2,515 research outputs found
Bloom Filters in Adversarial Environments
Many efficient data structures use randomness, allowing them to improve upon
deterministic ones. Usually, their efficiency and correctness are analyzed
using probabilistic tools under the assumption that the inputs and queries are
independent of the internal randomness of the data structure. In this work, we
consider data structures in a more robust model, which we call the adversarial
model. Roughly speaking, this model allows an adversary to choose inputs and
queries adaptively according to previous responses. Specifically, we consider a
data structure known as "Bloom filter" and prove a tight connection between
Bloom filters in this model and cryptography.
A Bloom filter represents a set of elements approximately, by using fewer
bits than a precise representation. The price for succinctness is allowing some
errors: for any it should always answer `Yes', and for any it should answer `Yes' only with small probability.
In the adversarial model, we consider both efficient adversaries (that run in
polynomial time) and computationally unbounded adversaries that are only
bounded in the number of queries they can make. For computationally bounded
adversaries, we show that non-trivial (memory-wise) Bloom filters exist if and
only if one-way functions exist. For unbounded adversaries we show that there
exists a Bloom filter for sets of size and error , that is
secure against queries and uses only
bits of memory. In comparison, is the best
possible under a non-adaptive adversary
Computational Evolutionary Embryogeny
Evolutionary and developmental processes are used to evolve the configurations of 3-D structures in silico to achieve desired performances. Natural systems utilize the combination of both evolution and development processes to produce remarkable performance and diversity. However, this approach has not yet been applied extensively to the design of continuous 3-D load-supporting structures. Beginning with a single artificial cell containing information analogous to a DNA sequence, a structure is grown according to the rules encoded in the sequence. Each artificial cell in the structure contains the same sequence of growth and development rules, and each artificial cell is an element in a finite element mesh representing the structure of the mature individual. Rule sequences are evolved over many generations through selection and survival of individuals in a population. Modularity and symmetry are visible in nearly every natural and engineered structure. An understanding of the evolution and expression of symmetry and modularity is emerging from recent biological research. Initial evidence of these attributes is present in the phenotypes that are developed from the artificial evolution, although neither characteristic is imposed nor selected-for directly. The computational evolutionary development approach presented here shows promise for synthesizing novel configurations of high-performance systems. The approach may advance the system design to a new paradigm, where current design strategies have difficulty producing useful solutions
The Journey from NP to TFNP Hardness
The class TFNP is the search analog of NP with the additional guarantee that any instance has a solution. TFNP has attracted extensive attention due to its natural syntactic subclasses that capture the computational complexity of important search problems from algorithmic game theory, combinatorial optimization and computational topology. Thus, one of the main research objectives in the context of TFNP is to search for efficient algorithms for its subclasses, and at the same time proving hardness results where efficient algorithms cannot exist.
Currently, no problem in TFNP is known to be hard under assumptions such as NP hardness, the existence of one-way functions, or even public-key cryptography. The only known hardness results are based on less general assumptions such as the existence of collision-resistant hash functions, one-way permutations less established cryptographic primitives (e.g. program obfuscation or functional encryption).
Several works explained this status by showing various barriers to proving hardness of TFNP. In particular, it has been shown that hardness of TFNP hardness cannot be based on worst-case NP hardness, unless NP=coNP. Therefore, we ask the following question: What is the weakest assumption sufficient for showing hardness in TFNP?
In this work, we answer this question and show that hard-on-average TFNP problems can be based on the weak assumption that there exists a hard-on-average language in NP. In particular, this includes the assumption of the existence of one-way functions. In terms of techniques, we show an interesting interplay between problems in TFNP, derandomization techniques, and zero-knowledge proofs
Congested Clique Algorithms for Graph Spanners
Graph spanners are sparse subgraphs that faithfully preserve the distances in the original graph up to small stretch. Spanner have been studied extensively as they have a wide range of applications ranging from distance oracles, labeling schemes and routing to solving linear systems and spectral sparsification. A k-spanner maintains pairwise distances up to multiplicative factor of k. It is a folklore that for every n-vertex graph G, one can construct a (2k-1) spanner with O(n^{1+1/k}) edges. In a distributed setting, such spanners can be constructed in the standard CONGEST model using O(k^2) rounds, when randomization is allowed.
In this work, we consider spanner constructions in the congested clique model, and show:
- a randomized construction of a (2k-1)-spanner with O~(n^{1+1/k}) edges in O(log k) rounds. The previous best algorithm runs in O(k) rounds;
- a deterministic construction of a (2k-1)-spanner with O~(n^{1+1/k}) edges in O(log k +(log log n)^3) rounds. The previous best algorithm runs in O(k log n) rounds. This improvement is achieved by a new derandomization theorem for hitting sets which might be of independent interest;
- a deterministic construction of a O(k)-spanner with O(k * n^{1+1/k}) edges in O(log k) rounds
Optimal Publishing Strategies on a Base Layer
A growing number of products use layer 2 solutions to expand the capabilities
of primary blockchains like Ethereum, where computation is off-loaded from the
root chain, and the results are published to it in bulk. Those include
optimistic and zero-knowledge rollups, information oracles, and app-specific
chains. This work presents an analysis of layer 2 blockchain strategies
determining the optimal times for publishing transactions on the root chain.
There is a trade-off between waiting for a better layer 1 gas price and the
urgency to finalize layer 2 transactions. We present a model for the problem
that captures this trade-off, generalizing previous works, and we analyze the
properties of optimal publishing strategies. We show that such optimal
strategies hold a computable simple form for a large class of cost functions.Comment: To be presented at Financial Cryptography and Data Security 2024 (FC
2024
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