In the first part,
we study some RSA-based semantically secure encryption schemes
(IND-CPA) in the standard model.
We first derive the exactly tight one-wayness
of Rabin-Paillier encryption scheme
which assumes that factoring Blum integers is hard.
We next propose the first IND-CPA scheme
whose one-wayness is equivalent to factoring {\it general} $n=pq$. In the second part, we present One-key CBC MAC (OMAC) and prove its security for arbitrary length messages. OMAC takes only one key, $K$ ($k$ bits) of a block cipher $E$. Previously, XCBC requires three keys, $(k+2n)$ bits in total, and TMAC requires two keys, $(k+n)$ bits in total, where $n$ denotes the block length of $E$. |