<![CDATA[how diffie hellman key exchange works]]>how diffie hellman key exchange works

(with as little math as possible)

]]>https://board.circlewithadot.net/topic/b8ca400c-8c7f-4ad7-a1e0-b32980a267a3/how-diffie-hellman-key-exchange-worksRSS for NodeMon, 06 Apr 2026 16:06:55 GMTThu, 26 Mar 2026 19:46:42 GMT60<![CDATA[Reply to how diffie hellman key exchange works on Fri, 27 Mar 2026 14:13:59 GMT]]>@b0rk The Wikipedia article uses a color-mixing analogy that I've always liked. I used to know someone who would do the color-mixing thing live in a class she taught!

]]>https://board.circlewithadot.net/post/https://recurse.social/users/lindsey/statuses/116301551366204210https://board.circlewithadot.net/post/https://recurse.social/users/lindsey/statuses/116301551366204210Fri, 27 Mar 2026 14:13:59 GMT<![CDATA[Reply to how diffie hellman key exchange works on Fri, 27 Mar 2026 13:09:53 GMT]]>@b0rk @agturcz Ik love the smiley operator!

]]>https://board.circlewithadot.net/post/https://fosstodon.org/users/gerbrand/statuses/116301299305728325https://board.circlewithadot.net/post/https://fosstodon.org/users/gerbrand/statuses/116301299305728325Fri, 27 Mar 2026 13:09:53 GMT<![CDATA[Reply to how diffie hellman key exchange works on Fri, 27 Mar 2026 12:06:01 GMT]]>@b0rk like how you used 'hard to undo'. I used to explain it by saying the inverse is really hard to do but that explanation is simpler.

]]>https://board.circlewithadot.net/post/https://social.dropbear.xyz/users/smallsees/statuses/116301048167824722https://board.circlewithadot.net/post/https://social.dropbear.xyz/users/smallsees/statuses/116301048167824722Fri, 27 Mar 2026 12:06:01 GMT<![CDATA[Reply to how diffie hellman key exchange works on Fri, 27 Mar 2026 11:43:20 GMT]]>@bmitch @SnoopJ oops yeah thanks

]]>https://board.circlewithadot.net/post/https://social.jvns.ca/users/b0rk/statuses/116300958964575697https://board.circlewithadot.net/post/https://social.jvns.ca/users/b0rk/statuses/116300958964575697Fri, 27 Mar 2026 11:43:20 GMT<![CDATA[Reply to how diffie hellman key exchange works on Fri, 27 Mar 2026 07:59:22 GMT]]>@SnoopJ what do you mean by mixed up punctuation?

it’s trying to explain how on an elliptic curve, you start with an initial point s on the elliptic curve, choose a random integer x , and then add that point s to itself x times (using elliptic curve addition) to get the result of the “magic function”

]]>https://board.circlewithadot.net/post/https://social.jvns.ca/users/b0rk/statuses/116300078262778293https://board.circlewithadot.net/post/https://social.jvns.ca/users/b0rk/statuses/116300078262778293Fri, 27 Mar 2026 07:59:22 GMT<![CDATA[Reply to how diffie hellman key exchange works on Fri, 27 Mar 2026 06:27:30 GMT]]>@b0rk that’s a great explainer. You made it straightforward for me to understand how it works without having to know how the functions involved work (I don’t).
And the keys are for symmetric encryption, I guess?

]]>https://board.circlewithadot.net/post/https://mastodon.green/users/arildsen/statuses/116299717041362963https://board.circlewithadot.net/post/https://mastodon.green/users/arildsen/statuses/116299717041362963Fri, 27 Mar 2026 06:27:30 GMT<![CDATA[Reply to how diffie hellman key exchange works on Fri, 27 Mar 2026 04:36:16 GMT]]>@b0rk@social.jvns.ca No such groups are known yet. However one can easily prove that discrete log solves CDH, whereas no general reduction from CDH to discrete log exists, which in a way tells that DL is a "harder or equivalent" problem.

There exists however such a reduction for some elliptic curves (e.g. the NIST curves and Curve25519); these curves are usually preferred, as we then only depend on one problem being hard.]]>https://board.circlewithadot.net/post/https://misskey.de/notes/akbz3qeomlhttps://board.circlewithadot.net/post/https://misskey.de/notes/akbz3qeomlFri, 27 Mar 2026 04:36:16 GMT<![CDATA[Reply to how diffie hellman key exchange works on Fri, 27 Mar 2026 03:57:36 GMT]]>@b0rk fantastic work as usual, thanks for sharing

]]>https://board.circlewithadot.net/post/https://hachyderm.io/users/SnoopJ/statuses/116299127630961380https://board.circlewithadot.net/post/https://hachyderm.io/users/SnoopJ/statuses/116299127630961380Fri, 27 Mar 2026 03:57:36 GMT<![CDATA[Reply to how diffie hellman key exchange works on Fri, 27 Mar 2026 03:57:20 GMT]]>@b0rk am I missing something or is "add the result s to itself x times) a result of mixed-up puncutation? Did a double-take at that

