Timeline for Knot Diffie–Hellman
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Apr 1 at 0:42 | comment | added | dvitek | For more general thoughts along these lines see a 2018 paper of Partala, "Algebraic generalization of Diffie–Hellman key exchange". | |
| Mar 31 at 17:03 | comment | added | dvitek | I wonder whether replacing connect-sum with an operation like taking satellites would work better, though I don't know offhand whether an "iterated satellite knot" construction is sensitive to the order of the companion knots. (Even if iterated satellite knots are sensitive to the order of companions, this might not show up at the level of whatever invariant you pick.) This would largely sidestep the problem I mentioned above. | |
| Mar 31 at 16:50 | comment | added | dvitek | One major difference between this proposal and finite-field Diffie-Hellman (FFDH) is that in FFDH the public key $(p,g)$ is a very different type of object than the secrets $(a, b)$, whereas here $P$, $A$, $B$ are all knots. This has a very concrete negative effect on your proposal, because it means that any knot invariant $I$ with nice connect-sum properties is likely to be unsuitable, since we can write something like the equation $I(P \oplus A \oplus B) = I(P \oplus A) + I(P \oplus B) - I(P)$ and get lots of information about the supposedly-secret value $I(P \oplus A \oplus B)$. | |
| Mar 31 at 3:03 | comment | added | Ryan Budney | The algorithm to compute the connect-sum decomposition (and full satellite decomposition) of a knot in $S^3$ is either exponential or double-exponential run-time, as implemented in Regina. In practice it's quite quick, and you only run into the full "slow" computations rarely. I imagine you can find the proper run-time estimate in a paper of Ben Burton's. | |
| Mar 31 at 2:26 | history | edited | yoyo | CC BY-SA 4.0 |
added 271 characters in body
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| Feb 4, 2023 at 23:07 | vote | accept | yoyo | ||
| Jan 28, 2023 at 0:24 | history | edited | yoyo | CC BY-SA 4.0 |
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| Jan 27, 2023 at 15:54 | history | edited | yoyo | CC BY-SA 4.0 |
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| Jan 27, 2023 at 15:24 | history | edited | yoyo | CC BY-SA 4.0 |
tried to make question more pointed
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| Jan 26, 2023 at 19:31 | answer | added | Sam Nead | timeline score: 10 | |
| Jan 26, 2023 at 16:59 | answer | added | kodlu | timeline score: 5 | |
| Jan 24, 2023 at 20:46 | history | edited | LSpice | CC BY-SA 4.0 |
Capitalise title
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| Jan 24, 2023 at 20:36 | history | asked | yoyo | CC BY-SA 4.0 |