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There Is No Diffie-Hellman but Elliptic Curve Diffie-Hellman

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Re: There Is No Diffie-Hellman but Elliptic Curve Diffie-Hellman

#21

Post by thaumasiotes »

willvarfar wrote: post #20
thaumasiotes wrote: post #19

Earlier quoted context omitted.

What would that help with? I know KaTeX supposedly lets you copy-and-paste the text, but that won't get you text that is fit for any purpose.

(hopefully modern screen reading software is clever enough to OCR and summarise images as it does text. And if not, then that seems to be something that is now within reach of modern AI and just needs application.)

It wouldn't really matter; the image includes a lot of structure that isn't present in the text that KaTeX provides. A text-only screen reader will never produce anything but gibberish if you feed it KaTeX output.

KaTeX will also style the text so that it visually resembles the image, stopping this problem from occurring for non-blind readers. You could have a screen reader that parsed all of the layout, but it seems like you might just as well OCR the image at that point.

Re: There Is No Diffie-Hellman but Elliptic Curve Diffie-Hellman

#22

Post by mti »

cionx wrote: post #10
pwdisswordfishz wrote: post #8

Earlier quoted context omitted.

It makes some sense in the category of rings, but basically only there.

It’s also the standard notation for zero objects, i.e., for terminal objects that are also initial. This entails all abelian/additive/preadditive categories, such as categories of modules, vector spaces, or abelian groups. (But there are also counterexamples, such as the categories of groups and of pointed sets.) But I’d agree that it’s not standard notation to use 0 for a terminal object in an arbitrary category. I’…

The relevant category is really abelian group schemes (because DH necessarily works in a cyclic group), so 0 is quite reasonable.

Re: There Is No Diffie-Hellman but Elliptic Curve Diffie-Hellman

#23

Post by cmrx64 »

vitalnodo wrote: post #16

Just wondering — has anyone come across a course or resource that explores how cryptographic systems are built up from smaller building blocks? Like, using something like SageMath for algebraic structures, a prover like Lean to verify properties — to get a feel for how things actually fit together. There's something cool about trying to reimplement known standards just to understand them better (with the usual "don’t…

the types of arguments and proofs used in cryptography are notoriously difficult to mechanize, a little bit of lean isn’t going to go get anywhere close to stating a security property.

eg CryptHOL needs a ton of infrastructure, and in still very limited: https://eprint.iacr.org/2017/753.pdf

Re: There Is No Diffie-Hellman but Elliptic Curve Diffie-Hellman

#24

Post by cmrx64 »

tgma wrote: post #6

Not a cryptographer, but my expectation of the admitted-to-be-clickbait title would be to see a proof or some claim of that sort that characterizes traditional finite-field integer DH as a special case of ECDH. However, --and please correct me if I am wrong as I am not a cryptographer or a math wiz anymore-- my understanding is you could characterize both as instantiations of an abstract protocol on a cyclic group wi…

isn’t that how the article ends? maybe I don’t understand what you mean

Re: There Is No Diffie-Hellman but Elliptic Curve Diffie-Hellman

#25

Post by oleganza »

vitalnodo wrote: post #16

Just wondering — has anyone come across a course or resource that explores how cryptographic systems are built up from smaller building blocks? Like, using something like SageMath for algebraic structures, a prover like Lean to verify properties — to get a feel for how things actually fit together. There's something cool about trying to reimplement known standards just to understand them better (with the usual "don’t…

When I learned crypto 5-10 years ago, it turned out that a lot of "building blocks" are mostly hacks. Looking back from 2020s we see that some of the standards that we use for the last 20-30 years can in principle be thrown out of the window (they can't for compatibility reasons, though) and replaced with much cleaner and more universal replacements.

If we do not talk about modern exotic stuff (post-quantum crypto, zkSNARKS, homomorphic encryption), the 99% of everyday cryptography is based on two building blocks:

1. Symmetric crypto for ciphers and hash functions.

2. Algebraic group with "hard discrete log problem" for key exchange, signatures, asymmetric encryption and simple zero-knowledge proofs.

Historically, these two categories are filled with a zoo of protocols. E.g. AES is a block cipher, but SHA(1,2) is a hash function.

Today, you can roughly achieve everything of the above with two universal building blocks:

- Keccak for all of symmetric crypto: it is suited both for encryption, hashing, duplex transcripts for ZK protocols etc.

