Comparing UC Security Variants

In this paper, the authors investigate the relations among various security notions. More precisely, they present a separation result between two variants of UC security definition: 1-bit specialized simulator UC security and specialized simulator UC security. This solves an open question and comes in contrast with the well-known equivalence result between 1-bit UC security and UC security. They also give a notion of weak security and they show that the induced weak security under 1-bounded concurrent general composition is equivalent to 1-bit specialized simulator UC security. As a consequence, they obtain that the notion of weak security and the notion of stand-alone security are not equivalent.