Inspiration

On ETHBerlin the Nucypher team has asked me to if their proxy re-encryption protocol can be implemented on mobile devices. By that time I've already started to implement a pure-Swift library (no C/C++ parts) for Elliptic curve arithmetics and pairings. On this hackathon, I've decided with the help of team members to start implementing their proxy re-encryption protocol Umbral as a demo for my library.

What it does

Allows arbitrary EC arithmetics (not in extension fields yet) to be used on mobile devices with good speed and without a mess of C/C++ integrations, so making Umbral proxy re-encryption will be trivial once it's finished and polished

How we BUIDL it

Part of the library was ready; now it required the following extensions

  • Define curve over the abstract field that can operate on any wide unsigned integer type that has some properties
  • Backport wide integers (UInt256/UInt512) for iOS devices. This library is universal for MacOS/iOS, but on MacOS it was using U256 implemented using AVX Intel processor instructions, so equivalent for iOS has to be backported (more precisely - polyfilled)
  • Start implementing Umbral itself

Challenges I ran into

  • Implementing fast wide arithmetics is always a challenge
  • For the ease of work with UInt256 some functionality had to be implemented for UInt512 (full multiplication UInt256 * UInt256 -> UInt512, modular reduction UInt512 -> UInt256)
  • Arithmetics of UInt256/UInt512 has to be tested first to event start testing elliptic curve arithmetics

Accomplishments that I'm proud of

  • UInt256 is entirely valid except modular reduction (see next point)
  • UInt512 is valid except of the division for some reason

What I learned

  • The naive implementation of wide integer types through arrays involves too many Copy-on-Write, so manual memory management is good if you know what you are doing

What's next for Keep your privacy with you

  • Finish and polish a library (testing mainly + documentation)
  • Finish and test Umbral
  • Ideally, add a backed that does proxy re-encryption and sends notifications re-encryption requests to the mobile device to get a fresh re-encryption key

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