Block Codes for Collusions-Nonpermissible Secret Sharing Systems

Abstract

The (n,k) block codes are translated into (1,p,r,n) secret sharing schemes in which collusion between players are not permitted. The performance of both linear block codes and random block codes as (1,p,r,n) SSSs in terms of the relationship between reconstructability and privacy；and the trade-off between privacy and resiliency is compared to the performance bounds derived from a secret sharing model GS3. It is demonstrated that linear codes, when viewed as (1,p,r,n) SSSs, can at best achieve one-half of the performance bounds asymptotically. It is also demonstrated t hat the random codes do not have privacy even though they can achieve the capacity of reconstructability and resiliency with high probability for sufficiently large n. Lastly, a hashed random cone (HRC) is presented and shown to achieve the performance bounds asymptotically. Secret Sharing Reconstructability Privacy Resiliency Collusios-nonpermisible (1,p,r,n) SSS secret sharing model Hashed random code HRC