]]>https://board.circlewithadot.net/post/https://hachyderm.io/users/SnoopJ/statuses/116299126587956532https://board.circlewithadot.net/post/https://hachyderm.io/users/SnoopJ/statuses/116299126587956532Fri, 27 Mar 2026 03:57:20 GMT<![CDATA[Reply to how diffie hellman key exchange works on Fri, 27 Mar 2026 01:19:36 GMT]]>@b0rk I love it. when I have taught this material, I have fallen back on the paint mixing analogy, but as a colorblind person this never felt right!

]]>https://board.circlewithadot.net/post/https://discuss.systems/users/palvaro/statuses/116298506322200467https://board.circlewithadot.net/post/https://discuss.systems/users/palvaro/statuses/116298506322200467Fri, 27 Mar 2026 01:19:36 GMT<![CDATA[Reply to how diffie hellman key exchange works on Fri, 27 Mar 2026 00:16:18 GMT]]>@esoteric_programmer will write some and let you know when it’s added

]]>https://board.circlewithadot.net/post/https://social.jvns.ca/users/b0rk/statuses/116298257451392990https://board.circlewithadot.net/post/https://social.jvns.ca/users/b0rk/statuses/116298257451392990Fri, 27 Mar 2026 00:16:18 GMT<![CDATA[Reply to how diffie hellman key exchange works on Thu, 26 Mar 2026 23:59:03 GMT]]>@b0rk I would boost it, but the attached image doesn't have any alt text, so I can't. What's the image about? is it showing a mathematical formula or something similar? a diagram?

]]>https://board.circlewithadot.net/post/https://social.stealthy.club/users/esoteric_programmer/statuses/01KMP9CNCKHZMMRTS2M563S95Vhttps://board.circlewithadot.net/post/https://social.stealthy.club/users/esoteric_programmer/statuses/01KMP9CNCKHZMMRTS2M563S95VThu, 26 Mar 2026 23:59:03 GMT<![CDATA[Reply to how diffie hellman key exchange works on Thu, 26 Mar 2026 23:04:38 GMT]]>@b0rk you can do it without maths at all. Say I want to give you my bicycle, but our schedules just will never work out for me to give you it directly. Well, we pick a place both of us can access, say outside the train station. I lock my bike up at a designated spot and go about my day. You come along with your own lock and use it to fasten the bike to the same spot without interfering with my lock, then go about your day. At some point I remove my lock, after which you can remove yours and gain a bicycle.

As I understand it, such a protocol was the inspiration for DH key exchange. Picking a spot is picking a generator. Locking is exponentiating. Locks not interfering is the commutativity property.

It's the explanation I always use when TAing cryptography

]]>https://board.circlewithadot.net/post/https://mathstodon.xyz/users/counting_is_hard/statuses/116297975623874396https://board.circlewithadot.net/post/https://mathstodon.xyz/users/counting_is_hard/statuses/116297975623874396Thu, 26 Mar 2026 23:04:38 GMT<![CDATA[Reply to how diffie hellman key exchange works on Thu, 26 Mar 2026 22:42:59 GMT]]>@b0rk Small typo in panel 4, choose = chose?

]]>https://board.circlewithadot.net/post/https://mastodon.social/users/ednl/statuses/116297890476560314https://board.circlewithadot.net/post/https://mastodon.social/users/ednl/statuses/116297890476560314Thu, 26 Mar 2026 22:42:59 GMT<![CDATA[Reply to how diffie hellman key exchange works on Thu, 26 Mar 2026 21:08:08 GMT]]>@b0rk I mean, there's a point where a metaphor doesn't work anymore, because it's not the truth, just a way to explain part of the truth. If you need perfect accuracy you're just explaining reality.

The paint metaphor also breaks down because there are tools for recreating paint colours accurately from pure pigments. Do that for (sxa), (sxb), and s, and you recover a and b. So it's not really suitable as a form of key exchange. But it is easy to understand on a basic level.

]]>https://board.circlewithadot.net/post/https://mastodon.online/users/pmb00cs/statuses/116297517561016043https://board.circlewithadot.net/post/https://mastodon.online/users/pmb00cs/statuses/116297517561016043Thu, 26 Mar 2026 21:08:08 GMT<![CDATA[Reply to how diffie hellman key exchange works on Thu, 26 Mar 2026 21:06:43 GMT]]>https://fedicy.us.to/Diffie-Hellman%20Key%20Exchange-Art%20of%20the%20Problem.webm]]>https://board.circlewithadot.net/post/https://fedicy.us.to/cy/p/1774559203.784376https://board.circlewithadot.net/post/https://fedicy.us.to/cy/p/1774559203.784376Thu, 26 Mar 2026 21:06:43 GMT<![CDATA[Reply to how diffie hellman key exchange works on Thu, 26 Mar 2026 21:00:11 GMT]]>@pmb00cs but I definitely have a tendency to be overly critical about the specifics of metaphors in a way that's not necessarily helpful 🙂

the paint thing is cool!

