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Definition
Modular arithmetic is almost the same as the usual arithmetic of whole numbers. The main difference is that operations involve remainders after division by a specified number (the modulus) rather than the integers themselves.
Background
Modular arithmetic is a key ingredient of many public key cryptosystems. It provides finite structures (called “rings”) which have all the usual arithmetic operations of the integers and which can be implemented without difficulty using existing computer hardware. An important property of these structures is that they appear to be randomly permuted by operations such as exponentiation, but the permutation is often easily reversed by another exponentiation. For suitably chosen cases, these operations enable encryption and decryption or signature generation and verification. Direct applications include RSA public-key encryption and the RSA digital signature...
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Contini, S., Kaya Koç, Ç., Walter, C.D. (2011). Modular Arithmetic. In: van Tilborg, H.C.A., Jajodia, S. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5906-5_49
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