Crate secret_sharing_and_dkg

Secret sharing and distributed key generation

Implements Secret Sharing (SS), Verifiable Secret Sharing (VSS), Distributed Verifiable Secret Sharing (DVSS), Distributed Key Generation (DKG) and Publicly Verifiable Secret Sharing (PVSS) algorithms. DVSS and DKG do not require a trusted dealer. Also implements a distributed discrete log check.

1. Shamir secret sharing (Requires a trusted dealer)
2. Pedersen Verifiable Secret Sharing
3. Pedersen Distributed Verifiable Secret Sharing
4. Feldman Verifiable Secret Sharing
5. Feldman Distributed Verifiable Secret Sharing
6. Gennaro DKG from the paper Secure Distributed Key Generation for Discrete-Log Based Cryptosystems
7. Distributed Key Generation from FROST
8. Distributed discrete log (DLOG) check
9. Publicly Verifiable Secret Sharing

Modules

• abcp_dkg
  Distributed Key Generation protocol as described in Fig. 4 of the paper VSS from Distributed ZK Proofs and Applications
• baghery_feldman_vss
  Feldman’s Verifiable Secret Sharing Scheme, with faster verification but slower sharing, by K. Baghery. As described in Fig 3 of the paper A Unified Framework for Verifiable Secret Sharing
• baghery_pvss
  Publicly verifiable secret sharing protocols
• common
• distributed_dlog_check
  Distributed discrete log (DLOG) check
• error
• feldman_dvss_dkg
  Feldman Distributed Verifiable secret sharing and distributed key generation.
• feldman_vss
  Feldman Verifiable Secret Sharing Scheme. Based on the paper A practical scheme for non-interactive verifiable secret sharing The scheme works as follows for threshold t and total n:
• frost_dkg
  This is the keygen implemented in the FROST paper in Figure 1. This is a slight addition to the DKG based on Feldman VSS as it contains a Schnorr proof of knowledge of the secret key.
• gennaro_dkg
  Based on the paper Secure Distributed Key Generation for Discrete-Log Based Cryptosystems Scheme is defined in Fig 2. The protocol is run in 2 phases: Phase1 where all participants generate a secret and share it using Pedersen VSS and in Phase 2 participants distribute commitments as per Feldman VSS and generate the public key at the end. The public key is assumed to be of the form G*x where x is the secret key and G is the group generator.
• pedersen_dvss
  Pedersen Distributed Verifiable secret sharing. Based on the paper “Non-interactive and information-theoretic secure verifiable secret sharing”, section 5. https://www.cs.cornell.edu/courses/cs754/2001fa/129.PDF Does not involve a trusted third party but assumes that all participants (and not just threshold) participate till the end. Even if one participant aborts, the protocol needs to be restarted. A workaround is for each participant to ignore the faulty participant’s share essentially making it such that the faulty participant was never there.
• pedersen_vss
  Pedersen Verifiable secret sharing. Based on the paper “Non-interactive and information-theoretic secure verifiable secret sharing”, section 4. https://www.cs.cornell.edu/courses/cs754/2001fa/129.PDF. The basic idea is the following
• shamir_ss
  Shamir secret sharing