Pseudorandom number generators with input (PRNGs) are cryptographic algorithms that generate pseudorandom bits from accumulated entropic inputs (e.g., keystrokes, interrupt timings, etc.). This paper studies in particular PRNGs that are secure against premature next attacks (Kelsey et al., FSE '98), a class of attacks leveraging the fact that a PRNG may produce an output (which could be seen by an adversary!) before enough entropy has been accumulated. Practical designs adopt either unsound entropy-estimation methods to prevent such attacks (as in Linux’s /dev/random) or sophisticated pool-based approaches as in Yarrow (MacOS/FreeBSD) and Fortuna (Windows). The only prior theoretical study of premature next attacks (Dodis et al., Algorithmica '17) considers either a seeded setting or assumes constant entropy rate, and thus falls short of providing and validating practical designs. Assuming the availability of random seed is particularly problematic, first because this requires us to somehow generate a random seed without using our PRNG, but also because we must ensure that the entropy inputs to the PRNG remain independent of the seed. Indeed, all practical designs are seedless. However, prior works on seedless PRNGs (Coretti et al., CRYPTO '19; Dodis et al., ITC '21, CRYPTO'21) do not consider premature next attacks. The main goal of this paper is to investigate the feasibility of theoretically sound seedless PRNGs that are secure against premature next attacks. To this end, we make the following contributions: 1) We prove that it is impossible to achieve seedless PRNGs that are secure against premature-next attacks, even in a rather weak model. Namely, the impossibility holds even when the entropic inputs to the PRNG are independent. In particular, our impossibility result holds in settings where seedless PRNGs are otherwise possible. 2) Given the above impossibility result, we investigate whether existing seedless pool-based approaches meant to overcome premature next attacks in practical designs provide meaningful guarantees in certain settings. Specifically, we show the following. 3) We introduce a natural condition on the entropic input and prove that it implies security of the round-robin entropy accumulation PRNG used by Windows 10, called Fortuna. Intuitively, our condition requires the input entropy "not to vary too wildly" within a given round-robin round. 4) We prove that the "root pool" approach (also used in Windows 10) is secure for general entropy inputs, provided that the system’s state is not compromised after system startup. more »« less
seedless PRNGspseudorandom number generatorsPRNGFortunapremature nextSecurity and privacy → Mathematical foundations of cryptographySecurity and privacy → Information-theoretic techniquesTheory of computation → Pseudorandomness and derandomization
Format(s):
Medium: X Size: 20 pages; 905502 bytes Other: application/pdf
Size(s):
20 pages905502 bytes
Right(s):
Creative Commons Attribution 4.0 International license; info:eu-repo/semantics/openAccess
We study the security of CTR-DRBG , one of NIST’s recommended Pseudorandom Number Generator (PRNG) designs. Recently, Woodage and Shumow (Eurocrypt’ 19), and then Cohney et al. (S&P’ 20) point out some potential vulnerabilities in both NIST specification and common implementations of CTR-DRBG . While these researchers do suggest counter-measures, the security of the patched CTR-DRBG is still questionable. Our work fills this gap, proving that CTR-DRBG satisfies the robustness notion of Dodis et al. (CCS’13), the standard security goal for PRNGs.
Fan, Lei; Katz, Jonathan; Lu, Zhenghao; Thai, Phuc; Zhou, Hong-Sheng
(, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)
Alistarh, Dan
(Ed.)
