suppose there is a group $\mathcal{N}$ of $n$ people with public/private key pairs $(pk_i,sk_i)$ $i=1,\cdots,n$. Is there any scheme that I can send message to a subset of users $i_1, \cdots, i_m$, only the users in $i_1, \cdots, i_m$ can decrypt the message?

I know Broadcast Encryption can do this, but the number of keys broadcast encryption may produce is 1.25$r$ times of the original one, where $r$ is the number of users who cannot accept the message. However, I want only a small portion of people that can decrypt the message. Thank you!


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