In this article we show the correctness of integer arithmetic based on Chinese Remainder theorem as described e.g. in [11]: Integers are transformed to finite sequences of modular integers, on which the arithmetic operations are performed. Retransformation of the results to the integers is then accomplished by means of the Chinese Remainder theorem. The method presented is a typical example for computing in homomorphic images.
@article{bwmeta1.element.doi-10_2478_v10037-008-0029-8,
author = {Christoph Schwarzweller},
title = {Modular Integer Arithmetic},
journal = {Formalized Mathematics},
volume = {16},
year = {2008},
pages = {247-252},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-008-0029-8}
}
Christoph Schwarzweller. Modular Integer Arithmetic. Formalized Mathematics, Tome 16 (2008) pp. 247-252. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-008-0029-8/
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