Pedersen Verifiable Secret Sharing (PVSS) Meaning

Secret Sharing

Let’s understand the concept of Secret Sharing before we dive deep into Pedersen Verifiable Secret Sharing (PVSS).

Secret Sharing is the method of splitting a secret value into multiple, smaller parts called shares or fragments and distributing them among a group of participants or custodians. Each participant holds only a fragment of the secret, and the original secret can only be reconstituted when a sufficient number of participants reassemble their shares. This renders individual shares useless. In cryptocurrency, the secret value being split is a secret recovery phrase, which is essential for the generation of private keys.

Pedersen Verifiable Secret Sharing (PVSS) Explained 

The Shamir Secret Sharing (SSS) scheme is used to predetermine the minimum number of shares required to reconstruct private keys. A variation of SSS, the Pedersen Verifiable Secret Sharing (PVSS), is used to verify the validity of shares custodians receive or submit during the reconstruction of the secret.

PVSS works by creating additional variables alongside the secret share, which is used to double-check that the shares are consistent with the original secret. The scheme follows an “honest-verifier zero-knowledge” principle to ensure that no intelligible information about the original secret is revealed whatsoever. The primary goal of PVSS is to ensure that the dealer does not send invalid shares to the shareholders, and that the shareholders don’t submit incorrect shares during reconstitution.

Unlike SSS, PVSS utilizes a commitment scheme that adds an extra layer of security and verifiability. The commitment scheme locks in shares to prevent participants from altering them after distribution. The shares submitted during reconstructions have to match with the shares bound with the commitment. 

PVSS is a valuable tool in systems or algorithms where secure and verifiable secret sharing is vital, such as private key management and multi-party computations. It aids in building solutions that are resilient to bad actors and data loss.