. Instead of relying on abstract statistical measures of entropy, Bernstein advocates for a more concrete and pragmatic approach: demonstrably obtaining unpredictable bits.
Bernstein begins by elucidating the conventional wisdom regarding entropy estimation. This approach typically involves analyzing the potential sources of randomness within a system, such as mouse movements, keyboard timings, or network activity. Each source is assigned an estimated entropy value, reflecting the perceived unpredictability of its output. These individual entropy estimations are then combined to determine the overall entropy of the generated random numbers.
However, Bernstein argues that these estimations are inherently imprecise and often overly optimistic. He points out that attackers may possess more knowledge about the system than assumed, enabling them to predict the supposedly random bits with higher accuracy than the entropy estimations would suggest. He illustrates this with several examples where seemingly random sources can be influenced or predicted by an astute attacker. For instance, an attacker might analyze network traffic patterns or exploit vulnerabilities in peripheral drivers to gather information about the "random" data being collected.
Furthermore, Bernstein criticizes the common practice of combining entropy estimates from different sources. He contends that simply adding the individual entropy values doesn't accurately represent the overall entropy, as the sources may be correlated or influenced by common factors. This can lead to a significant overestimation of the true randomness of the generated numbers.
Instead of relying on these potentially flawed entropy estimations, Bernstein proposes an alternative approach focused on acquiring demonstrably unpredictable bits. He suggests using sources of randomness that are inherently difficult to predict, even by a well-informed attacker. One such example is utilizing high-quality random number generators based on physical phenomena, like radioactive decay or thermal noise, which are inherently unpredictable. Another approach is to leverage publicly verifiable randomness beacons, which provide publicly accessible random bits generated through robust and transparent processes.
He further emphasizes the importance of rigorous testing and verification of the randomness generation process. Instead of relying on theoretical entropy estimations, Bernstein advocates for empirical testing using statistical randomness tests to ensure the generated numbers exhibit the expected properties of true randomness.
In conclusion, Bernstein's "Entropy Attacks" serves as a cautionary tale against overreliance on conventional entropy estimations in cryptography. He argues that these estimations are often inaccurate and can lead to a false sense of security. He advocates for a shift towards demonstrably acquiring unpredictable bits and rigorously testing the randomness of generated numbers, ensuring the security of cryptographic systems against potential attacks.
Summary of Comments ( 13 )
https://news.ycombinator.com/item?id=43470339
The Hacker News comments discuss the practicality and effectiveness of entropy-reduction attacks, particularly in the context of Bernstein's blog post. Some users debate the real-world impact, pointing out that while theoretically interesting, such attacks often rely on unrealistic assumptions like attackers having precise timing information or access to specific hardware. Others highlight the importance of considering these attacks when designing security systems, emphasizing defense-in-depth strategies. Several comments delve into the technical details of entropy estimation and the challenges of accurately measuring it. A few users also mention specific examples of vulnerabilities related to insufficient entropy, like Debian's OpenSSL bug. The overall sentiment suggests that while these attacks aren't always easily exploitable, understanding and mitigating them is crucial for robust security.
The Hacker News post titled "Entropy Attacks" links to a blog post by Daniel J. Bernstein on entropy estimation. The discussion in the comments section revolves around the complexities and nuances of entropy estimation, particularly in the context of cryptographic systems. Several commenters engage with the technical details presented in Bernstein's post.
One commenter highlights the difficulty of estimating entropy accurately, especially when dealing with real-world sources that might not exhibit ideal randomness. They mention the "haveged" program as an example of a tool attempting to generate entropy from hardware events, but acknowledge the challenges in ensuring its true randomness.
Another commenter delves into the distinction between Shannon entropy and min-entropy, emphasizing that cryptographic operations rely on min-entropy for security. They point out that measuring min-entropy is inherently more difficult than measuring Shannon entropy.
The idea of "compressing" randomness into a smaller, higher-entropy form is also discussed. Commenters explain that while it's possible to extract a shorter, more uniformly random string from a longer, less random one, this process doesn't magically create entropy. The output's entropy is fundamentally limited by the input's entropy.
One comment specifically references the use of cryptographic hash functions as randomness extractors. They explain how these functions can transform a source with uneven entropy distribution into a more uniformly random output, suitable for cryptographic keys.
A few commenters touch upon the practical implications of entropy estimation in system security. They acknowledge the difficulty of achieving truly random numbers in software and mention hardware random number generators (RNGs) as a more reliable source. They also discuss how insufficient entropy can lead to vulnerabilities in security systems.
Finally, some comments offer further reading on related topics, such as the NIST publication on entropy sources and various academic papers on randomness extraction. Overall, the comments section provides valuable insights and perspectives on the challenges of entropy estimation and its crucial role in cryptography.