Modular exponentiation evaluates a nonnegative integer power modulo . Repeated squaring according to the binary expansion of needs modular multiplications, with intermediate integers reduced modulo . This avoids constructing the potentially enormous integer . A reversible computation gives the coherent quantum modular exponentiation used in quantum order finding and discrete-logarithm Fourier sampling.
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Modular exponentiation is a mathematical operation that computes the value of \( b^e \mod m \), where \( b \) is the base, \( e \) is the exponent, and \( m \) is the modulus. It is particularly useful in fields such as cryptography, number theory, and computer science, especially when working with large numbers, because it allows for efficient computation without having to compute the potentially enormous number \( b^e \) directly.
Can be calculated efficiently with the Extended Euclidean algorithm.
The beauty of this algorithm is that because exponentiation grows really fast, there is no hope that we can ever learn all the digits of an exponential, as there is simply not enough time or memory for that. Therefore, a natural sub-question is if we can know some part of that number, and knowing the smallest digits is the most natural version of that question.