Non-Malleable Codes for Small-Depth Circuits

We construct efficient, unconditional non-malleable codes that are secure against tampering functions computed by small-depth circuits. For constant-depth circuits of polynomial size (i.e. $\mathsf{AC^0}$ tampering functions), our codes have codeword length $n = k^{1+o(1)}$ for a $k$-bit message. This is an exponential improvement of the previous best construction due to Chattopadhyay and Li (STOC 2017), which had codeword length $2^{O(\sqrt{k})}$. Our construction remains efficient for circuit depths as large as $\Theta(\log(n)/\log\log(n))$ (indeed, our codeword length remains $n\leq k^{1+\epsilon})$, and extending our result beyond this would require separating $\mathsf{P}$ from $\mathsf{NC^1}$. We obtain our codes via a new efficient non-malleable reduction from small-depth tampering to split-state tampering. A novel aspect of our work is the incorporation of techniques from unconditional derandomization into the framework of non-malleable reductions. In particular, a key ingredient in our analysis is a recent pseudorandom switching lemma of Trevisan and Xue (CCC 2013), a derandomization of the influential switching lemma from circuit complexity; the randomness-efficiency of this switching lemma translates into the rate-efficiency of our codes via our non-malleable reduction.Comment: 26 pages, 4 figure

On Pseudorandom Encodings

We initiate a study of pseudorandom encodings: efficiently computable and decodable encoding functions that map messages from a given distribution to a random-looking distribution. For instance, every distribution that can be perfectly and efficiently compressed admits such a pseudorandom encoding. Pseudorandom encodings are motivated by a variety of cryptographic applications, including password-authenticated key exchange, “honey encryption” and steganography. The main question we ask is whether every efficiently samplable distribution admits a pseudorandom encoding. Under different cryptographic assumptions, we obtain positive and negative answers for different flavors of pseudorandom encodings, and relate this question to problems in other areas of cryptography. In particular, by establishing a two-way relation between pseudorandom encoding schemes and efficient invertible sampling algorithms, we reveal a connection between adaptively secure multiparty computation for randomized functionalities and questions in the domain of steganography

Statistical validation of simulation models: A case study

Rigorous statistical validation requires that the responses of the model and the real system have the same expected values. However, the modeled and actual responses are not comparable if they are obtained under different scenarios (environmental conditions). Moreover, data on the real system may be unavailable; sensitivity analysis can then be applied to find out whether the model inputs have effects on the model outputs that agree with the experts' intuition. Not only the total model, but also its modules may be submitted to such sensitivity analyses. This article illustrates these issues through a case study, namely a simulation model for the use of sonar to search for mines on the sea bottom. The methodology, however, applies to models in general.Simulation Models;Statistical Validation;statistics

Self-Organized Structures: Modeling Polistes dominula Nest Construction with Simple Rules

The self-organized nest construction behaviors of European paper wasps (Polistes dominula) show potential for adoption in artificial intelligence and robotic systems where centralized control proves challenging. However, P. dominula nest construction mechanisms are not fully understood. This research investigated how nest structures stimulate P. dominula worker action at different stages of nest construction. A novel stochastic site selection model, weighted by simple rules for cell age, height, and wall count, was implemented in a three-dimensional, step-by-step nest construction simulation. The simulation was built on top of a hexagonal coordinate system to improve precision and performance. Real and idealized nest data were used to evaluate simulated nests via two parameters: outer wall counts and compactness numbers. Structures generated with age-based rules were not significantly different from real nest structures along both parameters

Why Philosophers Should Care About Computational Complexity

One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In particular, I argue that computational complexity theory---the field that studies the resources (such as time, space, and randomness) needed to solve computational problems---leads to new perspectives on the nature of mathematical knowledge, the strong AI debate, computationalism, the problem of logical omniscience, Hume's problem of induction, Goodman's grue riddle, the foundations of quantum mechanics, economic rationality, closed timelike curves, and several other topics of philosophical interest. I end by discussing aspects of complexity theory itself that could benefit from philosophical analysis.Comment: 58 pages, to appear in "Computability: G\"odel, Turing, Church, and beyond," MIT Press, 2012. Some minor clarifications and corrections; new references adde