Timeline for Is there a 3-D alternative for elliptic curves?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Dec 5, 2017 at 17:50 | comment | added | Alexander Vtyurin | Thank you for a very helpful answer. All these crypto-things seem so easy at first sight, but the more i read the less i understand. | |
| Dec 5, 2017 at 15:51 | comment | added | entrop-x | @tylo: I assumed that the question was formulated in the frame of DH, which implies a discrete log problem as far as I understand. I don't know how you can formulate a discrete log problem outside of a cyclic group, because you are asking for the power of the generator. How would you even define a discrete logarithm in a group that doesn't have a single generator (isn't cyclic) ? I read the question as what relationship exists between the encryption strength and the dimensionality in which to define a DH key exchange, not about what other ways there could be to establish a common secret. | |
| Dec 5, 2017 at 13:34 | comment | added | tylo | Well, the DLOG, CDH and DDH problem are defined with a single generator, but that does not mean they are not true outside of this type of construction. Logically speaking, it's an implication and not a biconditional. The question is asking for constructions beyond the common ones, and key exchange (and public key crypto) do not have to be based on those problems. | |
| Dec 5, 2017 at 12:07 | comment | added | entrop-x | @tylo: true of course, but a discrete log problem needs a cyclic group as far as I understand. You're right that elliptic groups aren't necessarily cyclic, but the cryptographic (sub)group used is cyclic, by choice of a (single) generator. | |
| Dec 5, 2017 at 11:00 | comment | added | tylo | Actually, cyclic groups are just a subset of the finite groups, which can be used as algebraic structure. Not all elliptic curves over finite groups are cyclic (they can also be the direct product of cyclic groups). | |
| Dec 5, 2017 at 5:52 | history | answered | entrop-x | CC BY-SA 3.0 |