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The Beginner's Textbook for Fully Homomorphic Encryption

arxiv.org

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Re: The Beginner's Textbook for Fully Homomorphic Encryption

#41

Post by dcminter »

hamburgererror wrote: post #40

Let's admit for a second that the problem around computational cost is solved and using FHE is similar to using plaintext data. My question might be very naive but I'd like to better understand the impact of FHE, discussions here seem to revolve very much around the use of FHE in ML, but are there other uses for FHE? For example, could it be used for everyday work in an OS or a messaging app? Also, is it the path for…

That's a big stretch for the premise, but...

There's no value to it in circumstances where you control all the hardware processing data, so "everyday work in an OS" - only if that OS is hosted on someone else's hardware, "a messaging app" - only if you expect some of the messages or metadata to undergo processing on someone else's hardware.

It seems wildly unlikely that the performance characteristics will improve dramatically, so in practice the uses are going to remain somewhat niche.

Re: The Beginner's Textbook for Fully Homomorphic Encryption

#42

Post by hamburgererror »

dcminter wrote: post #41
hamburgererror wrote: post #40

Let's admit for a second that the problem around computational cost is solved and using FHE is similar to using plaintext data. My question might be very naive but I'd like to better understand the impact of FHE, discussions here seem to revolve very much around the use of FHE in ML, but are there other uses for FHE? For example, could it be used for everyday work in an OS or a messaging app? Also, is it the path for…

That's a big stretch for the premise, but... There's no value to it in circumstances where you control all the hardware processing data, so "everyday work in an OS" - only if that OS is hosted on someone else's hardware, "a messaging app" - only if you expect some of the messages or metadata to undergo processing on someone else's hardware. It seems wildly unlikely that the performance characteristics will improve dr…

> There's no value to it in circumstances where you control all the hardware processing data

But what about the case where you don't have so much control about what runs next to your program? Could it be possible for an attacker to run a program in order to extract some data when your program is run?

Also, could FHE offer some protection against vulnerabilities like Meltdown and Spectre?

> It seems wildly unlikely that the performance characteristics will improve dramatically

Why? Are there some specific signs for this already? I had the impression that everytime people tend to believe that with technology they get proven wrong later.

Re: The Beginner's Textbook for Fully Homomorphic Encryption

#43

Post by GTP »

hamburgererror wrote: post #42
dcminter wrote: post #41

Earlier quoted context omitted.

That's a big stretch for the premise, but... There's no value to it in circumstances where you control all the hardware processing data, so "everyday work in an OS" - only if that OS is hosted on someone else's hardware, "a messaging app" - only if you expect some of the messages or metadata to undergo processing on someone else's hardware. It seems wildly unlikely that the performance characteristics will improve dr…

> There's no value to it in circumstances where you control all the hardware processing data But what about the case where you don't have so much control about what runs next to your program? Could it be possible for an attacker to run a program in order to extract some data when your program is run? Also, could FHE offer some protection against vulnerabilities like Meltdown and Spectre? > It seems wildly unlikely th…

The tipical, and also most useful, example use case for FHE is running computational tasks on some cloud service without having to trust it. And yes, it would provide protection against Meltdown and Spectre (if performed on the hardware running the computation), as the attacker would be able to only extract encrypted data.

Re: The Beginner's Textbook for Fully Homomorphic Encryption

#44

Post by ogogmad »

LeGrosDadai wrote: post #15
EGreg wrote: post #11

Funny thing is Since neural networks are differentiable, they can be homomorphically encrypted! That’s right, your LLM can be made to secretly produce stuff hehe

That's pretty cool, but isn't any computable function can be computed via FHE, so I'm not sure the differentiable part is necessary.

Any program which you apply FHE to needs to be expressed as a circuit, which implies that the time taken to run a computation needs to be fixed in advance. It's therefore impossible to express a branch instruction (or "if" statement, if you prefer).

The circuits are built out of "+" and "×" gates, which are enough to express any polynomial. In turn, these are enough to approximate any continuous function (Weierstrass's approximation theorem). In turn, every computable function on the real numbers is a continuous function - so FHE is very powerful.

