Constant weight strings in constant time: a building block for code-based post-quantum cryptosystems

Code based cryptosystems often need to encode either a message or a random bitstring into one of fixed length and fixed (Hamming) weight. The lack of an efficient and reliable bijective map presents a problem in building constructions around the said cryptosystems to attain security against active attackers. We present an efficiently computable, bijective function which yields the desired mapping. Furthermore, we delineate how the said function can be computed in constant time. We experimentally validate the effectiveness and efficiency of our approach, comparing it against the current state of the art solutions, achieving three to four orders of magnitude improvements in computation time, and validate its constant runtim

Postings List Compression with Run-length and Zombit Encodings

Inverted indices is a core index structure for different low-level structures, like search engines and databases. It stores a mapping from terms, numbers etc. to list of location in document, set of documents, database, table etc. and allows efficient full-text searches on indexed structure. Mapping location in the inverted indicies is usually called a postings list. In real life applications, scale of the inverted indicies size can grow huge. Therefore efficient representation of it is needed, but at the same time, efficient queries must be supported. This thesis explores ways to represent postings lists efficiently, while allowing efficient nextGEQ queries on the set. Efficient nextGEQ queries is needed to implement inverted indicies. First we convert postings lists into one bitvector, which concatenates each postings list's characteristic bitvector. Then representing an integer set efficiently converts to representing this bitvector efficiently, which is expected to have long runs of 0s and 1s. Run-length encoding of bitvector have recently led to promising results. Therefore in this thesis we experiment two encoding methods (Top-k Hybrid coder, RLZ) that encode postings lists via run-length encodes of the bitvector. We also investigate another new bitvector compression method (Zombit-vector), which encodes bitvectors by finding redundancies of runs of 0/1s. We compare all encoding to current state-of-the-art Partitioned Elisa-Fano (PEF) coding. Compression results on all encodings were more efficient than the current state-of-the-art PEF encoding. Zombit-vector nextGEQ query results were slighty more efficient than PEF's, which make it more attractive with bitvectors that have long runs of 0s and 1s. More work is needed with Top-k Hybrid coder and RLZ, so that those encodings nextGEQ can be compared to Zombit-vector and PEF

A prefix encoding for a constructed language

This work focuses in the formal and technical analysis of some aspects of a constructed language. As a first part of the work, a possible coding for the language will be studied, emphasizing the pre x coding, for which an extension of the Hu man algorithm from binary to n-ary will be implemented. Because of that in the language we can't know a priori the frequency of use of the words, a study will be done and several strategies will be proposed for an open words system, analyzing previously the existing number of words in current natural languages. As a possible upgrade of the coding, we'll take also a look to the synchronization loss problem, as well as to its solution: the self-synchronization, a t-codes study with the number of possible words for the language, as well as other alternatives. Finally, and from a less formal approach, several applications for the language have been developed: A voice synthesizer, a speech recognition system and a system font for the use of the language in text processors. For each of these applications, the process used for its construction, as well as the problems encountered and still to solve in each will be detailed

SicHash -- Small Irregular Cuckoo Tables for Perfect Hashing

A Perfect Hash Function (PHF) is a hash function that has no collisions on a given input set. PHFs can be used for space efficient storage of data in an array, or for determining a compact representative of each object in the set. In this paper, we present the PHF construction algorithm SicHash - Small Irregular Cuckoo Tables for Perfect Hashing. At its core, SicHash uses a known technique: It places objects in a cuckoo hash table and then stores the final hash function choice of each object in a retrieval data structure. We combine the idea with irregular cuckoo hashing, where each object has a different number of hash functions. Additionally, we use many small tables that we overload beyond their asymptotic maximum load factor. The most space efficient competitors often use brute force methods to determine the PHFs. SicHash provides a more direct construction algorithm that only rarely needs to recompute parts. Our implementation improves the state of the art in terms of space usage versus construction time for a wide range of configurations. At the same time, it provides very fast queries

Near-capacity joint source and channel coding of symbol values from an infinite source set using Elias Gamma Error correction codes

In this paper we propose a novel low-complexity Joint Source and Channel Code (JSCC), which we refer to as the Elias Gamma Error Correction (EGEC) code. Like the recently-proposed Unary Error Correction (UEC) code, this facilitates the practical near-capacity transmission of symbol values that are randomly selected from a set having an infinite cardinality, such as the set of all positive integers. However, in contrast to the UEC code, our EGEC code is a universal code, facilitating the transmission of symbol values that are randomly selected using any monotonic probability distribution. When the source symbols obey a particular zeta probability distribution, our EGEC scheme is shown to offer a 3.4 dB gain over a UEC benchmarker, when Quaternary Phase Shift Keying (QPSK) modulation is employed for transmission over an uncorrelated narrowband Rayleigh fading channel. In the case of another zeta probability distribution, our EGEC scheme offers a 1.9 dB gain over a Separate Source and Channel Coding (SSCC) benchmarker

Perfect Hash Function Generation on the GPU with RecSplit

Minimale perfekte Hashfunktionen (MPHFs) bilden eine statische Menge S von beliebigen Schlüsseln auf die Menge der ersten |S| natürlichen Zahlen bijektiv ab, d. h., jeder Hashwert wird exakt einmal verwendet. Sie sind in vielen Anwendungen hilfreich, zum Beispiel, um Hashtabellen mit garantiert konstanter Zugriffszeit zu implementieren. MPHFs können sehr kompakt sein — weniger als 2 Bit pro Schlüssel sind möglich. Andererseits sind MPHFs nicht in der Lage zu entscheiden, ob ein gegebener Schlüssel zu S gehört. Zurzeit ist RecSplit die speichereffizienteste MPHF. RecSplit bietet verschiedene Kompromisse zwischen Platzverbrauch, Konstruktionszeit und Anfragezeit an. RecSplit kann zum Beispiel eine MPHF mit 1.56 Bits pro Schlüssel in weniger als 2 ms pro Schlüssel konstruieren. Das ist jedoch zu langsam für große Eingaben. Diese Arbeit präsentiert neue RecSplit-Implementierungen, die Multithreading, SIMD und die Leistung von GPUs nutzen, um die Konstruktionszeit zu verbessern. Gemeinsam mit unserer neuen bijection-rotation-Methode erreichen wir Beschleunigungen um Faktoren bis zu 333 für unsere SIMD-Implementierung auf einer 8-Kern CPU und bis zu 1873 für unsere GPU-Implementierung verglichen mit der originalen, sequenziellen RecSplit-Implementierung. Dadurch können wir MPHFs mit 1.56 Bits pro Schlüssel in weniger als 1.5 μs pro Schlüssel konstruieren

Binary RDF for Scalable Publishing, Exchanging and Consumption in the Web of Data

El actual diluvio de datos está inundando la web con grandes volúmenes de datos representados en RDF, dando lugar a la denominada 'Web de Datos'. En esta tesis proponemos, en primer lugar, un estudio profundo de aquellos textos que nos permitan abordar un conocimiento global de la estructura real de los conjuntos de datos RDF, HDT, que afronta la representación eficiente de grandes volúmenes de datos RDF a través de estructuras optimizadas para su almacenamiento y transmisión en red. HDT representa efizcamente un conjunto de datos RDF a través de su división en tres componentes: la cabecera (Header), el diccionario (Dictionary) y la estructura de sentencias RDF (Triples). A continuación, nos centramos en proveer estructuras eficientes de dichos componentes, ocupando un espacio comprimido al tiempo que se permite el acceso directo a cualquier dat