Validation of partial key pairs currently omits a range proof in the validity proof and verification processes.

[woojucy]

Description

The current function for generating partial key pairs requires a zero-knowledge proof to ensure that the sum of the two secret values r and s, used as the exponents for the public key, is less than the value obtained by dividing the modulus N by the number of sequencers. Therefore, it is necessary to add logic to the prove_partial_key_validity function to generate this proof.

Accordingly, before aggregating the partial keys, there is also a need to verify the zero-knowledge proof that confirms the range of the secret values. Based on the current implementation, this verification is necessary in the verify_partial_key_validity function.