{"Abstract":["The proof-of-stake (PoS) protocols aim to reduce the unnecessary computing power waste seen in Bitcoin. Various practical and provably secure designs have been proposed, like Ouroboros Praos (Eurocrypt 2018) and Snow White (FC 2019). However, the essential security property of unpredictability in these protocols remains insufficiently explored. This paper delves into this property in the cryptographic setting to achieve the "best possible" unpredictability for PoS.\r\nWe first present an impossibility result for all PoS protocols under the single-extension design framework, where each honest player extends one chain per round. The state-of-the-art permissionless PoS protocols (e.g., Praos, Snow White, and more), are all under this single-extension framework. Our impossibility result states that, if a single-extension PoS protocol achieves the best possible unpredictability, then this protocol cannot be proven secure unless more than 73% of stake is honest. To overcome this impossibility, we introduce a new design framework called multi-extension PoS, allowing each honest player to extend multiple chains using a greedy strategy in a round. This strategy allows us to construct a class of PoS protocols that achieve the best possible unpredictability. It is noteworthy that these protocols can be proven secure, assuming a much smaller fraction (e.g., 57%) of stake to be honest."]}
In the backdoored random-oracle (BRO) model, besides access to a random function H , adversaries are provided with a backdoor oracle that can compute arbitrary leakage functions f of the function table of H . Thus, an adversary would be able to invert points, find collisions, test for membership in certain sets, and more. This model was introduced in the work of Bauer, Farshim, and Mazaheri (Crypto 2018) and extends the auxiliary-input idealized models of Unruh (Crypto 2007), Dodis, Guo, and Katz (Eurocrypt 2017), Coretti et al. (Eurocrypt 2018), and Coretti, Dodis, and Guo (Crypto 2018). It was shown that certain security properties, such as one-wayness, pseudorandomness, and collision resistance can be re-established by combining two independent BROs, even if the adversary has access to both backdoor oracles. In this work we further develop the technique of combining two or more independent BROs to render their backdoors useless in a more general sense. More precisely, we study the question of building an indifferentiable and backdoor-free random function by combining multiple BROs. Achieving full indifferentiability in this model seems very challenging at the moment. We however make progress by showing that the xor combiner goes well beyond security against preprocessing attacks and offers indifferentiability as long as the adaptivity of queries to different backdoor oracles remains logarithmic in the input size of the BROs. We even show that an extractor-based combiner of three BROs can achieve indifferentiability with respect to a linear adaptivity of backdoor queries. Furthermore, a natural restriction of our definition gives rise to a notion of indifferentiability with auxiliary input, for which we give two positive feasibility results. To prove these results we build on and refine techniques by Göös et al. (STOC 2015) and Kothari et al. (STOC 2017) for decomposing distributions with high entropy into distributions with more structure and show how they can be applied in the more involved adaptive settings.
Cachet, Chloe; Hamlin, Ariel; Rezapour, Maryam; Fuller, Benjamin
(, Applied Cryptography and Network Security)
Pöpper, Christina; Batina, Lejla
(Ed.)
Fuzzy extractors derive stable keys from noisy sources non-interactively (Dodis et al., SIAM Journal of Computing 2008). Since their introduction, research has focused on two tasks: 1) showing security for as many distributions as possible and 2) providing stronger security guarantees including allowing one to enroll the same value multiple times (reusability), security against an active attacker (robustness), and preventing leakage about the enrolled value (privacy). Given the need for progress on the basic fuzzy extractor primitive, it is prudent to seek generic mechanisms to transform a fuzzy extractor into one that is robust, private, and reusable so that it can inherit further improvements. This work asks if one can generically upgrade fuzzy extractors to achieve robustness, privacy, and reusability. We show positive and negative results: we show upgrades for robustness and privacy, but we provide a negative result on reuse. 1. We upgrade (private) fuzzy extractors to be robust under weaker assumptions than previously known in the common reference string model. 2. We show a generic upgrade for a private fuzzy extractor using multi-bit compute and compare (MBCC) obfuscation (Wichs and Zirdelis, FOCS 2017) that requires less entropy than prior work. 3. We show one cannot arbitrarily compose private fuzzy extractors. In particular, we show that assuming MBCC obfuscation and collision-resistant hash functions, there does not exist a private fuzzy extractor secure against unpredictable auxiliary inputs, strengthening a negative result of Brzuska et al. (Crypto 2014).
