skip to main content

Title: Towards Defeating Backdoored Random Oracles: Indifferentiability with Bounded Adaptivity
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 more » 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. « less
Authors:
; ; ;
Editors:
Pass, Rafael; Pietrzak, Krzysztof
Award ID(s):
1815546
Publication Date:
NSF-PAR ID:
10208486
Journal Name:
Lecture notes in computer science
Volume:
12552
Page Range or eLocation-ID:
241-273
ISSN:
0302-9743
Sponsoring Org:
National Science Foundation
More Like this
  1. We revisit the problem of finding B-block-long collisions in Merkle-Damg˚ard Hash Functions in the auxiliary-input random oracle model, in which an attacker gets a piece of S-bit advice about the random oracle and makes T oracle queries. Akshima, Cash, Drucker and Wee (CRYPTO 2020), based on the work of Coretti, Dodis, Guo and Steinberger (EUROCRYPT 2018), showed a simple attack for 2 ≤ B ≤ T (with respect to a random salt). The attack achieves advantage Ω( e ST B/2 n + T 2/2 n) where n is the output length of the random oracle. They conjectured that this attack is optimal. However, this so-called STB conjecture was only proved for B ≈ T and B = 2. Very recently, Ghoshal and Komargodski (CRYPTO 22) confirmed STB conjecture for all constant values of B, and provided an Oe(S 4T B2/2 n + T 2/2 n) bound for all choices of B. In this work, we prove an Oe((ST B/2 n)· max{1, ST2/2 n}+T 2/2 n) bound for every 2 < B < T. Our bound confirms the STB conjecture for ST2 ≤ 2 n, and is optimal up to a factor of S for ST2 > 2 n (note asmore »T 2 is always at most 2n, otherwise finding a collision is trivial by the birthday attack). Our result subsumes all previous upper bounds for all ranges of parameters except for B = Oe(1) and ST2 > 2 n. We obtain our results by adopting and refining the technique of Chung, Guo, Liu, and Qian (FOCS 2020). Our approach yields more modular proofs and sheds light on how to bypass the limitations of prior techniques. Along the way, we obtain a considerably simpler and illuminating proof for B = 2, recovering the main result of Akshima, Cash, Drucker and Wee.« less
  2. In a key-agreement protocol whose security is proven in the random oracle model (ROM), the parties and the eavesdropper can make bounded number of queries to a shared random function (an “oracle”). Such protocol are the alternative to key-agreement protocols whose security is based on “public-key assumptions”, assumptions that being more structured are presumingly more vulnerable to attacks. Barak and Mahmoody [Crypto ’09] (following Impagliazzo and Rudich [STOC ’89]) have shown the ROM key-agreement protocols can only guarantee limited secrecy: the key of any `l-query protocol can be revealed by an O(l^2 )-query adversary, a bound that matches the gap obtained by the Merkle’s Puzzles two-message protocol of Merkle [CACM ’78]. While this quadratic gap might not seem like much, if the honest parties are willing to work “hard enough” and given continuousness improvement in common hash functions evaluation time, this gap yields a good enough advantage (assuming the security of the protocol holds when initiating the random function with a fixed hash function). In this work we consider the communication complexity of ROM key-agreement protocols. In Merkle’s Puzzles, the honest parties need to exchange Ω(l) bits (ignoring logarithmic factors) to obtain secrecy against an eavesdropper that makes roughly l^2more »queries, which makes the protocol unrealizable in many settings. We show that for protocols with certain natural properties, such high communication is unavoidable. Specifically, this is the case if the honest parties’ queries are independent and uniformly random, or alternatively if the protocol uses non-adaptive queries and has only two rounds. Since two-round key-agreement protocol are equivalent to public-key encryption scheme (seeing the first message as the public-key), the latter result bounds the public-key and encryption size of public-key encryption scheme whose security is proven in the ROM.« less
