Restruct simple lottery

[rrtoledo]

Content

Blocked by #116.

This PR aims at restructuring the Simple Lottery code (similarly to PR #116 for Centralized telescope) to have a user facing structure from which we can directly prove and verify. More particularly,

• Moves code in implementation block
• Moves implementation block in struct file
• Renamed the user facing wrapper structure
• Removed the user parameter structure and renamed the internal parameter structure

Additionnally, this PR

• Fixed error in proof generation
• Add documentation to public facing functions

Pre-submit checklist

• Branch
  • Tests are provided (if possible)
  • 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
• Documentation
  • Update README file (if relevant)
  • Update documentation website (if relevant)

Comments

Issue(s)

Relates to #59