- Ristretto255 group based on Curve 25519: for diffie-hellman, signatures, key derivation, threshold schemes, encryption and more.

The problem is that none of the described features is implemented in a turnkey standard, and we are still stuck using older crypto. Heck, even Git is using SHA-1 still.

Then, after you have your building blocks, there are more hairy stuff such as application-specific protocols: TLS, Signal, PAKE/OPAQUE, proprietary hardware security schemes for full disk encryption and access controls etc.

Re: There Is No Diffie-Hellman but Elliptic Curve Diffie-Hellman

#26

Post by tgma »

cmrx64 wrote: post #24
tgma wrote: post #6

Not a cryptographer, but my expectation of the admitted-to-be-clickbait title would be to see a proof or some claim of that sort that characterizes traditional finite-field integer DH as a special case of ECDH. However, --and please correct me if I am wrong as I am not a cryptographer or a math wiz anymore-- my understanding is you could characterize both as instantiations of an abstract protocol on a cyclic group wi…

isn’t that how the article ends? maybe I don’t understand what you mean

As I see it, the article describes something in that vein, but then immediately flips and reasserts the title, which suggests integer DH is a special case of ECDH, which does not seem a convincing characterization to me (it could be my misunderstanding; maybe someone could further clarify if it is conclusive).

Re: There Is No Diffie-Hellman but Elliptic Curve Diffie-Hellman

#27

Post by eXpl0it3r »

oleganza wrote: post #25
vitalnodo wrote: post #16

Just wondering — has anyone come across a course or resource that explores how cryptographic systems are built up from smaller building blocks? Like, using something like SageMath for algebraic structures, a prover like Lean to verify properties — to get a feel for how things actually fit together. There's something cool about trying to reimplement known standards just to understand them better (with the usual "don’t…

When I learned crypto 5-10 years ago, it turned out that a lot of "building blocks" are mostly hacks. Looking back from 2020s we see that some of the standards that we use for the last 20-30 years can in principle be thrown out of the window (they can't for compatibility reasons, though) and replaced with much cleaner and more universal replacements. If we do not talk about modern exotic stuff (post-quantum crypto, z…

I'm absolutely clueless about crypto, isn't there also a trade-off between being mathematically superior and well optimized in software/hardware implementation?

Re: There Is No Diffie-Hellman but Elliptic Curve Diffie-Hellman

#28

Post by [deleted] »

thaumasiotes wrote: post #19
jhanschoo wrote: post #18

The author seems to be a busy person, but I would appreciate it if they would consider modifying their blog publishing software so that the math and definitions could be rendered in text and KaTeX instead of raster images.

What would that help with? I know KaTeX supposedly lets you copy-and-paste the text, but that won't get you text that is fit for any purpose.

[deleted]

Re: There Is No Diffie-Hellman but Elliptic Curve Diffie-Hellman

#29

Post by looofooo0 »

oleganza wrote: post #25
vitalnodo wrote: post #16

Just wondering — has anyone come across a course or resource that explores how cryptographic systems are built up from smaller building blocks? Like, using something like SageMath for algebraic structures, a prover like Lean to verify properties — to get a feel for how things actually fit together. There's something cool about trying to reimplement known standards just to understand them better (with the usual "don’t…

When I learned crypto 5-10 years ago, it turned out that a lot of "building blocks" are mostly hacks. Looking back from 2020s we see that some of the standards that we use for the last 20-30 years can in principle be thrown out of the window (they can't for compatibility reasons, though) and replaced with much cleaner and more universal replacements. If we do not talk about modern exotic stuff (post-quantum crypto, z…

sha-1 in git was just supposed to catch corruption, it was never intended to be used for security.

Re: There Is No Diffie-Hellman but Elliptic Curve Diffie-Hellman

#30

Post by k__ »

vitalnodo wrote: post #16

Just wondering — has anyone come across a course or resource that explores how cryptographic systems are built up from smaller building blocks? Like, using something like SageMath for algebraic structures, a prover like Lean to verify properties — to get a feel for how things actually fit together. There's something cool about trying to reimplement known standards just to understand them better (with the usual "don’t…

Not really, but I liked this one.

https://github.com/nakov/practical-cryptography-for-develope...

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