Fast modular power algorithm based on length limited run-length coding

The modular power of large integer is a research hotspot in the public-key cryptosystem. To improve the efficiency, many modified algorithms were proposed, among them, the algorithms based on sliding window coding are popular. In this paper, a novel length limited run-length coding method was proposed by modifying sliding window coding. In this method, the large exponent was recoded, so the modular power operation was changed into simple multiplication, addition and displacement operation. Then, a modular power algorithm based on the novel coding method was designed, and its time and space complexity was analyzed. Finally, its efficiency was compared with which based on the current optimal sliding window coding. Analysis shows that the both algorithms are equivalent in the space complexity, whereas the former is superior to the later in the time complexity. Tested under the same environment, the proposed algorithm´s efficiency increase 40%.