Recent Development of Multiuser Message Authentication, Application to Verifiable Secret Sharing and Key Management Schemes

In secure group communication, providing authentication for messages exchanged among a group of users is important. We create multiuser authentication techniques that are impenetrable to colluding malevolent users with fewer than k users, where all n users are allowed to transmit messages (simultaneously with being receivers). In our method, each user must keep2k log2 q1 bits of secret information, and tags to authenticate communications must be k log2 q long.. We use this to achieve a non-interactive verifiable secret sharing scheme for many dealers, in which shares reveal no information about the secret and dealers cannot trade inconsistent shares, in the scenario where participants are allowed to use previously released private keys. Without incurring additional storage costs, we also provide authentication to the group key management systems proposed by Blundo et al. and Fiat-Naor.