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The paper presents a novel method for modulo 2n-1 squaring using the exponent reduction property of powers of 2 modulo 2n-1. An exponent triangle is created to simplify the design approach. In contrast to methods based on the periodic properties of powers of 2 modulo 2n-1, our graph based design method is appealing and yields a solution with direct correspondence to the modulo squaring structure. Simulation results show that the carry saver adder (CSA) tree for the proposed method lowers the hardware cost by more than half of that generated by the multiplier-based method. The overall delay has also been reduced by two levels of the CSA tree in general.