Glossary (plain English)¶

Prereqs: none (lookup anytime)
Next: Orientation · How to read the math · Index

A quick dictionary for this curriculum. Each entry is one or two sentences plus a link to the teaching page. Skip freely; come back when a word feels fuzzy.

Habit: English first, symbols second. No page here uses school-grade labels — clarity is for everyone.

A–C¶

Term	Plain meaning	See
ADP	Area × delay — one circuit trade-off scalar in HW tables	Area–time honesty
Alternant code	Algebraic code family related to GRS; includes binary Goppa as a famous case	Goppa and alternant
Authenticity	Strangers cannot forge or silently edit a message	Why cryptography?
Bit	A \(0\) or \(1\)	Bits, XOR
Bit-flipping	Iterative decoder: flip bits that fail many parity checks	Bit-flipping decoding
Butterfly (NTT)	Local 2-in/2-out modular update with a twiddle	NTT butterfly
Ciphertext	Scrambled form that travels on the wire	Why cryptography?
Clock / register	Heartbeat + stored bits between ticks	Clocks, registers
Code / codeword	Allowed protected strings; a codeword is one allowed string	Error-correcting codes
Combinational logic	Outputs from current inputs only (no memory)	Clocks, registers
Confidentiality	Strangers cannot read the content	Why cryptography?
Critical path	Longest combo delay that limits the clock period (ns)	Clocks, registers
CVP	Closest vector problem — nearest lattice point to a target (slogan)	Lattices

D–G¶

Term	Plain meaning	See
DFR	How often honest Decaps fails to return the session key	DFR
Encaps / Decaps	KEM calls that create / recover a session key	KEM
Generator matrix \(G\)	Builds codewords from short messages	Generator and parity-check
Goppa code	Classic algebraic secret code for McEliece	Goppa and alternant
GRS	Generalized Reed–Solomon — strong algebra, often unsafe raw in McEliece	Goppa and alternant

H–K¶

Term	Plain meaning	See
Hamming distance	How many positions two strings disagree	Hamming metric
Hamming weight	How many nonzero positions (ones, for bits)	Hamming metric
Independence heuristic	Pretend noise coordinates are independent for easy tail bounds	Independence heuristics
IND-CPA / IND-CCA	Security games: chosen-plaintext vs also decryption-oracle powers	IND-CPA / CCA
ISD	Information-set decoding — main classical attack family on sparse decoding	ISD
KEM	Key encapsulation mechanism — API to ship a fresh session key	KEM
KEM accelerator	HW datapath + control that runs Encaps/Decaps hot paths	KEM accelerator anatomy
Key	Secret that controls scrambling / unscrambling	Why cryptography?
KL divergence	Score for how badly model \(Q\) describes reality \(P\)	KL divergence

L–N¶

Term	Plain meaning	See
Latency (cycles)	How many clock ticks until a result is ready	Clocks, registers
Lattice	Regular discrete grid of points	Lattices
Linear code	Code closed under XOR / field addition	Linear codes
LRPC	Low-rank parity-check codes (rank-metric family)	LRPC
LWE	Learning With Errors — noisy modular linear equations	LWE
MDPC / QC-MDPC	Moderate-density parity-check; QC = quasi-cyclic blocks	MDPC and QC-MDPC
McEliece	Public scramble of a secret easy code + intentional sparse error	McEliece in plain words
Minimum distance \(d\)	Smallest Hamming distance between distinct codewords	Hamming metric
Modular arithmetic	Clock / leftover wrap-around math	Modular arithmetic
Modular multiplier	HW/SW unit for \(a\cdot b \bmod q\)	Modular multiplier
Module-LWE	LWE with polynomial / module packaging (ML-KEM-shaped)	Module-LWE
Motivation (PQC)	Why migrate: quantum break of RSA/ECC + long-lived recorded traffic	Motivation
Niederreiter	Syndrome / parity-check packaging twin of McEliece	Niederreiter
NTT / INTT	Number-theoretic (inverse) transform — modular FFT for poly mul	NTT butterfly

P–S¶

Term	Plain meaning	See
Parity-check matrix \(H\)	Checklist of linear constraints; syndrome fingerprint	Generator and parity-check
Plaintext	Readable message before encryption	Why cryptography?
Poly-mul engine	Schoolbook / Karatsuba / NTT organization for polynomial multiply	Poly-mul engines
Public / secret key	Publishable padlock vs private opener	Public-key picture
PWM	Pointwise multiply of NTT-domain coefficients	Poly-mul engines
Quasi-cyclic (QC)	Structure from rotations / polynomials mod \(X^n-1\)	Quasi-cyclic codes
Rank metric	Error size = matrix rank after expanding symbols	Rank metric
Reaction attack	Learn secrets from decrypt success/fail bits	QC-MDPC reaction explainer
Redundancy	Extra symbols so noise can be corrected	From bits to codes
Security bits	Attack-work slogan (e.g. \(\sim 2^{128}\)), not DFR	Security bits
SNDL	Store now, decrypt later — record ciphertext today, break keys when quantum arrives	Motivation
Sparse	Low Hamming weight (few ones)	Hamming metric
Syndrome	\(He^\top\) — fingerprint of the error under checks \(H\)	Syndrome decoding
Syndrome decoding	Find sparse \(e\) matching a published syndrome	Syndrome decoding
SVP	Shortest nonzero lattice vector (slogan)	Lattices

T–Z¶

Term	Plain meaning	See
Trapdoor	Secret that makes a hard reverse easy for the owner	Hard problems
Twiddle	Precomputed root-of-unity power used inside NTT butterflies	NTT butterfly
XOR \(\oplus\)	Same bits → \(0\), different → \(1\); addition in \(\mathbb{F}_2\)	Bits, XOR
Wrap-around (\(X^n\equiv 1\))	Fold high powers back to fixed length \(n\)	Polynomial wrap-around

Symbol cheat strip¶

Symbol	Say aloud
\(\oplus\)	XOR
\(\equiv\pmod{n}\)	congruent mod \(n\) (same leftover)
\(\mathrm{wt}(e)\)	weight of \(e\)
\(H\mathbf{e}^\top=\mathbf{s}\)	\(H\) times \(e\) equals syndrome \(s\)
\(\Pr[\ldots]\)	probability that …
\(2^{-128}\)	astronomically small probability
\(2^{128}\)	enormous attack work (different job!)

More symbol practice: How to read the math.