Notation Preferences — Secure and Distributed Computing

Type your preferred LaTeX symbol and press Enter. Changes apply across all pages.

Key	Meaning	Your Symbol	Default
gauss	Real Gaussian distribution		$\mathcal{N}$
cgauss	Circularly symmetric complex Gaussian		$\mathcal{CN}$
covmat	Covariance matrix		$\boldsymbol{\Sigma}$
snr	Signal-to-noise ratio		$\text{SNR}$
n0	One-sided noise power spectral density		$N_0$
bw	Signal bandwidth (Hz)		$W$
noisevar	Noise variance / noise power		$\sigma^2$

Universal Conventions

Fixed conventions used throughout the SC book. These are standard across the secure-and-distributed-computing literature and are not customizable.

General Mathematics

Symbol	Meaning
$\mathbb{R}, \mathbb{C}$	Real and complex number fields
$\mathbb{F}_q$	Finite field of order $q$ (prime power)
$\mathbb{Z}_p$	Integers modulo $p$
$\mathbb{R}^n, \mathbb{C}^n, \mathbb{F}_q^n$	$n$ -dimensional vector spaces over the indicated field
$\|\mathcal{S}\|$	Cardinality of set $\mathcal{S}$
$\mathcal{O}(\cdot), \Theta(\cdot)$	Big-O and tight-bound asymptotic notation
$\triangleq$	Defined as

Distributed Computing System

Symbol	Meaning
$N$	Number of workers (Parts I–II) or databases (Part IV)
$n$	Number of users in federated learning (Parts III, V)
$K$	Recovery threshold (Part II); number of files (Part IV)
$T$	Collusion threshold (PIR) or Byzantine fault tolerance
$B$	Maximum number of Byzantine workers
$\mu \in [0, 1]$	Computation load: fraction of dataset stored per worker
$\Delta$	Communication load (bits exchanged, normalized)
$\mathbf{g}_k$	Local gradient (or message) of user/worker $k$
$\mathbf{G}$	Aggregated gradient: $\sum_{k=1}^n \mathbf{g}_k$

Cryptographic / Coding Primitives

Symbol	Meaning
$s$	Secret to be shared among parties
$s_k$	Secret share held by party $k$
$p(x)$	Encoding polynomial (Shamir / coded computing)
$(t, n)$ -threshold	Any $t$ shares reconstruct; any $t-1$ learn nothing
$C_{\text{PIR}}$	Private-information-retrieval capacity
$R_{\text{comp}}, R_{\text{comm}}$	Computation and communication rates

Wireless / Channel

Symbol	Meaning
$\mathbf{H}$	Channel matrix (where applicable, Part V)
$\mathbf{w}$	Additive white Gaussian noise vector
$\text{SNR}$	Signal-to-noise ratio