Arithmetic complexity via effective names for random sequences

We investigate enumerability properties for classes of sets which permit recursive, lexicographically increasing approximations, or left-r.e. sets. In addition to pinpointing the complexity of left-r.e. Martin-L\"{o}f, computably, Schnorr, and Kurtz random sets, weakly 1-generics and their complementary classes, we find that there exist characterizations of the third and fourth levels of the arithmetic hierarchy purely in terms of these notions. More generally, there exists an equivalence between arithmetic complexity and existence of numberings for classes of left-r.e. sets with shift-persistent elements. While some classes (such as Martin-L\"{o}f randoms and Kurtz non-randoms) have left-r.e. numberings, there is no canonical, or acceptable, left-r.e. numbering for any class of left-r.e. randoms. Finally, we note some fundamental differences between left-r.e. numberings for sets and reals

Small generic hardcore subsets for the discrete logarithm: short secret DL-Keys

Abstract Let G be a group of prime order q with generator g. We study hardcore subsets H ⊂ G of the discrete logarithm (DL) log g in the model of generic algorithms. In this model we count group operations such as multiplication and division, while computations with non-group data are for free. It is known from Nechaev [Math. Notes 55 (1994

Taxonomic Features and Comparison of the Gut Microbiome from Two Edible Fungus-Farming Termites (Macrotermes falciger, M. natalensis) Harvested in the Vhembe District of Limpopo, South Africa

Background Termites are an important food resource for many human populations around the world, and are a good supply of nutrients. The fungus-farming ‘higher’ termite members of Macrotermitinae are also consumed by modern great apes and are implicated as critical dietary resources for early hominins. While the chemical nutritional composition of edible termites is well known, their microbiomes are unexplored in the context of human health. Here we sequenced the V4 region of the 16S rRNA gene of gut microbiota extracted from the whole intestinal tract of two Macrotermes sp. soldiers collected from the Limpopo region of South Africa. Results Major and minor soldier subcastes of M. falciger exhibit consistent differences in taxonomic representation, and are variable in microbial presence and abundance patterns when compared to another edible but less preferred species, M. natalensis. Subcaste differences include alternate patterns in sulfate-reducing bacteria and methanogenic Euryarchaeota abundance, and differences in abundance between Alistipes and Ruminococcaceae. M. falciger minor soldiers and M. natalensissoldiers have similar microbial profiles, likely from close proximity to the termite worker castes, particularly during foraging and fungus garden cultivation. Compared with previously published termite and cockroach gut microbiome data, the taxonomic representation was generally split between termites that directly digest lignocellulose and humic substrates and those that consume a more distilled form of nutrition as with the omnivorous cockroaches and fungus-farming termites. Lastly, to determine if edible termites may point to a shared reservoir for rare bacterial taxa found in the gut microbiome of humans, we focused on the genus Treponema. The majority of Treponemasequences from edible termite gut microbiota most closely relate to species recovered from other termites or from environmental samples, except for one novel OTU strain, which clustered separately with Treponema found in hunter-gatherer human groups. Conclusions Macrotermes consumed by humans display special gut microbial arrangements that are atypical for a lignocellulose digesting invertebrate, but are instead suited to the simplified nutrition in the fungus-farmer diet. Our work brings to light the particular termite microbiome features that should be explored further as avenues in human health, agricultural sustainability, and evolutionary research

A Machine-Checked Formalization of the Generic Model and the Random Oracle Model

Most approaches to the formal analyses of cryptographic protocols make the perfect cryptography assumption, i.e. the hypothese that there is no way to obtain knowledge about the plaintext pertaining to a ciphertext without knowing the key. Ideally, one would prefer to rely on a weaker hypothesis on the computational cost of gaining information about the plaintext pertaining to a ciphertext without knowing the key. Such a view is permitted by the Generic Model and the Random Oracle Model which provide non-standard computational models in which one may reason about the computational cost of breaking a cryptographic scheme. Using the proof assistant Coq, we provide a machine-checked account of the Generic Model and the Random Oracle Mode