In this work we study the problem of minimizing the round complexity for securely evaluating multiparty functionalities while making black-box use of polynomial time assumptions. In Eurocrypt 2016, Garg et al. showed that assuming all parties have access to a broadcast channel, then at least four rounds of communication are required to securely realize non-trivial functionalities in the plain model. A sequence of works follow-up the result of Garg et al. matching this lower bound under a variety of assumptions. Unfortunately, none of these works make black-box use of the underlying cryptographic primitives. In Crypto 2021, Ishai, Khurana, Sahai, and Srinivasan came closer to matching the four-round lower bound, obtaining a five-round protocol that makes black-box use of oblivious transfer and PKE with pseudorandom public keys. In this work, we show how to realize any input-less functionality (e.g., coin-tossing, generation of key-pairs, and so on) in four rounds while making black-box use of two-round oblivious transfer. As an additional result, we construct the first four-round MPC protocol for generic functionalities that makes black-box use of the underlying primitives, achieving security against non-aborting adversaries. Our protocols are based on a new primitive called list two-party computation. This primitive offers relaxed security compared to the standard notion of secure two-party computation. Despite this relaxation, we argue that this tool suffices for our applications. List two-party computation is of independent interest, as we argue it can also be used for the generation of setups, like oblivious transfer correlated randomness, in three rounds. Prior to our work, generating such a setup required at least four rounds of interactions or a trusted third party.
Coretti, Sandro, Dodis, Yevgeniy, Karthikeyan, Harish, Stephens-Davidowitz, Noah, and Tessaro, Stefano.
"On Seedless PRNGs and Premature Next". Country unknown/Code not available: Schloss Dagstuhl – Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ITC.2022.9.https://par.nsf.gov/biblio/10568701.
@article{osti_10568701,
place = {Country unknown/Code not available},
title = {On Seedless PRNGs and Premature Next},
url = {https://par.nsf.gov/biblio/10568701},
DOI = {10.4230/LIPIcs.ITC.2022.9},
abstractNote = {Pseudorandom number generators with input (PRNGs) are cryptographic algorithms that generate pseudorandom bits from accumulated entropic inputs (e.g., keystrokes, interrupt timings, etc.). This paper studies in particular PRNGs that are secure against premature next attacks (Kelsey et al., FSE '98), a class of attacks leveraging the fact that a PRNG may produce an output (which could be seen by an adversary!) before enough entropy has been accumulated. Practical designs adopt either unsound entropy-estimation methods to prevent such attacks (as in Linux’s /dev/random) or sophisticated pool-based approaches as in Yarrow (MacOS/FreeBSD) and Fortuna (Windows). The only prior theoretical study of premature next attacks (Dodis et al., Algorithmica '17) considers either a seeded setting or assumes constant entropy rate, and thus falls short of providing and validating practical designs. Assuming the availability of random seed is particularly problematic, first because this requires us to somehow generate a random seed without using our PRNG, but also because we must ensure that the entropy inputs to the PRNG remain independent of the seed. Indeed, all practical designs are seedless. However, prior works on seedless PRNGs (Coretti et al., CRYPTO '19; Dodis et al., ITC '21, CRYPTO'21) do not consider premature next attacks. The main goal of this paper is to investigate the feasibility of theoretically sound seedless PRNGs that are secure against premature next attacks. To this end, we make the following contributions: 1) We prove that it is impossible to achieve seedless PRNGs that are secure against premature-next attacks, even in a rather weak model. Namely, the impossibility holds even when the entropic inputs to the PRNG are independent. In particular, our impossibility result holds in settings where seedless PRNGs are otherwise possible. 2) Given the above impossibility result, we investigate whether existing seedless pool-based approaches meant to overcome premature next attacks in practical designs provide meaningful guarantees in certain settings. Specifically, we show the following. 3) We introduce a natural condition on the entropic input and prove that it implies security of the round-robin entropy accumulation PRNG used by Windows 10, called Fortuna. Intuitively, our condition requires the input entropy "not to vary too wildly" within a given round-robin round. 4) We prove that the "root pool" approach (also used in Windows 10) is secure for general entropy inputs, provided that the system’s state is not compromised after system startup.},
journal = {},
volume = {230},
publisher = {Schloss Dagstuhl – Leibniz-Zentrum für Informatik},
author = {Coretti, Sandro and Dodis, Yevgeniy and Karthikeyan, Harish and Stephens-Davidowitz, Noah and Tessaro, Stefano},
editor = {Dachman-Soled, Dana}
}
Warning: Leaving National Science Foundation Website
You are now leaving the National Science Foundation website to go to a non-government website.
Website:
NSF takes no responsibility for and exercises no control over the views expressed or the accuracy of
the information contained on this site. Also be aware that NSF's privacy policy does not apply to this site.
An official website of the United States government