Re: The Beginner's Textbook for Fully Homomorphic Encryption

#45

Post by vishakh82 »

adgjlsfhk1 wrote: post #36
vishakh82 wrote: post #26

Earlier quoted context omitted.

It's really not that bad. We're close to using FHE in a production consumer app. https://vishakh.blog/2025/08/06/lessons-from-using-fhe-to-bu...

if you're talking about doing database queries on a 5mb database, why not just ship the database client side and have them do the computation?

You may wish to build a protocol where third parties can asynchronously operate on user data. You may also want to have separation between the end app and the compute layer for legal or practical purposes. Finally, you may not want to store large payloads on client devices.

Re: The Beginner's Textbook for Fully Homomorphic Encryption

#46

Post by jlokier »

ogogmad wrote: post #44
LeGrosDadai wrote: post #15

Earlier quoted context omitted.

That's pretty cool, but isn't any computable function can be computed via FHE, so I'm not sure the differentiable part is necessary.

Any program which you apply FHE to needs to be expressed as a circuit, which implies that the time taken to run a computation needs to be fixed in advance. It's therefore impossible to express a branch instruction (or "if" statement, if you prefer). The circuits are built out of "+" and "×" gates, which are enough to express any polynomial. In turn, these are enough to approximate any continuous function (Weierstrass…

> In turn, every computable function on the real numbers is a continuous function

That doesn't seem right. Consider the function f(x: ℝ) = 1 if x ≥ 0, 0 otherwise. That's computable but not continuous.

Re: The Beginner's Textbook for Fully Homomorphic Encryption

#47

Post by dcminter »

GTP wrote: post #43
hamburgererror wrote: post #42

Earlier quoted context omitted.

> There's no value to it in circumstances where you control all the hardware processing data But what about the case where you don't have so much control about what runs next to your program? Could it be possible for an attacker to run a program in order to extract some data when your program is run? Also, could FHE offer some protection against vulnerabilities like Meltdown and Spectre? > It seems wildly unlikely th…

The tipical, and also most useful, example use case for FHE is running computational tasks on some cloud service without having to trust it. And yes, it would provide protection against Meltdown and Spectre (if performed on the hardware running the computation), as the attacker would be able to only extract encrypted data.

The data has to be decrypted at some point in order to display it... unless we're envisioning FHME hardware in the monitor as well - honestly I think we're well across the threshold into fantasy already though.

Re: The Beginner's Textbook for Fully Homomorphic Encryption

#48

Post by adgjlsfhk1 »

vishakh82 wrote: post #45
adgjlsfhk1 wrote: post #36

Earlier quoted context omitted.

if you're talking about doing database queries on a 5mb database, why not just ship the database client side and have them do the computation?

You may wish to build a protocol where third parties can asynchronously operate on user data. You may also want to have separation between the end app and the compute layer for legal or practical purposes. Finally, you may not want to store large payloads on client devices.

5mb is hardly a "large payload"

Re: The Beginner's Textbook for Fully Homomorphic Encryption

#49

Post by ogogmad »

jlokier wrote: post #46
ogogmad wrote: post #44

Earlier quoted context omitted.

Any program which you apply FHE to needs to be expressed as a circuit, which implies that the time taken to run a computation needs to be fixed in advance. It's therefore impossible to express a branch instruction (or "if" statement, if you prefer). The circuits are built out of "+" and "×" gates, which are enough to express any polynomial. In turn, these are enough to approximate any continuous function (Weierstrass…

> In turn, every computable function on the real numbers is a continuous function That doesn't seem right. Consider the function f(x: ℝ) = 1 if x ≥ 0, 0 otherwise. That's computable but not continuous.

That's uncomputable because equality of real numbers is undecidable. Think infinite strings of digits.

Re: The Beginner's Textbook for Fully Homomorphic Encryption

#50

Post by vishakh82 »

adgjlsfhk1 wrote: post #48
vishakh82 wrote: post #45

Earlier quoted context omitted.

You may wish to build a protocol where third parties can asynchronously operate on user data. You may also want to have separation between the end app and the compute layer for legal or practical purposes. Finally, you may not want to store large payloads on client devices.

5mb is hardly a "large payload"

I'm giving you general reasons why this is the case. For our own app, we hope to build a protocol where third parties can operate async on user data (with consent).
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