Example - Centralized Telescope with BLS Signatures

[curiecrypt]

Content

This PR introduces an example demonstrating the ALBA Threshold Signature scheme with the following workflow:

Workflow

1. Define Telescope Parameters:
   • Set nb_elements to 1,000.
   • Configure soundness_param and completeness_param as 128.0.
   • Calculate the prover set size (set_size) as 80% of nb_elements and the lower bound as 20%.
   • Initialize the Telescope with these parameters.
2. Initialize Signers:
   • Create a list of candidate Signers with randomly generated keys.
3. Start Registration:
   • Open a new Registration.
   • Select and register a subset of candidate signers, tracking the number of successfully registered signers.
4. Close Registration:
   • Finalize the registration by computing the checksum of registered keys.
   • Update registered signers with the computed checksum.
5. Generate Individual Signatures:
   • Select a subset of registered signers.
   • Generate IndividualSignatures for each based on the input message.
6. Generate ALBA Threshold Signature:
   • Aggregate valid individual signatures to create an AlbaThresholdSignature.
   • Print details of the generated threshold signature if successful.
7. Verify ALBA Threshold Signature:
   • Validate the generated threshold signature using the Telescope, registration, and input message.
   • Print whether the verification succeeded or failed.

Purpose

This example provides a detailed implementation of the ALBA Threshold Signature workflow, showcasing the integration of Telescope parameters, signer registration, individual signature generation, and threshold signature verification.

Pre-submit checklist

• Branch
  • Commit sequence broadly makes sense
  • Key commits have useful messages
• PR
  • No clippy warnings in the CI
  • Self-reviewed the diff
  • Useful pull request description
  • Reviewer requested

Issue(s)

Closes #78

[rrtoledo]

Good work!

Some suggestions here and there to simplify the code (usnig type alias instead of struct, merging impl block potentially...) and make it more efficient (not using maps but sets, batching the verification).

I think the example would improve in clarity if you rename the folder "threshold_signature" "aggregate_signature" as we are only using these signature list (from registered signers) to create a threshold signature in centralized_telescope.rs. Perhaps renaming centralized_telescope.rs "centralized_threshold.rs" also?

[tolikzinovyev]

Thanks for working on this @curiecrypt! Do you need my review or @rrtoledo and @djetchev will be enough?

[rrtoledo]

LGTM.

I am not sure why we put tests here as this is an example but could you add asserts in each of these? We could add more tests, but let's do that in a disctint PR.

[djetchev]

LGTM!

[rrtoledo]

LGTM