An algorithm that computes modular nested exponentiation efficiently
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modular-nested-exponentiation
An algorithm that computes modular nested exponentiation efficiently
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Generalised modular exponentiation
We present an algorithm that takes as input an arbitrarily long sequence of positive integers a₁, a₂, a₃, ..., aₙ and a positive integer m and computes a₁^(a₂^(···^aₙ)) mod m efficiently (that is, without computing the value of the nested exponent).
Without this algorithm, this type of computation is unfeasible for modern computers even for short input sequences containing small integers.
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