[TDGPerson] It has one hole

[TDGperson]

These objects were used to solve a centuries old problem, and are now used for security purposes. They come in many forms, one of which is donut shaped.

[wunderland]

PM sent

[GalFisk]

Are they made from: metal? Glass? Paper/cardboard/pulp? Stone? Wood? Plastic? Food? Drink? Liquid? Ceramic/porcelain? Clay? Dirt? Cement/concrete? Leather/skin/fur? Hair/wool? Bone/teeth? Plant fiber? Plant? Security: locks? Deterrence? Surveillance? Armor? Restraint? Weapon? Centuries old problem: math problem? Science problem? Disease? Pests? Predators?

[TDGperson]

Are they made from: metal? Glass? Paper/cardboard/pulp? Stone? Wood? Plastic? Food? Drink? Liquid? Ceramic/porcelain? Clay? Dirt? Cement/concrete? Leather/skin/fur? Hair/wool? Bone/teeth? Plant fiber? Plant? none of these Security: locks? Deterrence? Surveillance? Armor? Restraint? Weapon? none of these Centuries old problem: math problem?this Science problem? Disease? Pests? Predators?

[GalFisk]

Are they alive? Manmade? Mechanical? Electrical? Biological? Security: of an area? Object? Person? Edit: are they digital? Cryptography relevant? Ciphers?

[Earnest]

Are passwords relevant? Can they have arbitrary shapes? I am thinking about phone graphical touch passwords.

centuries old problem --> ancient greeks times? Older? Modern times problem? (1700 or so?)
Is it necessary to discover which math problem specifically? Is it a geometrical problem? Are circular shapes relevant? To be sure: are they used to solve the problem or are they part of the problem?

Security: alarms? people security? house security? technological security? security in the sense of avoiding injuries? (e.g. in sports, like harness,) Is it a tool? is it life buoy? Moebius strip relevant? Something like the shape of the motor bikes races' platforms? (with a given speed they are guaranteed to never crash?) Are plans relevant?

in many forms = many shapes? Most common one: circular? Square? Regular polygon? cylinder? Tetrahedron? irregular shapes? Movie characters? Can they represent arbitrary figures?

donut shaped --> because people go inside the hole of the donut? Its the hole of the donut filled by a part of people's body? wrist? ankle? or is it left empty as in earrings?

[TDGperson]

wunderland:

PM sent correct but incomplete (doesn't solve the "donut shaped" part)

GalFisk:

Are they alive? Manmade? Mechanical? Electrical? Biological? none of these Security: of an area? Object? Person? Edit: are they digital? Cryptography relevant? thisCiphers? yes

Earnest:

Are passwords relevant? yes Can they have arbitrary shapes? no I am thinking about phone graphical touch passwords.

centuries old problem --> ancient greeks times? Older? Modern times problem? (1700 or so?)this
Is it necessary to discover which math problem specifically? yes Is it a geometrical problem?no/yope Are circular shapes relevant?no To be sure: are they used to solve the problem or are they part of the problem? used to solve

Security: alarms? people security? house security? technological security? thissecurity in the sense of avoiding injuries? (e.g. in sports, like harness,) Is it a tool? is it life buoy? Moebius strip relevant? Something like the shape of the motor bikes races' platforms? (with a given speed they are guaranteed to never crash?) Are plans relevant? none of these

in many forms = many shapes?yes Most common one: circular? Square? Regular polygon? cylinder? Tetrahedron? irregular shapes? this Movie characters? noCan they represent arbitrary figures?no

donut shaped --> because people go inside the hole of the donut? no Its the hole of the donut filled by a part of people's body? no wrist? ankle? or is it left empty as in earrings? no

[GalFisk]

Are they physical objects? Do they loop back on themselves? Elliptic curve cryptography relevant?

[Earnest]

so they are used to keep passwords secret? To generate random numbers? To generate random passwords?
Passwords = do phone passwords work? Passwords mainly in the sense of: mixture of letters and numbers? bits?

[TDGperson]

Galfisk

Are they physical objects? No Do they loop back on themselves? No Elliptic curve cryptography relevant?yes

Earnest

so they are used to keep passwords secret? thisTo generate random numbers? To generate random passwords?
Passwords = do phone passwords work? thisPasswords mainly in the sense of: mixture of letters and numbers? bits?this

Since multiple people have gotten it via PM and posting : the objects are elliptic curves. All that's left is to solve the "donut shaped" part

[GalFisk]

Are the actual curves donut shaped? Is the important feature of a donut: the hole? The the closed loop? The circle? The torus? The taste? Who eats them?

[wunderland]

Complex numbers relevant?
My original guess was that elliptic curves over complex numbers could be donut shaped, but on reflection I suppose they would be four dimensional while donuts are three dimensional. Perhaps a projection into 3D space?

[TDGperson]

GalFisk


Are the actual curves donut shaped? yes Is the important feature of a donut: the hole? The the closed loop? The circle? The torus? thisThe taste? Who eats them?

wunderland


Complex numbers relevant? yes
My original guess was that elliptic curves over complex numbers could be donut shaped , but on reflection I suppose they would be four dimensional while donuts are three dimensional. Perhaps a projection into 3D space? no

[Earnest]

is some regularity involved? Are donut shaped ellipses safer? Do they generate safer combinations? Its the key of cryptography relevant? Relevant the formula of torus? Relevant thee pi here? (maybe pi is involved in key) Relevant thee generation of unique bits sequences?

[TDGperson]

is some regularity involved? yes (by definition elliptic curves are regular)Are donut shaped ellipses safer? noDo they generate safer combinations?no Its the key of cryptography relevant?no Relevant the formula of torus? noRelevant thee pi here?no (maybe pi is involved in key) Relevant thee generation of unique bits sequences?no

[Hobbsicle]

Is the centuries old problem Fermat's Last Theorem? I'm not sure what we're looking for at this point. We've established that the donut-shape is a torus? As it relates to the complex plane, and the elliptic curves that result, or some such?

[TDGperson]

Is the centuries old problem Fermat's Last Theorem? YesI'm not sure what we're looking for at this point. We've established that the donut-shape is a torus? As it relates to the complex plane, and the elliptic curves that result, or some such?

************* SPOILER **************

I was originally planning to wait until someone mentioned Weierstrass's elliptic functions before calling this solved, as they are crucial in establishing the equivalence between complex elliptic curves and tori. But you've already got the rest of it and I don't think it would be good to keep waiting, so I'll just call it solved

The answer is elliptic curves. Wiles used them to solve Fermat's last theorem. The discrete logarithm problem for elliptic curves over finite fields is a computationally difficult problem that some cryptographic protocols are built from. Using Weierstrass's elliptic functions, every elliptic curve is isomorphic (as both a group and Riemann surface) to a complex torus, thus establishing an equivalence.