FHE glossary — the words of computing without opening the data

Computing on encrypted data

also: FHE · homomorphic encryption · fully homomorphic encryption

In everyday terms: A locked glass box with gloves built in: the jeweller makes the ring through the gloves without ever holding the key.
What it means here: A way of encrypting data that still lets a server compute on it. The server adds, multiplies and compares without opening it; only the key holder reads the result.
Where it appears: The tutorial 20 applications Maturity

The locked data

also: ciphertext · encrypted data

In everyday terms: The gold inside the box: it is there, you can work on it through the gloves, but nobody outside can take it.
What it means here: Data after encryption. It is much larger than the original (one encrypted vote in this section's ballot box takes about 1.5 MB) and carries a little deliberate noise, which is what makes it secure.
Where it appears: The tutorial The maths

The padlock anyone can close

also: public key

In everyday terms: An open padlock you hand out: anyone can close the box with it, but nobody can open it again.
What it means here: The key used to encrypt. It can be published: whoever has it can lock data, but cannot read anything.
Where it appears: The tutorial The maths

The key only the owner has

also: private key · secret key

In everyday terms: The only key that opens the box. It stays in the data owner's pocket and never goes to the server.
What it means here: The key that decrypts. If it leaves the owner, nothing else matters; that is why, in the voting demo, it is split among several authorities.
Where it appears: The tutorial The split key

The key that lets the server compute

also: evaluation key · relinearisation and rotation keys

In everyday terms: The box's gloves: they give the jeweller the power to work the gold, not the power to take it out.
What it means here: Extra keys, derived from the secret one, that the server receives to multiply and to move positions inside the locked data. They can be huge: for cleanup at real security, 10.26 GB sent before starting.
Where it appears: The frontier Maturity

The dirt every operation leaves

also: noise · noise budget

In everyday terms: Every time the jeweller works through the gloves, the glass fogs a little. After too much work, you can no longer see the gold.
What it means here: Encrypted data carries deliberate noise. Every operation adds to it; multiplication adds a lot. Past the limit, the result is wrong, and silently so: on our bench, the eighth multiplication returned 28323 where the answer was 282, with no warning.
Where it appears: 20 applications The maths

How many multiplications fit in a row

also: multiplicative depth · levels

In everyday terms: How many times you can work the gold before the glass fogs for good.
What it means here: The budget of multiplications in sequence, fixed before starting. At real security it is small: our bench found that the parameter where it counted 8 fits only 2 levels.
Where it appears: The frontier Maturity

The cleanup that removes the dirt

also: bootstrap · bootstrapping · re-encryption

In everyday terms: Stopping, cleaning the glass from inside without opening the box, and only then carrying on.
What it means here: The operation that removes accumulated noise and restores the operation budget. It exists and works, but it is expensive: 1 min 18 s per run and 10.26 GB of keys on our bench, at real security.
Where it appears: The frontier Maturity

The three dialects

also: schemes · BFV/BGV · CKKS · TFHE

In everyday terms: Three different workshops: one works with counted pieces, one with approximate measurements, one piece by piece, on or off.
What it means here: There is no single FHE. There are three families, and each application needs one: exact integers, approximate decimal numbers, and bit-by-bit logic gates. Mixing them is possible and expensive.
Where it appears: 20 applications Maturity

Exact integers

also: BFV · BGV

In everyday terms: Counting votes in a ballot box: every unit counts, nothing extra, nothing missing.
What it means here: The dialect for whole-number arithmetic, without rounding. It is the one in our encrypted vote: each vote is a 1 in the candidate's position, and the sum comes out exact.
Where it appears: The tutorial 20 applications

Approximate decimal numbers

also: CKKS

In everyday terms: A kitchen scale: it gives the weight to a few decimals, and nobody expects lab precision.
What it means here: The dialect for real numbers, which accepts a small error at the end. Good for averages, scores and the last layer of AI models; not for deciding "which is largest" precisely.
Where it appears: 20 applications The frontier

Logic gates, bit by bit

also: TFHE

In everyday terms: A switchboard: each operation turns a lamp on or off depending on two others.
What it means here: The dialect that computes one bit at a time, with the cleanup built into every step. Good for logic and branches ("if this, then that"); slow for large arithmetic.
Where it appears: 20 applications Maturity

Many operations under one lock

also: slots · SIMD · batching · packing

In everyday terms: An ice tray: you fill every cavity at once and freeze them together.
What it means here: A single locked value carries thousands of numbers side by side (16,384 in our vote), and each operation applies to all of them at once. The costly part is not multiplying: it is moving numbers from one position to another inside the pack.
Where it appears: The tutorial The frontier

