gloss.tex

\newglossaryentry{gls-nb}
{
    symbol={\ensuremath{\rvdist{NB}}},
    name={negative binomial distribution},
    description={the discrete probability distribution that describes the number of Bernoulli trials needed for a specific number of ``successes''}
}

\newglossaryentry{gls-geo}
{
    symbol={\ensuremath{\rvdist{GEO}}},
    name={geometric distribution},
    description={the discrete probability distribution that describes the number of Bernoulli trials needed for a ``success''}
}

\newglossaryentry{gls-exp}
{
    symbol={\ensuremath{\rvdist{EXP}}},
    name={exponential distribution},
    description={the continuous probability distribution that describes the time between memorless events that occur continuously and independently at a constant average rate and is the continuous analogue of the geometric distribution}
}

\newglossaryentry{gls-uri}
{
    name={uniform resource identifier},
    description={description here}
}

\newglossaryentry{gls-map}
{
    name={mean average precision},
    description={}
}

\newglossaryentry{gls-tfidf}
{
    name={term frequency-inverse document frequency},
    description={a numerical heuristic that measures how important a word is to a document in a collection, where importance is proportional to the word's document frequency but is offset by the frequency of the word in the collection}    
}

\newglossaryentry{gls-ir}
{
    name={information retrieval},
    description={}
}

\newglossaryentry{approximateset}
{
    name={approximate set},
    description={a set where false negatives never occur but false positives may occur}
}

\newglossaryentry{gls-phf}
{
    name={perfect hash filter},
    description={a data structure that implements the abstract data type of the \gls*{approximateset} and is a function of a \gls*{ph}}
}

\newglossaryentry{gls-bf}
{
    name={bloom filter},
    description={a popular data structure that implements the abstract data type of the \gls*{approximateset}}
}

\newglossaryentry{gls-psi}
{
    name={PHF secure index},
    description={a bag-of-words \gls*{si} that uses the perfect hash filter, a data structure implementing the approximate set. Since it is a bag-of-words, it only supports membership tests.}
}

\newglossaryentry{gls-bsi}
{
    name={BF secure index},
    description={a bag-of-words \gls*{si} that uses the bloom filter, a data structure implementing the approximate set. Since it is a bag-of-words, it only supports membership tests.}
}

\newglossaryentry{gls-es}
{
    name={Encrypted Search},
    description={enables untrusted systems to \emph{obliviously} retrieve documents that satisfy the \glspl*{infoneed} of authorized \glspl*{sa}},
    plural={Encrypted Searches}
}

\newglossaryentry{gls-ph}
{
    name={perfect hash function},
    description={a hash function that guarantees no collisions among members of a given set},
    plural={perfect hash functions}
}

\newglossaryentry{gls-si}
{
    name={secure index},
    description={a search index of a confidential document that facilitates efficient \gls*{es}} operations,
    plural={secure indexes}
}

\newglossaryentry{gls-esp}
{
    name={\gls*{gls-es} provider},
    description={an \emph{untrusted} system that provides \gls*{es} activities}
}

\newglossaryentry{gls-ds}
{
    name={document store},
    description={a collection of confidential documents}
}

\newglossaryentry{wordbag}
{
    name={bag-of-words},
    description={a set of words representing an \gls*{infoneed} in information retrieval}
}

\newglossaryentry{obfuscator}
{
    name={obfuscator},
    description={a trusted agent that transforms a sequence of \gls*{plaintext} \glspl*{query} into a sequence of \glspl*{hq}}
}

\newglossaryentry{avgprecision}
{
    name={average precision},
    description={description here}
}

\newglossaryentry{preimageres}
{
    name={pre-image resistant},
    description={given a hash function $\operatorname{h}$ and a hash $x$, finding a $y$ such that $y = \operatorname{h}(x)$ is intractable}
}
    
\newglossaryentry{preimageattack}
{
    name={pre-image attack},
    description={given a hash function and a hash $x$, the \gls*{adversary} searches for an input for the given hash function that outputs the given hash value}
}

