Optimal One Round Almost Perfectly Secure Message Transmission (Short Paper)

A General Construction for 1-Round δ-RMT and (0, δ)-SMT

“…For this network our approach will need q ≥ 16000, q 4 computation, the list size will be q 3 and δ = 42 q 4 = 6(10 −6 ), where q is the base field size. For q = 16000, the δ for the protocol in [22] is 0.0263. whereas, δ for the protocol in [21] is not defined (the protocol needs larger field size). To have the same δ as our protocol, [21] needs field size to be 1.2 × 10 14 .…”

“…This protocol uses a complex combination of secret sharing by the sender and elaborate verification of the received information by the receiver to determine the correct message block. There are two optimal and efficient 1-round (0, δ)-SMT protocols for N = 2t + 1 [14,22]. The protocol in [14] is based on the 1-round δ-RMT protocol of [18] and has similar complexity.…”

“…Moreover, to achieve the optimal transmission rate for higher connectivity, this protocol can not be directly used as the encrypted message blocks are broadcasted. The protocol of [22] suffers from the same problem as that of [14].…”

“…On the other hand, for N = (2 + c)t, c > 1 t , there are two optimal and efficient 1-round (0, δ)-SMT protocols [22,21]. The protocol of [21] uses two SMT protocols in two levels.…”

“…The shortcoming of this protocol is that to achieve optimal rate, the sender needs to send a very large information block (of size at least N 3 field elements). The protocol in [22] also uses multiple secret sharings in a clever way which results in a lower δ than that of [14].…”