International Association
for Cryptologic Research

We show that for certain class of unconditionally secure protocols and

target functionalities, static security implies adaptive security in the UC

model. Similar results were previously only known for models with

weaker security and/or composition guarantees. The result is, for

instance, applicable to a wide range of protocols based on secret

sharing. It ``explains\'\' why an often used proof technique for such

protocols works, namely where the simulator runs in its head a copy of

the honest players using dummy inputs and generates a protocol

execution by letting the dummy players interact with the

adversary. When a new player $P_i$ is corrupted, the simulator

adjusts the state of its dummy copy of $P_i$ to be consistent with

the real inputs and outputs of $P_i$ and gives the state to the

adversary. Our result gives a characterisation of the cases where this

idea will work to prove adaptive security. As a special case,

we use our framework to give the first proof of adaptive security

of the seminal BGW protocol in the UC framework.