Adaptively secure ABE for DFA from k-lin and more

In this work, we present:the first adaptively secure ABE for DFA from the k-Lin assumption in prime-order bilinear groups; this resolves one of open problems posed by Waters [CRYPTO’12];the first ABE for NFA from the k-Lin assumption, provided the number of accepting paths is smaller than the order of the underlying group; the scheme achieves selective security;the first compact adaptively secure ABE (supporting unbounded multi-use of attributes) for branching programs from the k-Lin assumption, which generalizes and simplifies the recent result of Kowalczyk and Wee for boolean formula (NC1) [EUROCRYPT’19]. Our adaptively secure ABE for DFA relies on a new combinatorial mechanism avoiding the exponential security loss in the number of states when naively combining two recent techniques from CRYPTO’19 and EUROCRYPT’19. This requires us to design a selectively secure ABE for NFA; we give a construction which is sufficient for our purpose and of independent interest. Our ABE for branching programs leverages insights from our ABE for DFA.