A New Variant of the Winternitz One Time Signature Scheme Based on Graded Encoding Schemes

The Winternitz one-time signature (WOTS) scheme, which can be described using a certain number of so-called ``function chains , plays an important role in the design of both stateless and stateful many-time signature schemes. This work introduces WOTS^GES, a new WOTS type signature scheme in which the need for computing all of the intermediate values of the chains is eliminated. This significantly reduces the number of required operations needed to calculate the algorithms of WOTS^GES. To achieve this results, we have used the concept of ``leveled multilinear maps which is also referred to as graded encoding schemes. In the context of provable security, we reduce the hardness of graded discrete-logarithm (GDL) problem to the EU-CMA security of WOTS^GES in the standard model

The complexity of the connected graph access structure on seven participants

In this paper, we study an important problem in secret sharing that determines the exact value or bound for the complexity. First, we used induced subgraph complexity of the graph G with access structure, Gama, to obtain a lower bound on the complexity of the graph G. Secondly, by applying decomposition techniques we obtain an upper bound on the complexity of the graph G. We determine the exact values of the complexity for each of the ten graph access structures on seven participants. Also, we improve the value bound of the complexity of the six graph access structures with seven participants