No abstract

We prove that Alekhnovich's algorithm can be used for row reduction of skew polynomial matrices. This yields an O(ℓ 3 n (ω+1)/2 log(n)) decoding algorithm for ℓ-Interleaved Gabidulin codes of length n, where ω is the matrix multiplication exponent, improving in the exponent of n compared to previous results.

Abstract-Gabidulin codes, originally defined over finite fields, are an important class of rank metric codes with various applications. Recently, their definition was generalized to certain fields of characteristic zero and a Welch-Berlekamp like algorithm with complexity O(n 3 ) was given. We propose a new application of Gabidulin codes over infinite fields: low-rank matrix recovery. Also, an alternative decoding approach is presented based on a Gao type key equation, reducing the complexity to at least O(n 2 ). This method immediately connects the decoding problem to well-studied problems, which have been investigated in terms of coefficient growth and numerical stability.

For preserving privacy, blockchains can be equipped with dedicated mechanisms to anonymize participants. However, these mechanism often take only the abstraction layer of blockchains into account whereas observations of the underlying network traffic can reveal the originator of a transaction request. Previous solutions either provide topological privacy that can be broken by attackers controlling a large number of nodes, or offer strong and cryptographic privacy but are inefficient up to practical unusability. Further, there is no flexible way to trade privacy against efficiency to adjust to practical needs. We propose a novel approach that combines existing mechanisms to have quantifiable and adjustable cryptographic privacy which is further improved by augmented statistical measures that prevent frequent attacks with lower resources. This approach achieves flexibility for privacy and efficency requirements of different blockchain use cases.

Dining-cryptographers networks (DCN) can achieve information-theoretical privacy. Unfortunately, they are not well suited for peer-to-peer networks as they are used in blockchain applications to disseminate transactions and blocks among participants. In previous but preliminary work, we proposed a threephase approach with an initial phase based on a DCN with a group size of k while later phases take care of the actual broadcast within a peer-to-peer network. This paper describes our DCN protocol in detail and adds a performance evaluation powered by our proof-of-concept implementation. Our contributions are (i) an extension of the DCN protocol by von Ahn for fair delivery of arbitrarily long messages sent by potentially multiple senders, (ii) a privacy and security analysis of this extension, (iii) various performance optimisation especially for best-case operation, and (iv) a performance evaluation. The latter uses a latency of 100 ms and a bandwidth limit of 50 Mbit s −1 between participants. The interquartile range of the largest test of the highly secured version took 35s ± 1.25s for a full run. All tests of the optimized common-case mode show the dissemination of a message within 0.5s ± 0.1s. These results compare favourably to previously established protocols for k-anonymous transmission of fixed size messages, outperforming the original protocol for messages as small as 2 KiB.