Proceedings ArticleDOI
Lower bounds on the efficiency of encryption and digital signature schemes
Rosario Gennaro,Yael Gertner,Jonathan Katz +2 more
- pp 417-425
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TLDR
It is shown that any black-box construction beating the authors' lower bounds would imply the unconditional existence of a one-way function, in an extension of the Impagliazzo-Rudich model.Abstract:
A central focus of modern cryptography is to investigate the weakest possible assumptions under which various cryptographic algorithms exist. Typically, a proof that a "weak" primitive (e.g., a one-way function) implies the existence of a "strong" algorithm (e.g., a private-key encryption scheme) proceeds by giving an explicit construction of the latter from the former. In addition to showing the existence of such a construction, an equally important research direction is to explore the efficiency of such constructions.Among the most fundamental cryptographic algorithms are digital signature schemes and schemes for public- or private-key encryption. Here, we show the first lower bounds on the efficiency of any encryption or signature construction based on black-box access to one-way or trapdoor one-way permutations. If S is the assumed security of the permutation π (i.e., no adversary of size S can invert π on a fraction larger than 1/S of its inputs), our results show that:Any public-key encryption scheme for m-bit messages must query π at least Ω(m log S) times.Any private-key encryption scheme for m-bit messages (with k-bit keys) must query π at least Ω(m-k/log S) times.Any signature verification algorithm for m-bit messages must query π at least Ω(m log S) times.Our bounds match known upper bounds for the case of encryption.We prove our results in an extension of the Impagliazzo-Rudich model. That is, we show that any black-box construction beating our lower bounds would imply the unconditional existence of a one-way function.read more
Citations
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Book ChapterDOI
Notions of Reducibility between Cryptographic Primitives
TL;DR: Starting with the seminal paper of Impagliazzo and Rudich [17], there has been a large body of work showing that various cryptographic primitives cannot be reduced to each other via “black-box” reductions.
Book ChapterDOI
Optimal structure-preserving signatures in asymmetric bilinear groups
TL;DR: This work uses the generic group model to prove a lower bound on the complexity of digital signature schemes and gives constructions of structure-preserving signatures that consist of 3 group elements only.
Book ChapterDOI
On the generic insecurity of the full domain hash
TL;DR: This work investigates the question if it is possible to instantiate the random oracle h with a “real” family of hash functions such that the corresponding schemes can be proven secure in the standard model, under some natural assumption on the family $\mathcal{F}$.
Journal ArticleDOI
Bounds on the Efficiency of Generic Cryptographic Constructions
TL;DR: It is shown that any black-box construction beating the authors' efficiency bound would yield the unconditional existence of a one-way function and thus, in particular, prove $P
eq NP$.
Proceedings ArticleDOI
Finding Collisions in Interactive Protocols - A Tight Lower Bound on the Round Complexity of Statistically-Hiding Commitments
TL;DR: In this paper, a tight lower bound on the round complexity of any fully-black-box construction of a statistically-hiding commitment scheme from oneway permutations, and even front trapdoor permutations was derived.
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Proceedings ArticleDOI
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