Let N be an n bit positive integer, and let a, b, c, and k be positive integers less than N Assume that the multiplicative inverse (mod N) of a is a k 1 Give an O(n 3 ) algorithm for computing a (b c) mod N (i e , a raised to the power b c with the result taken mod N) Any solution that requires computing b c is so inefficient that it will receive no credit

Question: Let N be an n-bit positive integer, and let a, b, c, and k be positive integers less than N. Assume that the multiplicative inverse

Let N be an n-bit positive integer, and let a, b, c, and k be positive integers less than N. Assume that the multiplicative inverse (mod N) of a is a ^k-1.

Give an O(n ³) algorithm for computing a ^{(b^c)} mod N (i.e., a raised to the power b ^c with the result taken mod N). Any solution that requires computing b ^c is so inefficient that it will receive no credit.

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