Sustainable Energy Storage

This Final Design Review document covers the work we, students at California Polytechnic State University – San Luis Obispo, have performed in collaboration with Mr. Harish Bhutani and Dr. Mohammad Noori. The project’s intent is to create an energy storage system for off-grid and developing region applications using alternative technologies to lithium-ion battery storage. We plan to manufacture and assemble a scale model of the energy storage system to prove effectiveness and practicality. This system will store enough energy to power basic appliances and essential devices for a house or community. The chosen design direction will be a flywheel, as it is very energy dense and is less complex than other options. The following will outline the entire design process, including the ideas we created, the design challenges, and the testing of our physical build. To meet climate change goals set around the globe, our world needs to head towards a more sustainable future, and the energy sector is no exception. This project aims to help with the research and design of this new field and present a final product that will have a meaningful impact on our world

Gradual sub-lattice reduction and a new complexity for factoring polynomials

We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type structure, where the target vectors are boundably short. For such applications, the complexity of the algorithm improves traditional lattice reduction by replacing some dependence on the bit-length of the input vectors by some dependence on the bound for the output vectors. If the bit-length of the target vectors is unrelated to the bit-length of the input, then our algorithm is only linear in the bit-length of the input entries, which is an improvement over the quadratic complexity floating-point LLL algorithms. To illustrate the usefulness of this algorithm we show that a direct application to factoring univariate polynomials over the integers leads to the first complexity bound improvement since 1984. A second application is algebraic number reconstruction, where a new complexity bound is obtained as well

Universal fluctuations in subdiffusive transport

Subdiffusive transport in tilted washboard potentials is studied within the fractional Fokker-Planck equation approach, using the associated continuous time random walk (CTRW) framework. The scaled subvelocity is shown to obey a universal law, assuming the form of a stationary Levy-stable distribution. The latter is defined by the index of subdiffusion alpha and the mean subvelocity only, but interestingly depends neither on the bias strength nor on the specific form of the potential. These scaled, universal subvelocity fluctuations emerge due to the weak ergodicity breaking and are vanishing in the limit of normal diffusion. The results of the analytical heuristic theory are corroborated by Monte Carlo simulations of the underlying CTRW

A Tale of Three Signatures: practical attack of ECDSA with wNAF

One way of attacking ECDSA with wNAF implementation for the scalar multiplication is to perform a side-channel analysis to collect information, then use a lattice based method to recover the secret key. In this paper, we reinvestigate the construction of the lattice used in one of these methods, the Extended Hidden Number Problem (EHNP). We find the secret key with only 3 signatures, thus reaching the theoretical bound given by Fan, Wang and Cheng, whereas best previous methods required at least 4 signatures in practice. Our attack is more efficient than previous attacks, in particular compared to times reported by Fan et al. at CCS 2016 and for most cases, has better probability of success. To obtain such results, we perform a detailed analysis of the parameters used in the attack and introduce a preprocessing method which reduces by a factor up to 7 the overall time to recover the secret key for some parameters. We perform an error resilience analysis which has never been done before in the setup of EHNP. Our construction is still able to find the secret key with a small amount of erroneous traces, up to 2% of false digits, and 4% with a specific type of error. We also investigate Coppersmith's methods as a potential alternative to EHNP and explain why, to the best of our knowledge, EHNP goes beyond the limitations of Coppersmith's methods

The invertibility of the XOR of rotations of a binary word

We prove the following result regarding operations on a binary word whose length is a power of two: computing the exclusive-or of a number of rotated versions of the word is an invertible (one-to-one) operation if and only if the number of versions combined is odd. (This result is not new; there is at least one earlier proof, due to Thomsen [Cryptographic hash functions, PhD thesis, Technical University of Denmark, 28 November 2008]. Our proof may be new.