![]() Hence, our results show that, even if one-way functions do not exist, we still have ABE schemes with meaningful security. Our main technical contribution is constructing ABE schemes without using pairing or the Diffie-Hellman assumption. Previously, all of these schemes were unknown in fine-grained cryptography. By properly instantiating the underlying encoding, we can obtain different types of ABE schemes, including identity-based encryption. Our construction is adaptively secure under the widely accepted worst-case assumption, $NC1 \subsetneq \oplus L/poly$, and it is presented in a generic manner using the notion of predicate encodings (Wee, TCC’14). In this paper, we enrich the available tools in fine-grained cryptography by proposing the first fine-grained secure attribute-based encryption (ABE) scheme. Currently, only simple form of encryption schemes, such as secret-key and public-key encryption, are constructed in this setting. Springer, Berlin, pp 557–578, 2015).įine-grained cryptography is constructing cryptosystems in a setting where an adversary’s resource is a-prior bounded and an honest party has less resource than an adversary. (in: Public-key cryptography-PKC 2015, volume 9020 of LNCS. Particularly, our construction simplifies and unifies the result due to Qin et al. We then show that NMFs give rise to a generic construction of RKA-secure authenticated key derivation functions, which have proven to be very useful in achieving RKA security for numerous cryptographic primitives. We first show that, somewhat surprisingly, the implication AOW $$\Rightarrow $$ ⇒ ANM sheds light on addressing non-trivial copy attacks in RKA security. Finally, we explore applications of NMFs in security against related-key attacks (RKA). This partially solves an open problem posed by Boldyreva et al. Toward efficient realizations of NMFs, we give a deterministic construction from adaptive trapdoor functions as well as a randomized construction from all-but-one lossy functions and one-time signature. We also study the relations between standard OW/NM and hinting OW/NM, where the latter notions are typically more useful in practice. These results establish theoretical connections between non-malleability and one-wayness for functions and extend to trapdoor functions as well, resolving the open problems left by Kiltz et al. In the adaptive setting, we show that for most algebra-induced transformation classes, adaptive non-malleability (ANM) is equivalent to adaptive one-wayness (AOW) for injective functions. In the non-adaptive setting, we show that non-malleability generally implies one-wayness for poly-to-one functions but not vice versa. We investigate the relations between non-malleability and one-wayness in depth. ![]() We also consider the adaptive notion, which stipulates that non-malleability holds even when an inversion oracle is available. Our non-malleable notion is strong in the sense that only trivial copy solution $$(\mathsf $$ id is the identity transformation. Roughly, a function f is non-malleable if given an image $$y^* \leftarrow f(x^*)$$ y ∗ ← f ( x ∗ ) for a randomly chosen $$x^*$$ x ∗, it is hard to output a value y together with a transformation $$\phi $$ ϕ from some prefixed transformation class such that y is an image of $$\phi (x^*)$$ ϕ ( x ∗ ) under f. We formalize a game-based definition for NMFs. NMFs focus on basic functions, rather than one-way/hash functions considered in the literature of NMOWHFs. (in: Advances in cryptology-ASIACRYPT 2009, pp 524–541, 2009) and refined by Baecher et al. We formally study “non-malleable functions” (NMFs), a general cryptographic primitive which simplifies and relaxes “non-malleable one-way/hash functions” (NMOWHFs) introduced by Boldyreva et al. ![]()
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