Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFinding Collisions in Interactive Protocols -- Tight Lower Bounds on the Round and Communication Complexities of Statistically Hiding Commitments
95
0
0.0
(
0
)
Added by
Iftach Haitner
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We study the round and communication complexities of various cryptographic protocols. We give tight lower bounds on the round and communication complexities of any fully black-box reduction of a statistically hiding commitment scheme from one-way permutations, and from trapdoor permutations. As a corollary, we derive similar tight lower bounds for several other cryptographic protocols, such as single-server private information retrieval, interactive hashing, and oblivious transfer that guarantees statistical security for one of the parties. Our techniques extend the collision-finding oracle due to Simon (EUROCRYPT 98) to the setting of interactive protocols and the reconstruction paradigm of Gennaro and Trevisan (FOCS 00).
rate research
Read More
We put forth a new computational notion of entropy, measuring the (in)feasibility of sampling high-entropy strings that are consistent with a given generator. Specifically, the ith output block of a generator G has accessible entropy at most k if the following holds: when conditioning on its prior coin tosses, no polynomial-time strategy $widetilde{G}$ can generate valid output for Gs ith output block with entropy greater than k. A generator has inaccessible entropy if the total accessible entropy (summed over the blocks) is noticeably smaller than the real entropy of Gs output. As an application of the above notion, we improve upon the result of Haitner, Nguyen, Ong, Reingold, and Vadhan [Sicomp 09], presenting a much simpler and more efficient construction of statistically hiding commitment schemes from arbitrary one-way functions.
We investigate the randomized and quantum communication complexities of the well-studied Equality function with small error probability $epsilon$, getting the optimal constant factors in the leading terms in a number of different models. In the randomized model, 1) we give a general technique to convert public-coin protocols to private-coin protocols by incurring a small multiplicative error, at a small additive cost. This is an improvement over Newmans theorem [Inf. Proc. Let.91] in the dependence on the error parameter. 2) Using this we obtain a $(log(n/epsilon^2)+4)$-cost private-coin communication protocol that computes the $n$-bit Equality function, to error $epsilon$. This improves upon the $log(n/epsilon^3)+O(1)$ upper bound implied by Newmans theorem, and matches the best known lower bound, which follows from Alon [Comb. Prob. Comput.09], up to an additive $loglog(1/epsilon)+O(1)$. In the quantum model, 1) we exhibit a one-way protocol of cost $log(n/epsilon)+4$, that uses only pure states and computes the $n$-bit Equality function to error $epsilon$. This bound was implicitly already shown by Nayak [PhD thesis99]. 2) We show that any $epsilon$-error one-way protocol for $n$-bit Equality that uses only pure states communicates at least $log(n/epsilon)-loglog(1/epsilon)-O(1)$ qubits. 3) We exhibit a one-way protocol of cost $log(sqrt{n}/epsilon)+3$, that uses mixed states and computes the $n$-bit Equality function to error $epsilon$. This is also tight up to an additive $loglog(1/epsilon)+O(1)$, which follows from Alons result. Our upper bounds also yield upper bounds on the approximate rank and related measures of the Identity matrix. This also implies improved upper bounds on these measures for the distributed SINK function, which was recently used to refute the randomized and quant
Key-agreement protocols whose security is proven in the random oracle model are an important alternative to protocols based on public-key cryptography. In the random oracle model, the parties and the eavesdropper have access to a shared random function (an oracle), but the parties are limited in the number of queries they can make to the oracle. The random oracle serves as an abstraction for black-box access to a symmetric cryptographic primitive, such as a collision resistant hash. Unfortunately, as shown by Impagliazzo and Rudich [STOC 89] and Barak and Mahmoody [Crypto 09], such protocols can only guarantee limited secrecy: the key of any $ell$-query protocol can be revealed by an $O(ell^2)$-query adversary. This quadratic gap between the query complexity of the honest parties and the eavesdropper matches the gap obtained by the Merkles Puzzles protocol of Merkle [CACM 78]. In this work we tackle a new aspect of key-agreement protocols in the random oracle model: their communication complexity. In Merkles Puzzles, to obtain secrecy against an eavesdropper that makes roughly $ell^2$ queries, the honest parties need to exchange $Omega(ell)$ bits. We show that for protocols with certain natural properties, ones that Merkles Puzzle has, such high communication is unavoidable. Specifically, this is the case if the honest parties queries are uniformly random, or alternatively if the protocol uses non-adaptive queries and has only two rounds. Our proof for the first setting uses a novel reduction from the set-disjointness problem in two-party communication complexity. For the second setting we prove the lower bound directly, using information-theoretic arguments.
A $k$-collision for a compressing hash function $H$ is a set of $k$ distinct inputs that all map to the same output. In this work, we show that for any constant $k$, $Thetaleft(N^{frac{1}{2}(1-frac{1}{2^k-1})}right)$ quantum queries are both necessary and sufficient to achieve a $k$-collision with constant probability. This improves on both the best prior upper bound (Hosoyamada et al., ASIACRYPT 2017) and provides the first non-trivial lower bound, completely resolving the problem.
We prove tight network topology dependent bounds on the round complexity of computing well studied $k$-party functions such as set disjointness and element distinctness. Unlike the usual case in the CONGEST model in distributed computing, we fix the function and then vary the underlying network topology. This complements the recent such results on total communication that have received some attention. We also present some applications to distributed graph computation problems. Our main contribution is a proof technique that allows us to reduce the problem on a general graph topology to a relevant two-party communication complexity problem. However, unlike many previous works that also used the same high level strategy, we do not reason about a two-party communication problem that is induced by a cut in the graph. To `stitch back the various lower bounds from the two party communication problems, we use the notion of timed graph that has seen prior use in network coding. Our reductions use some tools from Steiner tree packing and multi-commodity flow problems that have a delay constraint.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