  3. Tessaro, Stefano (Ed.)
    A Proof of Sequential Work (PoSW) allows a prover to convince a resource-bounded verifier that the prover invested a substantial amount of sequential time to perform some underlying computation. PoSWs have many applications including time-stamping, blockchain design, and universally verifiable CPU benchmarks. Mahmoody, Moran, and Vadhan (ITCS 2013) gave the first construction of a PoSW in the random oracle model though the construction relied on expensive depth-robust graphs. In a recent breakthrough, Cohen and Pietrzak (EUROCRYPT 2018) gave an efficient PoSW construction that does not require expensive depth-robust graphs. In the classical parallel random oracle model, it is straightforward to argue that any successful PoSW attacker must produce a long ℋ-sequence and that any malicious party running in sequential time T-1 will fail to produce an ℋ-sequence of length T except with negligible probability. In this paper, we prove that any quantum attacker running in sequential time T-1 will fail to produce an ℋ-sequence except with negligible probability - even if the attacker submits a large batch of quantum queries in each round. The proof is substantially more challenging and highlights the power of Zhandry’s recent compressed oracle technique (CRYPTO 2019). We further extend this result to establish post-quantum securitymore »of a non-interactive PoSW obtained by applying the Fiat-Shamir transform to Cohen and Pietrzak’s efficient construction (EUROCRYPT 2018).« less
  4. The quantum random oracle model (QROM) has become the standard model in which to prove the post-quantum security of random-oracle-based constructions. Unfortunately, none of the known proof techniques allow the reduction to record information about the adversary’s queries, a crucial feature of many classical ROM proofs, including all proofs of indifferentiability for hash function domain extension. In this work, we give a new QROM proof technique that overcomes this “recording barrier”. We do so by giving a new “compressed oracle” which allows for efficient on-the-fly simulation of random oracles, roughly analogous to the usual classical simulation. We then use this new technique to give the first proof of quantum indifferentiability for the Merkle-Damgård domain extender for hash functions. We also give a proof of security for the Fujisaki-Okamoto transformation; previous proofs required modifying the scheme to include an additional hash term. Given the threat posed by quantum computers and the push toward quantum-resistant cryptosystems, our work represents an important tool for efficient post-quantum cryptosystems.
  5. The random-permutation model (RPM) and the ideal-cipher model (ICM) are idealized models that offer a simple and intuitive way to assess the conjectured standard-model security of many important symmetric-key and hash-function constructions. Similarly, the generic-group model (GGM) captures generic algorithms against assumptions in cyclic groups by modeling encodings of group elements as random injections and allows to derive simple bounds on the advantage of such algorithms. Unfortunately, both well-known attacks, e.g., based on rainbow tables (Hellman, IEEE Transactions on Information Theory ’80), and more recent ones, e.g., against the discrete-logarithm problem (Corrigan-Gibbs and Kogan, EUROCRYPT ’18), suggest that the concrete security bounds one obtains from such idealized proofs are often completely inaccurate if one considers non-uniform or preprocessing attacks in the standard model. To remedy this situation, this work defines the auxiliary-input (AI) RPM/ICM/GGM, which capture both non-uniform and preprocessing attacks by allowing an attacker to leak an arbitrary (bounded-output) function of the oracle’s function table; derives the first non-uniform bounds for a number of important practical applications in the AI-RPM/ICM, including constructions based on the Merkle-Damgård and sponge paradigms, which underly the SHA hashing standards, and for AI-RPM/ICM applications with computational security; and using simpler proofs, recovers the AI-GGMmore »security bounds obtained by Corrigan-Gibbs and Kogan against preprocessing attackers, for a number of assumptions related to cyclic groups, such as discrete logarithms and Diffie-Hellman problems, and provides new bounds for two assumptions. An important step in obtaining these results is to port the tools used in recent work by Coretti et al. (EUROCRYPT ’18) from the ROM to the RPM/ICM/GGM, resulting in very powerful and easy-to-use tools for proving security bounds against non-uniform and preprocessing attacks.« less