]]>https://board.circlewithadot.net/post/https://social.jvns.ca/users/b0rk/statuses/116297486256128438https://board.circlewithadot.net/post/https://social.jvns.ca/users/b0rk/statuses/116297486256128438Thu, 26 Mar 2026 21:00:11 GMT<![CDATA[Reply to how diffie hellman key exchange works on Thu, 26 Mar 2026 20:59:28 GMT]]>@pmb00cs one interesting way the mixing paint metaphor doesn't work (imo) is that when you're mixing paint the two colours you're mixing both have the same "type", and it's a symmetric operation (a mixed with b is the same as b mixed with a)

but in diffie hellman the operation is not symmetric at all, like the type of the function is more like f(type1, type2) => type1

I think saying that "s" and "a" are both "numbers" might be a bit of an oversimplification in that sense

]]>https://board.circlewithadot.net/post/https://social.jvns.ca/users/b0rk/statuses/116297483480919832https://board.circlewithadot.net/post/https://social.jvns.ca/users/b0rk/statuses/116297483480919832Thu, 26 Mar 2026 20:59:28 GMT<![CDATA[Reply to how diffie hellman key exchange works on Thu, 26 Mar 2026 20:49:54 GMT]]>@b0rk that's fair enough, and I think you've done an excellent job of it. I just like the paint analogy because it's easy to grasp that unmixing paint is hard.

]]>https://board.circlewithadot.net/post/https://mastodon.online/users/pmb00cs/statuses/116297445819655050https://board.circlewithadot.net/post/https://mastodon.online/users/pmb00cs/statuses/116297445819655050Thu, 26 Mar 2026 20:49:54 GMT<![CDATA[Reply to how diffie hellman key exchange works on Thu, 26 Mar 2026 20:47:45 GMT]]>@pmb00cs i have! i wanted to write something a little closer to the mathematical reality

]]>https://board.circlewithadot.net/post/https://social.jvns.ca/users/b0rk/statuses/116297437348411567https://board.circlewithadot.net/post/https://social.jvns.ca/users/b0rk/statuses/116297437348411567Thu, 26 Mar 2026 20:47:45 GMT<![CDATA[Reply to how diffie hellman key exchange works on Thu, 26 Mar 2026 20:44:17 GMT]]>@b0rk have you seen the paint explainer for Diffie-Helman? That's quite a good way to get the idea across.

]]>https://board.circlewithadot.net/post/https://mastodon.online/users/pmb00cs/statuses/116297423777449532https://board.circlewithadot.net/post/https://mastodon.online/users/pmb00cs/statuses/116297423777449532Thu, 26 Mar 2026 20:44:17 GMT<![CDATA[Reply to how diffie hellman key exchange works on Thu, 26 Mar 2026 20:43:39 GMT]]>@b0rk @divVerent Not sure what you're asking but might it be like the mixing paint example in the video I linked to?

In that example, Alice and Bob share a common paint color to which they mix their secret color. They share that combination with each other, add their secret color again to arrive at a shared secret key. Horrible explanation on my part which the video does a much better job at.

But I probably am completely misunderstanding your question in which case ignore this!

]]>https://board.circlewithadot.net/post/https://mastodon.social/users/samirparikh/statuses/116297421252178689https://board.circlewithadot.net/post/https://mastodon.social/users/samirparikh/statuses/116297421252178689Thu, 26 Mar 2026 20:43:39 GMT<![CDATA[Reply to how diffie hellman key exchange works on Thu, 26 Mar 2026 20:35:33 GMT]]>@b0rk 😭😭😭😭this is so well done and clear 💖💖💖💖

]]>https://board.circlewithadot.net/post/https://narrativ.es/users/janl/statuses/116297389377448243https://board.circlewithadot.net/post/https://narrativ.es/users/janl/statuses/116297389377448243Thu, 26 Mar 2026 20:35:33 GMT<![CDATA[Reply to how diffie hellman key exchange works on Thu, 26 Mar 2026 20:34:07 GMT]]>RE: https://infosec.exchange/@sophieschmieg/116246805758237078

@b0rk you don't just get Diffie to sign it?

]]>https://board.circlewithadot.net/post/https://social.lol/users/ballpointcarrot/statuses/116297383776000898https://board.circlewithadot.net/post/https://social.lol/users/ballpointcarrot/statuses/116297383776000898Thu, 26 Mar 2026 20:34:07 GMT