\newglossaryentry{compression}
{
    name={compression},
    description={substituting a bit string $x$ with a bit string $x' = \Compress(x)$ where $\BL(x') < \BL(x)$ and $x = \Decompress(x')$}
}

\newglossaryentry{adversary}
{
    name={adversary},
    description={an agent that is not authorized to comprehend the \gls*{es} activities, such as the \glspl*{infoneed} of \glspl*{sa}},
    plural={adversaries}
}

\newglossaryentry{randomoracle}
{
    name={random oracle},
    description={a theoretical hash function that \emph{uniformly} distributes inputs in the domain to outputs in the range}
}

\newglossaryentry{biword}
{
    name={biword model},
    description={sequences of \glspl*{word} are coded by a set of \glspl*{bigram} to facilitate search operations like \emph{exact phrase} matching}
}

\newglossaryentry{trapdoor}
{
    name=trapdoor,
    description={is a cryptographic transformation of a term in a search query}
}

\newglossaryentry{documentidentifier}
{
    name={document identififier},
    description={description here},
    plural={document identifiers}
}

\newglossaryentry{salt}
{
    name={salt},
    description={description here}, plural={salts}
}

\newglossaryentry{invertedindex}
{
    name={inverted index},
    description={description here}
}

\newglossaryentry{infoneed}
{
    name={information need},
    description={description here}
}

\newglossaryentry{hq}
{
    name=hidden query,
    description={a search \gls*{query} composed of \glspl*{trapdoor} to facilitate \gls*{es} operations}, plural={hidden queries}
}

\newglossaryentry{query}
{
    name={query},
    description={a string of characters, such as \glspl*{word}, that represents some \gls*{infoneed}}, plural={queries}
}

\newglossaryentry{bm25}
{
    name={BM25},
    description={a family of \gls*{tfidf}-like functions used in rank-ordered document retrieval}
}

\newglossaryentry{oblivioussearch}{name={oblivious search}, plural={oblivous searches}, description={description here}}
\newglossaryentry{homophonic}{name={Homophonic substitution}, description={is where the distribution of cipher-text symbols in a substitution cipher is made uniform by mapping a plain-text token to one or more cipher-text tokens}}
\newglossaryentry{obliviousram}{name={Oblivious RAM}, description={description here}}
\newglossaryentry{zipf}{name={Zipf}, description={description here}}
\newglossaryentry{queryobfuscation}{name={query obfuscation}, description={description here}}
\newglossaryentry{queryobrate}{name={query obfuscation rate}, description={is the probability that a \gls*{trapdoor} in a \gls*{hq} is an \emph{artificial} \gls*{trapdoor}}}


\newglossaryentry{gls-mle}
{
    name={maximum likelihood estimation},
    description={description here}
}

\newglossaryentry{trigram}
{
    name={trigram},
    description={3-gram}
}

\newglossaryentry{bigram}
{
    name={bigram},
    description={1-gram}
}

\newglossaryentry{unigram}
{
    name={unigram},
    description={1-gram}
}

\newglossaryentry{ngram}
{
    name={$n$-gram},
    description={a tuple of $n$ \glspl*{words}}
}

\newglossaryentry{plaintext}
{
    name={plain-text},
    description={description here}
}

\newglossaryentry{ciphertext}
{
    name={cipher-text},
    description={description here}
}

\newglossaryentry{precision}
{
    name={precision},
    description={description here}
}

\newglossaryentry{recall}
{
    name={recall},
    description={description here}
}

\newglossaryentry{symmetricencryption}
{
    name={symmetric encryption},
    description={description here}
}

\newglossaryentry{asymmetricencryption}
{
    name={asymmetric encryption},
    description={description here}
}

\newglossaryentry{booleansearch}
{
    name={Boolean search},
    description={description here},
    plural={Boolean searches}
}

\newglossaryentry{rankorderedsearch}
{
    name={rank-ordered search},
    description={description here},
    plural={rank-ordered searches}
}

\newglossaryentry{confidentiality}
{
    name={confidentiality},
    description={description here}
}

\newglossaryentry{documentconf}
{
    name={document confidentiality},
    description={description here}
}

\newglossaryentry{queryprivacy}
{
    name={query privacy},
    description={description here}
}

