A Simple Construction of iO for Turing Machines

We give a simple construction of indistinguishability obfus- cation for Turing machines where the time to obfuscate grows only with the description size of the machine and otherwise, independent of the running time and the space used. While this result is already known [Koppula, Lewko, and Waters, STOC 2015] from iO for circuits and injective pseudorandom generators, our construction and its analysis are conceptually much simpler. In particular, the main technical com- ponent in the proof of our construction is a simple combinatorial peb- bling argument [Garg and Srinivasan, EUROCRYPT 2018]. Our con- struction makes use of indistinguishability obfuscation for circuits and somewhere statistically binding hash functions

Output-Compressing Randomized Encodings and Applications

We consider randomized encodings (RE) that enable encoding a Turing machine Pi and input x into its ``randomized encoding\u27\u27 \hat{Pi}(x) in sublinear, or even polylogarithmic, time in the running-time of Pi(x), independent of its output length. We refer to the former as sublinear RE and the latter as compact RE. For such efficient RE, the standard simulation-based notion of security is impossible, and we thus consider a weaker (distributional) indistinguishability-based notion of security: Roughly speaking, we require indistinguishability of \hat{Pi}_0(x_0) and \hat{Pi}_0(x_1) as long as Pi_0,x_0 and Pi_1,x_1 are sampled from some distributions such that Pi_0(x_0),Time(Pi_0(x_0)) and Pi_1(x_1),Time(Pi_1(x_1)) are indistinguishable. We first observe that compact RE is equivalent to a variant of the notion of indistinguishability obfuscation (iO)---which we refer to as puncturable iO---for the class of Turing machines without inputs. For the case of circuits, puncturable iO and iO are equivalent (and this fact is implicitly used in the powerful ``punctured program\u27\u27 paradigm by Sahai and Waters [SW13]). We next show the following: - Impossibility in the Plain Model: Assuming the existence of subexponentially secure one-way functions, subexponentially-secure sublinear RE does not exists. (If additionally assuming subexponentially-secure iO for circuits we can also rule out polynomially-secure sublinear RE.) As a consequence, we rule out also puncturable iO for Turing machines (even those without inputs). - Feasibility in the CRS model and Applications to iO for circuits: Subexponentially-secure sublinear RE in the CRS model and one-way functions imply iO for circuits through a simple construction generalizing GGM\u27s PRF construction. Additionally, any compact (even with sublinear compactness) functional encryption essentially directly yields a sublinear RE in the CRS model, and as such we get an alternative, modular, and simpler proof of the results of [AJ15,BV15] showing that subexponentially-secure sublinearly compact FE implies iO. We further show other ways of instantiating sublinear RE in the CRS model (and thus also iO): under the subexponential LWE assumption, it suffices to have a subexponentially secure FE schemes with just sublinear ciphertext (as opposed to having sublinear encryption time). - Applications to iO for Unbounded-input Turing machines: Subexponentially-secure compact RE for natural restricted classes of distributions over programs and inputs (which are not ruled out by our impossibility result, and for which we can give candidate constructions) imply iO for unbounded-input Turing machines. This yields the first construction of iO for unbounded-input Turing machines that does not rely on (public-coin) differing-input obfuscation

How crystals that sense and respond to their environments could evolve

An enduring mystery in biology is how a physical entity simple enough to have arisen spontaneously could have evolved into the complex life seen on Earth today. Cairns-Smith has proposed that life might have originated in clays which stored genomes consisting of an arrangement of crystal monomers that was replicated during growth. While a clay genome is simple enough to have conceivably arisen spontaneously, it is not obvious how it might have produced more complex forms as a result of evolution. Here, we examine this possibility in the tile assembly model, a generalized model of crystal growth that has been used to study the self-assembly of DNA tiles. We describe hypothetical crystals for which evolution of complex crystal sequences is driven by the scarceness of resources required for growth. We show how, under certain circumstances, crystal growth that performs computation can predict which resources are abundant. In such cases, crystals executing programs that make these predictions most accurately will grow fastest. Since crystals can perform universal computation, the complexity of computation that can be used to optimize growth is unbounded. To the extent that lessons derived from the tile assembly model might be applicable to mineral crystals, our results suggest that resource scarcity could conceivably have provided the evolutionary pressures necessary to produce complex clay genomes that sense and respond to changes in their environment

Algorithmic Complexity for Short Binary Strings Applied to Psychology: A Primer

Since human randomness production has been studied and widely used to assess executive functions (especially inhibition), many measures have been suggested to assess the degree to which a sequence is random-like. However, each of them focuses on one feature of randomness, leading authors to have to use multiple measures. Here we describe and advocate for the use of the accepted universal measure for randomness based on algorithmic complexity, by means of a novel previously presented technique using the the definition of algorithmic probability. A re-analysis of the classical Radio Zenith data in the light of the proposed measure and methodology is provided as a study case of an application.Comment: To appear in Behavior Research Method