We develop a couple of new methods to reduce transmission overheads in broadcast encryption. The methods are based on the idea of assigning one key per each partition using one-way key chains after partitioning the users. One method adopts skipping chains on partitions containing up to p revoked users and the other adopts cascade chains on partitions with layer structure. The scheme using the former reduces the transmission overhead down to r p+1 asymptotically as r grows, and the scheme using the latter keeps the transmission overhead very small when r approaches 0, where r is the number of revoked users. Combining the two schemes, we propose a new broadcast encryption scheme with least transmission overhead. Our schemes also possess a remarkable feature that any number of new users can join at any time without key update, which is not available for most of known practical schemes. Keyword: Broadcast encryption, Revocation, One-way key chain, Skipping chain, Cascade chain, Combined ch...