Develop a generalization of square-and-multiply algorithm

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Advanced problem!) There are ways to improve the square-and-multiply algorithm, that is, to reduce the number of operations required. Although the number of squarings is fixed, the number of multiplications can be reduced. Your task is to come up with a modified version of the square-and-multiply algorithm which requires fewer multiplications. Give a detailed description of how the new algorithm works and what the complexity is (number of operations). Hint: Try to develop a generalization of the square-and-multiply algorithm which processes more than one bit at a time. The basic idea is to handle k (e.g., k = 3) exponent bit per iteration rather than one bit in the original square-and-multiply algorithm.

Reference no: EM131329274

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