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Successive square method

The successive square method is an algorithm to compute in a finite field . The first step is to decompose in successive powers of two,(1)where , which gives in base 2. can then be represented as(2)(3)This term can be computed by successive steps as(4)(5)(6)(7)For example, to compute in the finite field , first decompose into , then follow the above steps: (8)(9)(10)(11)(12)From there, the final answer can be computed as(13)The successive square method is implemented in the Wolfram Language as PowerMod[a, b, n].

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