Which of the following algorithms has better computational complexity than standard division algorithms?(a) Montgomery algorithm(b) Classical modular exponentiation algorithm(c) ASM algorithm(d) FSM algorithmI got this question in an international level competition.I need to ask this question from Number Theory in division Number Theory and Cryptography of Discrete Mathematics

Which of the following algorithms has better computational complexity

1.	Which of the following algorithms has better computational complexity than standard division algorithms?(a) Montgomery algorithm(b) Classical modular exponentiation algorithm(c) ASM algorithm(d) FSM algorithmI got this question in an international level competition.I need to ask this question from Number Theory in division Number Theory and Cryptography of Discrete Mathematics
Answer» The correct answer is (b) Classical modular exponentiation algorithm The best I can explain: To MULTIPLY m and N, they are CONVERTED to Montgomery form: mR mod X and nR mod X. When multiplied, these produce mnR^2 mod X, and the Montgomery reduction produces abR mod N which is the Montgomery form of the desired product. After that, the low bits are DISCARDED which gives a result less than 2X. One final subtraction reduces this to less than X. Hence, this procedure can have a better computational complexity than standard division algorithms.

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