4 ms·

According to https://hcrypt.com/scarab-library/ https://hcrypt.com/scarab-library/, the functions that you can do on encrypted texts are Add cyphertexts (= X

by guelo 12y ago

According to https://hcrypt.com/scarab-library/ https://hcrypt.com/scarab-library/, the functions that you can do on encrypted texts are Add cyphertexts (= XOR) Multiply cyphertexts (= AND) Add with carry in and carry out Add with carry out I'm not really familiar with homomorphic theory, but it doesn't seem like you could build that much on top of these primitives.

CGamesPlay 12y ago
You could run transactions on a signed wallet and even compute interest... I'm sure there are also other, less obvious, use cases as well. Add with carry-out seems like it could be use to build some complex systems.
danbruc 12y ago
You can build everything on top of that - (a AND b) XOR 1 = a NAND b and you can build any boolean function out of NAND gates. So just make the cipher text the (encrypted) memory of a virtual machine, design a processor out of the mentioned primitives just like you design any ordinary processor and then execute it. And that is what they actually did with the Shape CPU [1]. [1] https://hcrypt.com/shape-cpu/ https://hcrypt.com/shape-cpu/
dvanduzer 12y ago
You may want to start here: https://en.wikipedia.org/wiki/Group_homomorphism https://en.wikipedia.org/wiki/Group_homomorphism The way I've understood it is that only addition has been possible so far. With a multiplication operation, you can get a field, and do "everything" with the real/complex numbers.
- darkxanthos 12y ago
  Well a homomorphism applies to a group and a group can only have one operator by definition. That won't change probably. Rings have two operators, fields are rings that support cancellation and integral fields I believe support inverses as a rule and where you'd get "everything" I believe.
  - wging 12y ago
    "Well a homomorphism applies to a group" Not so. The notion's far more general: https://en.wikipedia.org/wiki/Ring_homomorphism https://en.wikipedia.org/wiki/Ring_homomorphism This gives us a notion of homomorphisms between fields. https://en.wikipedia.org/wiki/Homomorphism https://en.wikipedia.org/wiki/Homomorphism for more general notions of homomorphisms.
    - darkxanthos 12y ago
      You're right. My bad. Thanks for correcting me.

by guelo 12y ago

CGamesPlay 12y ago

You could run transactions on a signed wallet and even compute interest... I'm sure there are also other, less obvious, use cases as well. Add with carry-out seems like it could be use to build some complex systems.

danbruc 12y ago

You can build everything on top of that - (a AND b) XOR 1 = a NAND b and you can build any boolean function out of NAND gates. So just make the cipher text the (encrypted) memory of a virtual machine, design a processor out of the mentioned primitives just like you design any ordinary processor and then execute it. And that is what they actually did with the Shape CPU [1]. [1] https://hcrypt.com/shape-cpu/ https://hcrypt.com/shape-cpu/

dvanduzer 12y ago

You may want to start here: https://en.wikipedia.org/wiki/Group_homomorphism https://en.wikipedia.org/wiki/Group_homomorphism The way I've understood it is that only addition has been possible so far. With a multiplication operation, you can get a field, and do "everything" with the real/complex numbers.

darkxanthos 12y ago
Well a homomorphism applies to a group and a group can only have one operator by definition. That won't change probably. Rings have two operators, fields are rings that support cancellation and integral fields I believe support inverses as a rule and where you'd get "everything" I believe.
- wging 12y ago
  "Well a homomorphism applies to a group" Not so. The notion's far more general: https://en.wikipedia.org/wiki/Ring_homomorphism https://en.wikipedia.org/wiki/Ring_homomorphism This gives us a notion of homomorphisms between fields. https://en.wikipedia.org/wiki/Homomorphism https://en.wikipedia.org/wiki/Homomorphism for more general notions of homomorphisms.
  - darkxanthos 12y ago
    You're right. My bad. Thanks for correcting me.