The hard problem holding the lock

also: lattice · LWE · RLWE

In everyday terms: Finding an exact point in a gigantic grid, in hundreds of dimensions, when someone nudged every coordinate a little.
What it means here: The mathematical problem FHE relies on. It is the same kind of problem behind the new post-quantum locks, which is why FHE also resists a quantum computer.
Where it appears: The maths Post-quantum

The size of the lock

also: parameter · logN · ring size

In everyday terms: A luggage padlock and a safe lock: both close, but one opens with a hairpin.
What it means here: The number that sets how large (and secure) the locked data is. The "toy" one (logN=13) is ~40 times faster than the real-security one (logN=16). When reading a vendor figure, ask which one they used.
Where it appears: Maturity The frontier

Real security

also: 128-bit security

In everyday terms: A password that, tried at the fastest possible pace, would take longer than the age of the universe to guess.
What it means here: The level the standard requires before calling a lock serious. Several published measurements (including some of our older ones) used weaker parameters than the label; on our pages, every figure says which level it was measured at.
Where it appears: The frontier Maturity

Deciding under encryption

also: comparison · argmax · "which is largest"

In everyday terms: Asking a blindfolded person which of two boxes is heavier, without lifting either.
What it means here: Only two moves exist under encryption: add and multiply. Comparing two values becomes a long chain of operations that uses 40 levels of the budget; without cleanup it is impossible, with cleanup picking the largest of 4 took 23 min 31 s.
Where it appears: The frontier

The open-result attack

also: IND-CPA-D · reaction attack

In everyday terms: A salesman who, just from seeing you accept or refuse offers, works out how much is in your wallet.
What it means here: When the encrypting side hands back to the server anything that depends on the decrypted result ("accepted or refused"), the server can learn the secret without attacking the key. In our measurements, in about 47 queries.
Where it appears: Maturity 20 applications

The control positions

also: canary

In everyday terms: The canary miners took into the mine: if it fell ill, there was gas.
What it means here: Positions with known values hidden in the pack. If they come back changed, someone tampered. They catch 100% of blind tampering and only 0.37% of someone who picks where to tamper: hygiene, not a guarantee.
Where it appears: Maturity 20 applications

Secrecy is not integrity

also: confidentiality vs integrity · verifiable FHE

In everyday terms: A sealed envelope guarantees nobody read the letter; it does not guarantee the postman delivered the right letter.
What it means here: FHE hides the data but does not prove the server did the agreed computation. If the server may be malicious, you need a proof of the computation or an attested machine, with published overheads from ~2% to over 1000%.
Where it appears: 20 applications Maturity

Proving without showing

also: zero-knowledge proof · ZKP · Sigma protocol

In everyday terms: Proving you know the safe's combination by opening it in front of someone, without saying the combination.
What it means here: A mathematical proof that something is true which does not reveal the secret. In the encrypted vote, each ballot carries a proof that it marks exactly one candidate, without saying which.
Where it appears: The tutorial

Stamping without seeing

also: blind signature · Chaum

In everyday terms: A notary stamping a paper inside a carbon-lined envelope: the stamp goes through, the contents stay hidden.
What it means here: A signature given without seeing what is signed. In the vote, the notary authorises the voter without knowing which credential will be used at the ballot box, so nobody can link the vote to the voter.
Where it appears: The tutorial

The split key: three of five

also: threshold · Shamir secret sharing

In everyday terms: A bank vault with five managers, where three must turn their keys together to open it.
What it means here: The decryption key is split among five authorities; any three together can decrypt the result, none alone can. In our demo: electoral court, bar association, public prosecutor, university and civil society.
Where it appears: The tutorial

The ballot box that shuffles

also: mixnet · mix network

In everyday terms: Shaking the ballot box before opening it, so nobody knows whose ballot was first.
What it means here: Even encrypted, the order of votes can reveal who voted ("vote 42 belongs to whoever came in at 14:03"). Three servers shuffle and re-lock them, each without knowing the others' order.
Where it appears: The tutorial

The receipt you can check

also: cryptographic receipt · hash · hash chain · bulletin board

In everyday terms: The ATM slip: you keep a number and later check on the public statement that the transaction is there.
What it means here: When you vote, you get the fingerprint of your locked ballot. On a public board, each entry chains to the previous one; changing a vote breaks the chain, and anyone can redo the sum and check the result.
Where it appears: The tutorial

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Sources

Quoted figures come from The frontier, Maturity and 20 applications, measured on our bench (Lattigo v6), and from the tutorial. Post-quantum terms are in the Post-quantum section glossary.