Secret Sharing

Impossibility

  • There is a result that says that: for any sharp threshold secret sharing scheme, irrespective of whether it is linear or non-linear, it must hold that each share size is as long as the secret size. (Source: On the size of shares for secret sharing schemes. R. M. Capocelli, A. De Santis, L. Gargano, and U. Vaccaro. 1993, I learnt it from Scalable Multiparty Computation from Non-linear Secret Sharing. Sanjam Garg, Abhishek Jain, Pratyay Mukherjee, and Mingyuan Wang. 2024)

Notes

  • First introduced by How to share a secret. Adi Shamir. 1979 and Safeguarding cryptographic keys. G. R. Blakley. 1979 (Source of this info: Computational Verifiable Secret Sharing Revisited. Michael Backes, Aniket Kate, and Arpita Patra. 2011)

Types

  1. Verifiable Secret Sharing (Chor, Gennaro IKR - Round complexity of VSS)
  2. Publicly Verifiable Secret Sharing (Heidervand et al.)
  3. Proactive Secret Sharing
  4. Asynchronous Proactive Secret Sharing (APSS: Zhou et al)
  5. Asynchronous Verifiable Secret Sharing (Cachin Async VSS and proactive cryptosystems)