I have seen through the literature the implementation and the solution of the Chinese Remainder Theorem (CRT) over integers. Is it possible to implement and solve the CRT over finite fields e.g. a Galois Field 2^128?
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What do you mean by "solving" a theorem? Do you mean solving a problem by using the theorem?
Yes. If it is possible to implement the CRT for solving a problem over a Finite field.
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