Design and Implementation of Layer Extended Shortest Addition Chains Database for Fast Modular Exponentiation in RSA

The shortest addition chains can provide high efficiency for the modular exponentiation in RSA, but the time and space complexity of finding out the shortest addition chains is extremely high. This research adopts addition chains tree to produce addition chains and store them into a database,in which the number of child nodes of each node is uncertain until the children of this node in the tree is completed. When we retrieve a number which does not exist in the database in this method, the system will automatically expand the tree to reach it; meanwhile, if the number is already available in the database, we can get the result very quickly without the further data calculation. The favorable results of the theoretical analysis and the experiments demonstrate that the proposed algorithm is more efficient than the other methods.