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Date: 13-10-2020
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Date: 14-9-2020
578
Date: 2-2-2016
2122
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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) |
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(3) |
This term can be computed by successive steps as
(4) |
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(5) |
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(6) |
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(7) |
For example, to compute in the finite field , first decompose into , then follow the above steps:
(8) |
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(9) |
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(10) |
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(11) |
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(12) |
From there, the final answer can be computed as
(13) |
REFERENCES:
Bressoud, D. and Wagon, S. Computational Number Theory. New York: Key College Publishing, pp. 30-40, 2000.
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