Explain like I'm five · InfoSec

What is Homomorphic Encryption?

Homomorphic encryption, told as a story about a sealed letter whose number you can add without breaking the seal.

adding these three means breaking their sealssecret amount Asecret amount Bsecret amount C

The scribe needs to add up three merchants' secret amounts.He needs the total — but until now, adding meant breaking the seal first.

30opened it to read itnow the scribe knows A's amount is 30each amount added gives away one secret

Open a seal to add an amount, and the scribe learns it.Each amount added gives away one secret: every amount had to be shown to whoever does the adding.

the sealed totalonly the key's owner opens itthe scribe added them without ever breaking a seal

Homomorphic encryption adds the cards while they're still sealed.The scribe added them without ever breaking a seal. Only the owner holding the key can open the total.

Add while still sealedmath, without opening it
Some can multiply toofully homomorphic schemes both add and multiply
The one computing can't peekeven the scribe never sees the number
Slow and heavyfar slower than doing the math unsealed
plain computation① open the seals② add the amounts③ the amounts and total are exposedhomomorphic computation① add while sealed② the result stays sealed③ only the owner opens it58the same sum: plain math reveals it to the scribe, homomorphic math only to the owner

Plain computation and homomorphic computation, side by side.The same sum — but plain computation shows the amounts to the scribe, while homomorphic computation shows only the total, only to the key's owner.

a simpler kind supports just one operationthe add-and-multiply kind runs far slower than add-onlyuseful for computing on medical or financial data handed to the cloud

Which math works depends on the type of homomorphic encryption, and all of it is far slower than plain computation.Homomorphic encryption is useful for computing on medical or financial data handed to the cloud. Other ways to mine statistics while protecting individuals exist too → PPDM

In one breath

Homomorphic encryption = a cipher that lets you add or multiply a letter while it stays sealed. Whoever computes never sees the content, and the result comes out sealed too — only the owner can open it.

A cryptographic technique that lets you operate directly on ciphertext and get a result that, once decrypted, matches applying the same operation to the plaintext. Partial homomorphic encryption (PHE) supports just one operation, addition or multiplication (Paillier, for example, adds); fully homomorphic encryption (FHE) supports both addition and multiplication. It lets a cloud compute on sensitive data without ever seeing it, though the computational cost is still very high.

When grown-ups say it

Homomorphic encryption
A letter you can do math on while sealed. You operate on the ciphertext itself. Decrypt the result, and it matches operating on the plaintext.
Partial HE
A simpler version with one operation. Supports either addition or multiplication directly on ciphertext.
Fully HE
A version that both adds and multiplies. Far more flexible than partial HE, but far slower too.
Ciphertext computation
Doing the math while it's sealed. The one computing never needs to know the content.
Confidential computing
Hiding the data even while it's being computed on. The term usually means hardware-protected enclaves (TEEs). Homomorphic encryption reaches the same goal a different way, through cryptography.
Decryption
Opening the seal. Ordinary encryption has to be opened before you compute. → the letter no one reads without the key
Outsourced cloud computation
Handing the computing to a rented warehouse. Homomorphic encryption lets you hand over the computing without ever showing the data.
PPDM
Other techniques for mining statistics while protecting individuals. Homomorphic encryption is one tool PPDM uses. → PPDM
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