4 ms·

> this is the first to actually illustrate how they work on a small field That means a lot, thanks! That was my design goal with the page: figuring out the bes

> this is the first to actually illustrate how they work on a small field That means a lot, thanks! That was my design goal with the page: figuring out the best way to get the idea across _without_ the user having to read a lot of text and stare at the wall until they got it. I've been casting around for the next idea to do a visualization of, adding yours to the list. (as for a partial answer your second question: the answer is going to be that Montgomery curves like Curve25519 have a method [Montgomery ladder] to quickly and timing-safely calculate only the x values of point multiplication. Faster _and_ more likely to be implemented securely than NIST curves, by design. Unfortunately I don't know the details of BrainPool, yet?) Yes, Curve25519 is the curve itself (and associate params), Ed25519 is the signature system implemented on top of C25519, and X25519 is the ECDHE mechanism implemented on top of C25519. This page talks mostly about the C and a little of the X, and doesn't go into Ed.

geoduck14 4y ago
I'll agree with GP - this is the best I've seen, too. If I may offer a critique: the final example with Alice and Bob went too fast. I watched it 5 times and I'm a bit lost. I'll rewatch it again later
- syncsynchalt 4y ago
  That’s good feedback. There’s a lot of steps, where should I slow it down? (“All” is an acceptable answer): - Alice computes A - Bob computes B - there’s a 3? second delay - Alice and Bob simultaneously compute the shared secret by multiplying their private key by the others’ public key
  - miketery 4y ago
    Amazing work. For me, I think breaking it up after the Public Keys are generated would have helped. I lost track the first time after the public keys are computed and exchanged. The exchange is what I think I missed.
  - codedokode 4y ago
    I noticed this problem with other images too. Sometimes animations change too fast, you see points moving, you look at them, but at the same time the formula changes, and you miss it. Especially bad when the formula is written under the image, far away from moving points. Basically, you should not have several things changing in different places at the same time because human can only focus at one point. Maybe it would be better to add pauses in the sequence, animate one thing, wait a little, then animate other thing. Let the user stop and think a bit about what he/she have seen. For example, in the image "Repeated addition of a point P" the points and lines are constantly moving, and I don't have time to look at the formula. I see that it is changing, but I cannot read it while looking at the animation. Maybe it would be better if the points stopped moving for a while, then the formula would change, then you give some time to read and comprehend it and then points continue moving. Or maybe you could write all the formulas on the side, and have a box or selection moving over them. This way the viewer can see how the formulas are related to each other and doesn't have to remember previous ones. Also, in the image "Point addition is associative and commutative" formulas seem to be random and do not illustrate anything. For example, I see 5P + P = 6P, then 2P + P = 3P, then 6P + P = 7P. So what it should mean? Maybe a better way to illustrate these laws would be to have two images that produce the same result, for example P + 6P = 7P and 3P + 4P = 7P. It is easier to compare images side-by-side. Instead of percent sign it might be better to use "mod" as percent sign is understood only by programmers but not by people familiar with mathematical notation. To illustrate addition you might use a circle (or an ellipse, or even a square, why not) instead of a straight line. This way the wrapping behaviour would be more obvious. To illustrate multiplication, you could draw several sequential arcs (so that the multiplication is represented as several additions). And for negation, two arcs extending in the opposite direction from zero. I don't understand how to illustrate inverse numbers though. Maybe several arcs that start at zero, end at 1 and number of them is the inverse value? For the last illustration it definitely would help if it had some key points on the side, showing what we have done and what we are doing now.
  - turysaz 4y ago
    I can imagine that play/pause/step buttons could help a lot (for all of the animations), so each reader could "slow it down" manually and take all the time they need. PS: Great work, thank you! :)
    - syncsynchalt 4y ago
      Ah, hmm. Every animation on the page does have a play/pause _except_ the exchange demo (laugh). I’ll play around with having it pause itself at key points and/or giving it a step button.

geoduck14 4y ago

I'll agree with GP - this is the best I've seen, too. If I may offer a critique: the final example with Alice and Bob went too fast. I watched it 5 times and I'm a bit lost. I'll rewatch it again later

syncsynchalt 4y ago
That’s good feedback. There’s a lot of steps, where should I slow it down? (“All” is an acceptable answer): - Alice computes A - Bob computes B - there’s a 3? second delay - Alice and Bob simultaneously compute the shared secret by multiplying their private key by the others’ public key
- miketery 4y ago
  Amazing work. For me, I think breaking it up after the Public Keys are generated would have helped. I lost track the first time after the public keys are computed and exchanged. The exchange is what I think I missed.
- codedokode 4y ago
  I noticed this problem with other images too. Sometimes animations change too fast, you see points moving, you look at them, but at the same time the formula changes, and you miss it. Especially bad when the formula is written under the image, far away from moving points. Basically, you should not have several things changing in different places at the same time because human can only focus at one point. Maybe it would be better to add pauses in the sequence, animate one thing, wait a little, then animate other thing. Let the user stop and think a bit about what he/she have seen. For example, in the image "Repeated addition of a point P" the points and lines are constantly moving, and I don't have time to look at the formula. I see that it is changing, but I cannot read it while looking at the animation. Maybe it would be better if the points stopped moving for a while, then the formula would change, then you give some time to read and comprehend it and then points continue moving. Or maybe you could write all the formulas on the side, and have a box or selection moving over them. This way the viewer can see how the formulas are related to each other and doesn't have to remember previous ones. Also, in the image "Point addition is associative and commutative" formulas seem to be random and do not illustrate anything. For example, I see 5P + P = 6P, then 2P + P = 3P, then 6P + P = 7P. So what it should mean? Maybe a better way to illustrate these laws would be to have two images that produce the same result, for example P + 6P = 7P and 3P + 4P = 7P. It is easier to compare images side-by-side. Instead of percent sign it might be better to use "mod" as percent sign is understood only by programmers but not by people familiar with mathematical notation. To illustrate addition you might use a circle (or an ellipse, or even a square, why not) instead of a straight line. This way the wrapping behaviour would be more obvious. To illustrate multiplication, you could draw several sequential arcs (so that the multiplication is represented as several additions). And for negation, two arcs extending in the opposite direction from zero. I don't understand how to illustrate inverse numbers though. Maybe several arcs that start at zero, end at 1 and number of them is the inverse value? For the last illustration it definitely would help if it had some key points on the side, showing what we have done and what we are doing now.
- turysaz 4y ago
  I can imagine that play/pause/step buttons could help a lot (for all of the animations), so each reader could "slow it down" manually and take all the time they need. PS: Great work, thank you! :)
  - syncsynchalt 4y ago
    Ah, hmm. Every animation on the page does have a play/pause _except_ the exchange demo (laugh). I’ll play around with having it pause itself at key points and/or giving it a step button.