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- W2951004906 abstract "We revisit security proofs for various cryptographic primitives in the auxiliary-input random-oracle model (AI-ROM), in which an attacker (mathcal A) can compute arbitrary S bits of leakage about the random oracle (mathcal O) before attacking the system and then use additional T oracle queries to (mathcal O) during the attack. This model has natural applications in settings where traditional random-oracle proofs are not useful: (a) security against non-uniform attackers; (b) security against preprocessing. We obtain a number of new results about the AI-ROM:Unruh (CRYPTO’07) introduced the pre-sampling technique, which generically reduces security proofs in the AI-ROM to a much simpler P-bit-fixing random-oracle model (BF-ROM), where the attacker can arbitrarily fix the values of (mathcal O) on some P coordinates, but then the remaining coordinates are chosen at random. Unruh’s security loss for this transformation is (sqrt{ST/P}). We improve this loss to the optimal value O(ST / P), obtaining nearly tight bounds for a variety of indistinguishability applications in the AI-ROM.While the basic pre-sampling technique cannot give tight bounds for unpredictability applications, we introduce a novel “multiplicative version” of pre-sampling, which allows to dramatically reduce the size of P of the pre-sampled set to (P=O(ST)) and yields nearly tight security bounds for a variety of unpredictability applications in the AI-ROM. Qualitatively, it validates Unruh’s “polynomial pre-sampling conjecture”—disproved in general by Dodis et al. (EUROCRYPT’17)—for the special case of unpredictability applications.Using our techniques, we reprove nearly all AI-ROM bounds obtained by Dodis et al. (using a much more laborious compression technique), but we also apply it to many settings where the compression technique is either inapplicable (e.g., computational reductions) or appears intractable (e.g., Merkle-Damgard hashing).We show that for any salted Merkle-Damgard hash function with m-bit output there exists a collision-finding circuit of size (varTheta (2^{m/3})) (taking salt as the input), which is significantly below the (2^{m/2}) birthday security conjectured against uniform attackers.We build two compilers to generically extend the security of applications proven in the traditional ROM to the AI-ROM. One compiler simply prepends a public salt to the random oracle, showing that salting generically provably defeats preprocessing." @default.
- W2951004906 created "2019-06-27" @default.
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- W2951004906 date "2017-01-01" @default.
- W2951004906 modified "2023-09-26" @default.
- W2951004906 title "Random Oracles and Non-Uniformity." @default.
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