Abstract: Described is system for secure mobile proactive multi-party computation. The system securely evaluates a circuit in the presence of an adversary. The circuit receives secret inputs comprising secret values from a set of servers. Sharings of random values for the random and input gates are generated. For each input gate, a sharing of a random value associated with the input gate is opened toward a server Pi. A sum of the server Pi's secret values and the random value is broadcast to the set of servers. Each server uses the sum to adjust its sharing of the random value, generating a sharing of server Pi's secret values. The secret values are re-randomized to preserve privacy of the secret values. A sharing of the secret values is determined for each output gate, and each sharing of secret values is revealed to an intended recipient.

Abstract: Described is system for generation of elliptic curve digital signature algorithm (ECDSA) based digital signatures. A Secret-Share protocol is initialized between a client and a set of servers to share a set of shares of a private key s among the set of servers. The set of servers initializes a protocol to generate a digital signature on a message using the set of shares of the private key s without reconstructing or revealing the private key s. The set of servers periodically initializes a Secret-Redistribute protocol on each share of the private key s to re-randomize the set of shares. A Secret-Open protocol is initialized to reveal the private key s to an intended recipient, wherein the private key s is used to compute the digital signature.

Abstract: Described is system for transforming a SHARE protocol into a proactively secure secret sharing (PSS) protocol. A PREFRESH protocol is performed that includes execution of the SHARE protocol. The PREFRESH protocol refreshes shares of secret data among multiple parties. The SHARE protocol is a non-proactively secure secret sharing protocol.

Abstract: Described is system for secure proactive multi-party computation. The system securely evaluates a circuit in the presence of an adversary. The circuit receives inputs of secret values from a set of servers. A RobustShare protocol is initialized to allow each server to distribute their secret values among the other servers. A RauDouSha protocol is initialized to generate random sharings of the secret values. A Block-Redistribute protocol is initialized to redistribute the secret values amount the set of servers. For each layer of the circuit, a permutation of the secret values is performed, and each layer of the circuit is evaluated. The Block-Redistribute is protocol is initialized to re-randomize the secret values such that privacy of the secret values is preserved. A sharing of the secret values is determined for each output gate, and a Reco protocol is initialized to reveal each sharing of secret values to an intended recipient.

Abstract: Described is a system for mobile proactive secret sharing. The system utilizes a Secret-Share protocol to share, by server Pj, a secret s among a set of servers , such that a degree of polynomials used to share the secret s is d and a shared secret is denoted as [s]. A GenPoly protocol is used to cause the servers in the set of servers to generate l random polynomials of degree D. A Secret-Redistribute protocol is used to redistribute the shared secret [s] to a set of new servers ?. Finally, a Secret-Open protocol is used to open the shared secret [s].