Constructive tt-secure Homomorphic Secret Sharing for Low Degree Polynomials

This paper proposes $t$-secure homomorphic secret sharing schemes for low degree polynomials. Homomorphic secret sharing is a cryptographic technique to outsource the computation to a set of servers while restricting some subsets of servers from learning the secret inputs. Prior to our work, at Asiacrypt 2018, Lai, Malavolta, and Schröder proposed a $1$-secure scheme for computing polynomial functions. They also alluded to $t$-secure schemes without giving explicit constructions; constructing such schemes would require solving set cover problems, which are generally NP-hard. Moreover, the resulting implicit schemes would require a large number of servers. In this paper, we provide a constructive solution for threshold-$t$ structures by combining homomorphic encryption with the classic secret sharing scheme for general access structure by Ito, Saito, and Nishizeki. Our scheme also quantitatively improves the number of required servers from $O(t^2)$ to $O(t)$, compared to the implicit scheme of Lai et al. We also suggest several ideas for future research directions

FairBlock: Preventing Blockchain Front-running with Minimal Overheads

While blockchain systems are quickly gaining popularity, front-running remains a major obstacle to fair exchange. Front-running is a family of strategies in which a malicious party manipulates the order of transactions such that a transaction tx_2 which is broadcasted in time t_2 executes before the transaction of victim tx_1 which is broadcasted earlier in time t_1 (t_1 < t_2). In this thesis, we show how to apply Identity-Based Encryption (IBE) to prevent front-running with minimal bandwidth overheads. In our approach, to decrypt a block of N transactions, the number of messages sent across the network only grows linearly with the size of decrypting committees, S. That is, to decrypt a set of N transactions sequenced at a specific block, a committee only needs to exchange S decryption shares (independent of N). In comparison, previous solutions are based on threshold decryption schemes, where each transaction in a block must be decrypted separately by the committee, resulting in bandwidth overhead of N*S. Along the way, we present a model for fair block processing, explore technical challenges, and build prototype implementations. We show that on a sample of 1000 messages with 1000 validators our work saves 42.53 MB of bandwidth which is 99.6% less compared with the standard threshold decryption paradigm

Sublinear Computation Paradigm

This open access book gives an overview of cutting-edge work on a new paradigm called the “sublinear computation paradigm,” which was proposed in the large multiyear academic research project “Foundations of Innovative Algorithms for Big Data.” That project ran from October 2014 to March 2020, in Japan. To handle the unprecedented explosion of big data sets in research, industry, and other areas of society, there is an urgent need to develop novel methods and approaches for big data analysis. To meet this need, innovative changes in algorithm theory for big data are being pursued. For example, polynomial-time algorithms have thus far been regarded as “fast,” but if a quadratic-time algorithm is applied to a petabyte-scale or larger big data set, problems are encountered in terms of computational resources or running time. To deal with this critical computational and algorithmic bottleneck, linear, sublinear, and constant time algorithms are required. The sublinear computation paradigm is proposed here in order to support innovation in the big data era. A foundation of innovative algorithms has been created by developing computational procedures, data structures, and modelling techniques for big data. The project is organized into three teams that focus on sublinear algorithms, sublinear data structures, and sublinear modelling. The work has provided high-level academic research results of strong computational and algorithmic interest, which are presented in this book. The book consists of five parts: Part I, which consists of a single chapter on the concept of the sublinear computation paradigm; Parts II, III, and IV review results on sublinear algorithms, sublinear data structures, and sublinear modelling, respectively; Part V presents application results. The information presented here will inspire the researchers who work in the field of modern algorithms