Use standard way of generating a EC public key for the Schnorr signature

[FilipLaurentiu]

Use standard way of generating a EC public key for the Schnorr signature

Description

Description of the pull request changes and motivation.

Type of change

Please delete options that are not relevant.

• New feature
• Bug fix
• Optimization

Checklist

• Linked to Github Issue
• Unit tests added
• This change requires new documentation.
  • Documentation has been added/updated.
• This change is an Optimization
  • Benchmarks added/run

[greptile-apps]

Greptile Overview

Greptile Summary

Changed Schnorr signature implementation from non-standard to standard cryptographic convention by modifying public key generation from $h = g^{-k}$ to $h = g^{k}$ and updating verification accordingly.

• Changed get_public_key() to compute g^k instead of g^{-k}, aligning with standard Schnorr protocol (consistent with FROST implementation in this codebase)
• Updated verify_signature() to use h^{-e} instead of h^e to maintain mathematical correctness
• Added use std::ops::Neg import for negation operation
• Updated README documentation to reflect standard formulas
• Fixed typo in comment ("the the" → "the")

The change is mathematically sound and makes the implementation consistent with widely-accepted cryptographic standards and other implementations in the repository.

Confidence Score: 5/5

• This PR is safe to merge with minimal risk
• The changes correctly convert a non-standard but mathematically valid Schnorr signature implementation to the standard cryptographic convention. Both the old and new implementations are mathematically correct, but the new version aligns with widely-accepted standards and the repository's own FROST implementation. The mathematical transformation is sound, documentation is updated accordingly, and existing tests validate correctness.
• No files require special attention

Important Files Changed

Filename	Overview
examples/schnorr-signature/src/schnorr_signature.rs	Changed public key generation from g^{-k} to standard g^{k} and updated verification to use h^{-e} instead of h^e, aligning with cryptographic standards
examples/schnorr-signature/README.md	Updated documentation to reflect standard Schnorr signature scheme formulas for public key and verification steps