\newglossaryentry{obfuscation}
{
    name={obfuscation},
    description={description here}
}

\newglossaryentry{encryption}
{
    name={encryption},
    description={description here}
}

\newglossaryentry{sa}
{
    name={search agent},
    description={description here},
    plural={search agents}
}

\newglossaryentry{knownplaintextattack}
{
    name={known-plaintext attack},
    description={description here},
    plural={known-plaintext attacks}
}

\newglossaryentry{resultset}
{
    name={result set},
    description={description here},
    plural={result sets}
}

\newglossaryentry{entropy}
{
    name={entropy},
    description={description here}
}

\newglossaryentry{queryalphabet}
{
    name={\gls*{plaintext} \gls*{query} alphabet},
    description={the set of all \gls*{plaintext} \gls*{query} \glspl*{word}, a subset of $\cisb$}
}

\newglossaryentry{queryalphabetsizeparam}
{
    name={\ensuremath{m}},
    description={the cardinality of the set of all \gls*{plaintext} \gls*{query} \glspl*{word}},
    type=symbols
}

\newglossaryentry{trapdooralphabet}
{
    name={\ensuremath{m'}},
    description={the cardinality of the set of all \glspl*{trapdoor}, a subset of $\cisb_{m'}$},
    type=symbols
}

\newglossaryentry{trapdooralphabetsizeparam}
{
    name={\ensuremath{m'}},
    description={The cardinality of the set of all \gls*{plaintext} \gls*{query} \glspl*{word}},
    type=symbols
}

\newglossaryentry{sanumparam}
{
    name={\ensuremath{k}},
    description={the number of unique \glspl*{sa}},
    type=symbols
}

\newglossaryentry{queryarrivalrate}
{
    name={query arrival rate},
    description={the average number of queries to arrive at the \gls*{esp} per second}
}

\newglossaryentry{queryarrivalrateparam}
{
    name={\ensuremath{\lambda}},
    description={the expected number of queries to arrive at the \gls*{esp} per second},
    type=symbols
}

\newglossaryentry{integerset}
{
    name={\ensuremath{\mathbb{Z}}},
    description={The set of integers},
    type=symbols
}

\newglossaryentry{posintegerset}
{
    name=\ensuremath{\mathbb{Z}_{>0}},
    description={the set of positive integers $\{1,2,\ldots\}$},
    type=symbols
}

\newglossaryentry{nonnegativeintegerset}
{
    name={\ensuremath{\mathbb{Z}_{\geq 0}}},
    description={the set of non-negative integers $\mathbb{Z}_{>0} \cup \{0\}$},
    type=symbols
}

\newglossaryentry{realnumset}
{
    name={\ensuremath{\mathbb{R}}},
    description={is the set that includes integers, such as $1$, rational numbers, such as $\frac{1}{2}$, and irrational numbers, such as $\pi$},
    type=symbols
}

\newglossaryentry{posrealnumset}
{
    name={\ensuremath{\mathbb{R}_{>0}}},
    description={the set of positive real numbers},
    type=symbols
}

\newglossaryentry{bitstringset}
{
    name={\ensuremath{\cisb}},
    description={the set of all bit strings, $\{b \colon \{0,1\}^*\}$, where $*$ is all non-negative integers},
    type=symbols
}

\newglossaryentry{bitstringsetm}
{
    name={\ensuremath{\cisb_m}},
    description={the set of all bit strings of length $m$, $\{b \colon \{0,1\}\^m\}$, where $m$ is a non-negative integer},
    type=symbols
}

\newglossaryentry{rvplainwordssym}
{
    name={\ensuremath{\rv{\vec{M_j}}}},
    description={a random vector where each component is an element from the \gls*{queryalphabet}},
    type=symbols
}

\newglossaryentry{seqxsym}
{
    name={\ensuremath{x_{<j}}},
    description={a sequence $x_1 \cdots x_{j-1}$, e.g., $a_{<3} \equiv a_1 a_2$},
    type=symbols
}

\newglossaryentry{word}
{
    name={word},
    description={a \emph{searchable} bit string $x \in \cisb$}
}